Operable flying and bouncing robot

Abstract

A robot is provided that includes an aerial unit, a passive leg mechanism operably coupled with the aerial unit, and a controller. The controller is configured to control operation of the aerial unit such that the robot is operable in at least a flight mode and a jump mode.

Description

Technical Field

[0001] The present invention relates to an operable flying and bouncing robot (eg, a hybrid bouncing-flying robot) and a control method thereof. Background Art

[0002] Many organisms in nature achieve hybrid locomotion by integrating jumping and flight behaviors. Arboreal foraging birds such as parrots and sparrows exhibit high agility by combining branch-to-branch hopping with intermittent flight (1). Insects such as locusts, cicadas, and fleas integrate jumping and flight behaviors to navigate complex environments and avoid predators (2–4). Flying squirrels (5) and dragon lizards (6) perform hybrid jumping and gliding to achieve long jumping distances. These examples demonstrate the potential benefits of hybrid jumping-flight locomotion for improving maneuverability, agility, efficiency, and versatility.

[0003] Developing hybrid jumping-flying robots capable of continuous jumping and flight is challenging, especially considering the limitations and complexity of conventional jumping mechanisms. Although some combustion-driven robotic jumpers have been reported (7–10), existing robots capable of jumping are mainly based on latch-actuated mechanisms (11–29) or latch-free mechanisms (30–36).

[0004] Jumpers with latch-actuated mechanisms use a latch mechanism to rapidly release energy from a mounted elastic body, which makes varying jump height and continuous jumping difficult. If the explosive energy release is passively triggered (e.g., via a cam escapement or pawl-ratchet mechanism) (11–15, 19, 22–24, 26–29), the jump height is fixed according to a predetermined tension, limiting the robot's capabilities. On the other hand, if the explosive energy release is actively triggered, the jump height is variable, but continuous jumping remains difficult because the release must be triggered precisely when the robot lands (17, 18, 20, 25), affecting the robot's jumping agility.

[0005] Jumpers with latchless drive mechanisms can utilize drivers to directly drive their legs (30, 37-39), thereby achieving highly variable continuous jumping. However, in the absence of energy storage, they are unable to generate enough instantaneous power for high jumping. In order to address this limitation, elastomers are used in parallel elastic jumping mechanisms (34, 36) or series elastic jumping mechanisms (31-33) for temporarily storing the energy generated by the driver and amplifying the output power during the support phase. Utilizing carefully designed connecting rods and nonlinear spring stiffness, these robots can benefit from variable mechanical advantages, demonstrating agile continuous jumping and excellent vertical jumping agility (21, 31-33). However, they require relatively complex mechanical structures, higher driver power and non-negligible support phase time. These limit jumping agility to a certain extent, because the robot must spend a certain amount of time in the support phase to utilize the driver to inject energy into the system.

[0006] Existing attempts to create robots capable of jumping and flying have directly integrated jumping mechanisms with aerial platforms (15–18, 40–42). This allows the robot to quickly gain altitude through jump-assisted takeoff. However, these existing robots are unable to achieve continuous jumping, fine-tune jumping height, and / or sustained flight. Summary of the Invention

[0007] In some embodiments of the present invention, a hybrid jumping-flying robot is provided that enhances a micro-aircraft (MAV) by passively elastically retracting legs (FIG. 1). This results in a mechanically simple and efficient design that directly utilizes the rotors of an existing MAV for jumping. A robot (43) that can jump and fly is known, but it can only perform isolated jumps between flights and cannot perform continuous jumping. Unlike existing robots, the hybrid jumping-flying robot in some embodiments of the present invention is driven in the air phase rather than the support phase, thereby achieving continuous jumping and adjustable jumping height.

[0008] Passive elastic legs distinguish the hybrid hopping-flight robot (i.e., referred to herein as a "hopcopter") in some embodiments of the present invention from existing jumping robots, allowing the hybrid hopping-flight robot to achieve unprecedented jumping agility. The absence of a stance phase actuation allows for a shorter stance phase time, thereby achieving higher jumping frequency and agility. To demonstrate high jumping agility, a 42-gram hopcopter prototype was constructed, and the robot's jumping dynamics were identified and characterized. Based on the results, a model-based hop controller was developed to stabilize the robot during jumping using external feedback. For each jump, the passive retractable legs absorb and store kinetic energy through elastic recoil, while thrust-based actuation compensates for energy losses and stabilizes attitude and velocity. Experimental results demonstrate that the robot can accurately track a reference trajectory, validating the proposed three-dimensional hopping model and indicating that the average hop velocity of the hopcopter is close to the theoretical ballistic limit, surpassing state-of-the-art jumping robots including the Salto-1P (32). This distinguishes the proposed method from methods that rely on latched elastic actuation, which imposes limitations on continuous bouncing and variable jump heights, and from methods that rely on latch-free serial elastic actuation, which requires a longer support phase. In flight mode, the robot in some embodiments of the present invention can function as a conventional micro air vehicle, allowing stable hovering, agile maneuvering, and smooth flight-to-bouncing transitions. Intermittent bouncing during flight greatly enhances instantaneous acceleration for rapid, tight turns.

[0009] To achieve stable hopping using only onboard sensors, the robot is equipped with active aerodynamic stabilizers. These aerodynamic surfaces dynamically influence the landing attitude without external feedback or vision, stabilizing the hopping velocity and attitude. The resulting hybrid hopping-flight locomotion of the hopping rotorcraft offers unprecedented versatility in navigating complex environments. Unlike wheeled aircraft (44–50), which struggle to navigate rough terrain, the hopping capability allows the robot to overcome obstacles and traverse uneven terrain. Compared to bipedal robots capable of flight (51–54), the hopping mechanism is more efficient and requires less energy to propel itself. By seamlessly integrating flight and hopping, our approach achieves collaborative hybrid locomotion, where the flight mechanism facilitates passive hopping, while intermittent hopping generates high accelerations for rapid turns during flight. This multimodal locomotion capability has the potential to radically expand the range of environments in which robots can operate effectively and efficiently, from cluttered indoor spaces to rugged outdoor terrain.

[0010] According to one aspect of the present invention, there is provided a robot comprising an aerial unit, a passive leg mechanism operably coupled to the aerial unit, and a controller configured to control the operation of the aerial unit so that the robot is operable in at least a flying mode and a bouncing mode.

[0011] In some embodiments, the controller may be configured to control operation of the aerial unit such that the robot alternates between a flying mode and a bouncing mode during operation.

[0012] In some embodiments, the passive leg mechanism may consist of only a single telescopic leg assembly.

[0013] In some embodiments, a single telescopic leg apparatus may include an upper leg section fixed to the aerial unit, a lower leg section movably connected to the upper leg section via one or more connectors, and an elastic mechanism operably coupled between the upper leg section and the lower leg section.

[0014] In some embodiments, the controller can be configured to predict the landing location of the robot in the bouncing mode.

[0015] In some embodiments, the controller may be configured to determine a landing position for a next hop cycle of the robot based on a landing pose of a current hop cycle of the robot.

[0016] In some embodiments, the aerial unit may comprise a mini drone or a micro drone.

[0017] In some embodiments, the aerial unit may include a micro quadcopter.

[0018] In some embodiments, the telescopic leg assembly may further include one or more guide wheel assemblies, each of which is operably coupled between a corresponding one of the one or more connectors and the lower leg section to limit the movement of the lower leg section to translation only and reduce friction. The guide wheel assemblies may include, for example, bearings.

[0019] In some embodiments, the lower leg section may include a foot for contacting the ground or environment.

[0020] In some embodiments, the lower leg section may include a first hook for supporting a portion of the elastic mechanism, and at least one of the connectors may include a second hook for supporting another portion of the elastic mechanism.

[0021] In some embodiments, the elastic mechanism may include one or more elastic elements.

[0022] In some embodiments, the one or more elastic elements may be mounted between the upper leg section and the lower leg section such that the one or more elastic elements are tensioned to provide a spring force operable to exceed the weight of the robot.

[0023] In some embodiments, the length measured from the lowermost end of the lower leg section to the center of mass (CoM) of the robot is at least twice the wheelbase length of the aerial unit.

[0024] In some embodiments, the robot may further include a stabilizer operable to interact with the airflow to stabilize the robot.

[0025] In some embodiments, the stabilizer can be configured to control landing attitude and stabilize bounce speed and attitude without external feedback or vision.

[0026] In some embodiments, the stabilizer may include one or more horizontally articulated aerodynamic surfaces.

[0027] In some embodiments, the one or more horizontally articulated aerodynamic surfaces may be driven by a cable arrangement connected to a drive unit.

[0028] In some embodiments, the one or more horizontally articulated aerodynamic surfaces may be arranged to become rigid when the cable arrangement is actuated, and to be free to oscillate in response to airflow when the cable arrangement is de-actuated.

[0029] In some embodiments, the controller can be configured to: predict the landing position and speed of the robot's current bounce cycle (k); determine the take-off posture and take-off speed of the robot's current bounce cycle (k) based on the predicted landing position and speed, the pre-specified landing position and the bounce height set point of the next bounce cycle (k+1); determine the expected landing posture of the current bounce cycle (k) to achieve the determined take-off posture and take-off speed of the robot's current bounce cycle (k); and stabilize the robot and control the landing position of the next bounce cycle (k+1) by adjusting the landing posture of the current bounce cycle (k).

[0030] In some embodiments, the controller can be configured to determine the landing location for the next hop cycle (k+1) based on the lateral component of the takeoff velocity and the amount of time the robot spends in the air phase, where the takeoff velocity is affected by the landing attitude.

[0031] Other features and aspects of the invention will become apparent by consideration of the detailed description and accompanying drawings. Where appropriate and applicable, any feature described herein with respect to one aspect or embodiment may be combined with any other feature described herein with respect to any other aspect or embodiment. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Embodiments of the present invention will now be described by way of example with reference to the accompanying drawings, in which:

[0033] Figure 1A A hybrid jumping-flying robot according to an embodiment of the present invention is shown.

[0034] Figure 1B yes Figure 1A A magnified view of section A of the hybrid jumping-flying robot, showing the retractable leg mechanism.

[0035] Figure 2A is a schematic diagram showing the dynamics of the hybrid bouncing-flying robot and the two phases of a complete jumping cycle.

[0036] Figure 2B Is from landing (t LD ) to take-off (t TO ) is a graphic representation of the support phase dynamics.

[0037] Figure 2C Takeoff prediction using identified support phase dynamics is shown.

[0038] Figure 3A is a schematic diagram showing example bounce trajectories in different stages from a control perspective.

[0039] Figure 3B is a block diagram illustrating a hierarchical structure of a controller according to an embodiment of the present invention.

[0040] Figure 4 Shows the trajectory tracking experiment in bouncing mode: Figure 4 A in FIG. 1 shows a reference circular trajectory and an achieved circular trajectory; Figure 4 B in FIG. 4 shows the reference step trajectory and the achieved step trajectory; and Figure 4 C in FIG. 5 shows a diagram illustrating the robot tracking a step trajectory.

[0041] Figure 5A FIG. 4 is a graph showing bounce period relative to bounce height predicted by a model according to an embodiment of the present invention.

[0042] Figure 5B is a graph showing jumping agility relative to jumping height of a robot according to an embodiment of the present invention and a conventional jumping robot.

[0043] Figure 6A and Figure 6B A demonstration of hybrid jumping and flying motion of a hybrid jumping-flying robot according to an embodiment of the present invention is shown to illustrate the robot's use of the ground to decelerate from lateral translation.

[0044] Figure 6C and Figure 6DA composite image and time course of the position of a hybrid jumping-flying robot is shown to illustrate the robot utilizing the ground to perform a sharp 90° turn, in accordance with an embodiment of the present invention.

[0045] Figure 6E and Figure 6F Two consecutive composite images and data are shown to illustrate the robot's use of walls and inclined planes to reverse its flight direction (U-turn) and brake.

[0046] Figure 7A A hybrid jumping-flying robot including a detachable active pneumatic stabilizer according to an embodiment of the present invention is shown.

[0047] Figure 7B yes Figure 7A An enlarged view of portion C of a hybrid jumping-flying robot illustrating a stabilizer according to an embodiment of the present invention.

[0048] Figure 7C It is a graph showing the relationship between landing speed, landing attitude, and takeoff speed.

[0049] Figure 7D The Poincaré map is shown, depicting the z | k and φ| k The landing speed angle θ as a function of z According to θ z | k+1 / θ z | k evolution.

[0050] Figure 8A is a schematic diagram of an example setup for a drop test of the robot for parameter identification.

[0051] Figure 8B Figure 2 is an example of a robot and tracked features from a high-speed video.

[0052] Figure 8C The height of the robot in the free-fall experiment is shown, wherein the dark curve and the light curve represent the descending phase and the ascending phase (downstroke phase and upstroke phase).

[0053] Figure 8D The relationship between the vertical acceleration and the compressed length of the robot during the support phase after falling is shown.

[0054] Figure 9 Example trajectories of the robot's leg contractions l(t) are shown, where the dark solid and light solid lines represent the analytical solutions of l(t) during the downstroke and upstroke, respectively, and the dashed line represents the extended solution.

[0055] Figure 10 The trajectory of a mixed travel of the robot with longitudinal acceleration and deceleration is shown.

[0056] Figure 11 A trajectory of a mixed travel of the robot with 90° turns is shown.

[0057] Figure 12 A trajectory of mixed travel with a U-turn is shown.

[0058] Figure 13 A trajectory of mixed travel with a non-horizontal surface is shown.

[0059] Figure 14 shows the Poincare map, depicted as θ z | k and φ| k The landing speed angle θ as a function of z According to θ z | k+1 / θ z | k Evolution of: (A) shows the prediction for a 0.4 m jump height; (B) shows the prediction for a 0.6 m jump height; (C) shows the prediction for a 0.7 m jump height; and (D) shows the prediction for a 0.8 m jump height.

[0060] Figure 15A and Figure 15B The trajectories of the robot are shown for three cases in the passive stability test: stable bouncing (implemented with both pneumatic stabilizers and attitude controller), bouncing with attitude controller only, and bouncing with pneumatic stabilizers only.

[0061] Figure 16 Shows the height of the robot in the agility evaluation.

[0062] Figure 17 The results of the endurance test are shown: (A) shows the height of the robot when it bounces and the corresponding motor commands; and (B) shows the onboard battery voltage when the robot jumps and flies.

[0063] Before explaining any embodiments of the present invention in detail, it should be understood that the application of the present invention is not limited to the details and arrangement of components of the embodiments set forth in the following description or illustrated in the following figures. The present invention is capable of other embodiments and can be practiced or implemented in various ways. Furthermore, it should be understood that the phraseology and terminology used herein are for descriptive purposes only and should not be considered as limiting. DETAILED DESCRIPTION

[0064] The present invention generally relates to a robot comprising an aerial unit, a passive leg mechanism operably coupled to the aerial unit, and a controller configured to control operation of the aerial unit such that the robot is operable in at least a flying mode and a bouncing mode. The following disclosure provides some example embodiments of the robot of the present invention.

[0065] Jump rotorcraft platform in some embodiments

[0066] A hybrid hopping-flying robot (or aircraft) according to an embodiment is provided. The hybrid hopping-flying robot is referred to herein as a "hopping rotorcraft". Figure 1A As shown, the hybrid jumping-flying robot 100 includes an aerial unit 10 and a passive leg mechanism 20 operably coupled to the aerial unit 10. The aerial unit 10 may include a mini drone or a micro drone. The aerial unit 10 may include a micro quadcopter (e.g., Bitcraze's Crazyflie 2.1, 27 grams). The passive leg mechanism 20 may include a telescopic leg mechanism or a retractable leg mechanism. The passive leg mechanism 20 is characterized by an upper leg segment 22 rigidly fixed to the aerial unit 10, a sliding rod serving as a lower leg segment 24, and an elastic element (e.g., a rubber band) serving as an elastic mechanism 30. The upper leg segment 22 may be made of two carbon fiber rods (e.g., diameter: 1.8 mm), which are rigidly mounted below the aerial unit 10 via, for example, fasteners. The fasteners may include 3D-printed fasteners (e.g., Formlab Form 3, Tough 2000). Figure 1B It shows Figure 1A An enlarged view of part A in FIG. Figure 1A and Figure 1B As shown, the lower leg section 24 includes a single rod, a pointed foot 26 and a hook 28 (e.g., a 3D printed hook) for mounting a rubber band. The lower leg section 24 can constitute the main moving component of the bouncing mechanism. The lower leg section 24 can be made of a single carbon fiber rod (e.g., 2×2 mm 2 The lower leg section 24 is movably connected to the upper leg section 22 via one or more connectors 41. The passive leg mechanism 20 further includes one or more guide wheel assemblies 25a and 25b between the connectors 41 and the lower leg section 24 to limit movement to vertical translation. In other words, each of the one or more guide wheel assemblies is operably coupled between a corresponding one of the one or more connectors 41 and the lower leg section 24 to limit movement of the lower leg section 24 to translation only. Figure 1BPart B in FIG provides a partial cross-sectional view to show the guide wheel group 25a arranged between the connector 41 and the lower leg segment 24. In particular, the lower leg segment 24 is connected to the upper leg segment 22 via two guide wheel groups 25a and 25b, limiting the movement to vertical translation (movement direction D) and minimizing sliding friction. The guide wheel groups 25a and 25b may include, for example, bearings. In this configuration, the translation axis passes through the center of mass (CoM) of the robot 100. Two rubber bands 30 (e.g., diameter: ≈1.5mm and ring radius: ≈20mm) are anchored between the tips of the upper leg segment 22 and the lower leg segment 24 as elastic elements. The rubber bands 30 are installed so that they are pre-stretched and further extend when the legs contract. In addition, one or more reflective spherical markers 40 are fixed to the robot 100 to obtain posture measurement results from the motion capture system. For example, the one or more reflective spherical markers 40 may include four reflective spherical markers. In an embodiment, the entire jump rotor aircraft weighs 34.8 grams, which is less than the maximum takeoff weight of 42 grams.

[0067] This design incorporates two key features to simplify stance phase dynamics. First, the passive leg mechanism 20 (i.e., the telescoping leg) is 22 cm long (from the foot to the robot's CoM), more than twice the 9 cm wheelbase length of the quadcopter 10. Second, the rubber band 30 is pre-stretched, allowing the elastic force to exceed, for example, the weight of the robot 100. These features allow the robot 100 to be treated as a point mass during stance phase and decouple its dynamics from gravity orientation, as detailed in subsequent sections.

[0068] Aerial and support phase dynamics

[0069] In flight, the dynamics of a hopping rotorcraft are characterized by the torques (roll, pitch, and yaw) and resultant thrust produced by the propellers, which are not different from those of a conventional rotorcraft (55–57). However, when acting as a monopedal hopper, the robot is a hybrid dynamic system, in which a jump cycle alternates between an air phase and a ground phase separated by ground contact (58–60). For modeling purposes, in this work, the movement of the hybrid robot's CoM in each jump cycle is divided into two phases: the air phase (AP) and the support phase (SP), which are separated by two key timestamps: landing (t LD ) and takeoff (t TO ),like Figure 2A shown.

[0070] In the absence of ground contact, in AP, the robot shares the same flight dynamics as a conventional quadcopter with six degrees of freedom (DoF) in the form of rotational and translational motion. Upon landing, the robot's posture and position are physically coupled without slipping between the feet and the ground (58, 59). The ground contact point acts as the swing axis of the body posture, where its distance to the CoM changes as the leg contracts. The foot collision marks the transition between AP and SP. The comprehensive model consists of two sets of dynamics and the state transition between them. Inspired by the classic spring-loaded inverted pendulum (SLIP) model (59, 61), embodiments of the present invention propose a simplified but complete three-dimensional jumping model that captures the dominant effects and is suitable for real-time jumping control.

[0071] Air Phase

[0072] When flying, the robot is modeled as a gravitational field with a mass of mg and an inertia tensor of I = diag (I x ,I y ,I z ). The lightweight telescopic leg is abstracted as a thin rod with a preloaded elastic body. The leg axis passes through the robot's CoM and is aligned with the thrust direction of the thruster, as shown in Figure 2A and Figure 2B shown. Figure 2A is a schematic diagram showing the two phases and dynamics of a complete jump cycle. Figure 2B Is from landing (t LD ) to take-off (t TO ) is a graphic representation of the support phase dynamics. Figure 2C The figure shows the takeoff state prediction using the identified support phase dynamics, where 130 data points show the landing and takeoff states of the robot measured in the jumping model verification experiment.

[0073] During the airborne phase, the equations of motion are the same as those for conventional multirotor aircraft (55-57, 62) and are given by

[0074]

[0075]

[0076] Where p = [x, y, z] T The CoM of the robot is in the inertial coordinate system {x w ,y w ,z w}The position vector in the body-fixed frame {x b ,y b ,zb The z-axis of the inertial coordinate system represents the direction of the thrust of the propeller: b = Re3, where R∈SO(3) is the rotation matrix that maps the body coordinate system to the inertial coordinate system, and e3 = [0,0,1] T is a basis vector. ω=[ω x ,ω y ,ω z ] T is the body center angular velocity. ∑f i Indicates the total thrust, τ p is the sum of the torques generated by the thrusters in the body coordinate system. ∑f i and τ p Together are the control inputs that can be controlled by distributing power among the four rotors. In normal flight conditions, aerodynamic drag (56, 62) can be ignored.

[0077] Landing Transition

[0078] Once you land ( Figure 2A Timestamp t in LD ), the ground support force causes the legs to contract, reducing the leg length l(t) from its normal state (e.g., l0 = 22 cm). Without any influence from the thrust generated by the propellers, the SP dynamics are completely passive. The robot body extends and retracts the legs with the restoring force f generated by the elastic body. e Since the robot can be considered as a point mass (32,58,59) rather than a rigid body (due to the long leg length, As discussed in Note S1 of the Supplementary Notes section provided at the end of the description), the robot follows the equation of motion

[0079]

[0080] Based on the measurements from the drop test (see Materials and Methods and Figures 8A to 8D ), in the size of f c In the case of constant friction (possibly due to bearing or elastic hysteresis), the elastic force f e The constant k is related to the deformation of the elastic body l-l0-l p In linear proportion:

[0081] For l <l0 (4)

[0082] Where l-l0 is the contracted length of the leg, l p is the pre-stretched length of the elastomer. The friction term results in dissipated energy, which results in loading / downstroke Movement and unloading / upstroke Elastic hysteresis behavior caused by motion (see Figure 8D ). According to the design, the preload kl p Dominant relative to the robot's weight (kl p = 3.35 N vs mg = 0.34 N, see Materials and Methods and Table S1). Therefore, the support phase dynamics is determined by f e Given (nominate), and Equation 3 simplifies to

[0083]

[0084] Assuming no slippage (due to the pointed feet), the ground contact point can be viewed as a freely rotating spherical hinge, and the robot's CoM is constrained to translation along the leg axis and rotation around the foot, as Figure 2A and Figure 2B As shown. Due to the elastic force f e is always in the axial direction, so the angular momentum measured in SP relative to the ground contact is conserved, and the trajectory of CoM can be described as axial motion and angular motion, respectively, and is independent of the direction of gravity. The landing speed is expressed as And θ LD ∈[0,π) is represented by With leg axis z b (t LD ), we derive the leg contraction velocity at touchdown As long as the angular velocity of the body center immediately before landing is minimized, the angular velocity of the CoM relative to the ground for Orthogonal to z b The component in the direction of like Figure 2B As shown, the subsequent angular motion is characterized by The defined rotation axis is perpendicular to and z b (t LD ). Axial speed and angular velocity Become the initial condition of the robot in SP.

[0085] Support phase and takeoff transition

[0086] Unlike existing 3D SLIP model studies (58, 63), the complexity of the support phase dynamics of the hopping rotorcraft is further reduced due to the strategic design decision to significantly pre-stretch the elastic body. As detailed in Note S2, when and z b (t LD) are largely aligned, the centrifugal acceleration is negligible, and the SP is governed by the axial and angular dynamics in the form of the following two semi-coupled differential equations:

[0087]

[0088] Given the initial conditions ( and θ LD ), the axial dynamics are independent of ψ and are determined by the natural frequency We obtain the analytical solution of l(t) and the corresponding elastic force disappearance (l(t TO )=l0) time stamp of takeoff t TO , as detailed in Note S3. Using the expression for l(t), Equation (7) shows that Time integration The robot's posture at takeoff is provided as the support phase (t SP , from t LD to t TO , see Figure 2B ) around the axis e ψ Rotation z b (t). Therefore, the body posture z in the whole SP b (t) is also completely determined by the change of Δψ. and θ LD Reprojected to the inertial coordinate system, the take-off attitude of the robot is given by the following equation:

[0089] R(t TO )=R(e ψ ,Δψ)R(t LD ) (8)

[0090] Among them, R(e ψ ,Δψ) is the rotation matrix based on axis-angle representation. Let z b (t TO )=R(t TO )e3 is t TO The main axis at takeoff speed By placing the robot in t TO Axial speed at and tangential velocity This is obtained by projecting into the inertial coordinate system. The direction is z b (t TO )and The angle between In vector form, this is given by the following equation:

[0091]

[0092] like Figure 2B As shown, due to the conservation of angular momentum, the vector z b (t LD ), z b (t TO )and are coplanar and perpendicular to e ψ , and the takeoff speed is directly affected by the landing attitude. Therefore, the takeoff speed can be controlled by b (t LD ) to control the jump trajectory.

[0093] The model parameters identified from the drop test (Table S1) f c / m and l p ) (see Materials and Methods), according to Figure 2C Landing state (θ LD and ) to predict the TO and The takeoff state of the specified robot. These maps show that for a given landing speed By being in landing attitude z b (t LD ) form of θ LD Direct control of liftoff speed This forms the basis of a model-based bounce controller.

[0094] Model-based Bounce Controller

[0095] Similar to other spring-mass monopeds, the passive jumping dynamics of a hopping gyrocopter are unstable and lossy. Stabilizing the robot’s posture during the air phase to ensure an upright landing posture is not sufficient to prevent horizontal velocity divergence after consecutive jumps (58, 63, 64). At the same time, energy must be injected into the system to compensate for losses during the stance and air phases. However, unlike monopedal hoppers with direct leg actuation (e.g., the linear hydraulic and hip actuators in (65) or the serial elastic actuators in (32)), the stance phase of a hopping gyrocopter is completely passive. This unique jumping mechanism requires a dedicated control framework.

[0096] The proposed controller for a hop rotorcraft differs from the widely adopted strategies (32-34, 64) based on Raibert's hop rotorcraft (65) and other hop controllers (34, 36, 38, 58, 63, 66). The controller according to the embodiment allows the robot to take off in a desired direction in three dimensions. This capability enables the robot to track a trajectory while bouncing and facilitates smooth transitions between air mode and ground mode, thereby achieving complex hybrid travel. For example, during high-speed flight, the hop rotorcraft uses ground contact or the environment to generate instantaneous acceleration bursts and bounce to slow down, turn, or accelerate, which significantly improves agility beyond just flying.

[0097] The control strategy utilizes a model derived from SP dynamics in order to (i) reduce the control forces and (ii) decouple the altitude control problem from the landing control problem as much as practical. Therefore, the robot's trajectory during the air phase is mostly ballistic, and the landing position is controlled in a similar manner to the control of the landing angle in (32) by controlling the landing attitude z b (t LD ) is accomplished. This is different from existing jumping quadrotors (43), in which position control is directly achieved during the air phase using a flight controller designed for small rotorcraft. This framework makes jumping travel significantly more efficient than flying. In addition, since the elastic force present in the SP dominates the propulsion thrust, position control using the ground reaction force through the elastic legs produces excellent jumping agility.

[0098] Bounce Control Strategy Overview

[0099] Since hop motion is periodic and the air phase of the trajectory is primarily ballistic, embodiments of the present invention adjust the landing attitude of the current hop cycle (indexed as k) to achieve the same landing attitude in the subsequent hop (indexed as k+1, e.g. Figure 3A ) to produce the desired landing position. The proposed method strategically decouples the robot's attitude, altitude, and lateral dynamics by ignoring aerodynamic drag and leveraging the robot's ability to skillfully control its attitude during the air phase. Embodiments of the present invention utilize the developed dynamic model to create a set of equations that predict the landing point at time step k+1 based on the landing attitude at time step k, and embodiments of the present invention rely on these equations to numerically solve the set point landing attitude that leads to the desired landing position at time step k+1. The structure of the controller may include five submodules, labeled (i) to (v), as shown. Figure 3B As outlined in [1], starting from jump cycle k, (i) the landing position and velocity are predicted. In (ii) this information is used together with the pre-specified landing attitude and jump height set points to predict the takeoff state for cycle k. In (iii), the numerical optimizer relies on the output of (ii) to form an algebraic loop ( Figure 3B (in bold in [ ]), the algebraic loop determines the desired landing state for cycle k and the thrust requirements to achieve the bounce altitude setpoint during the climb in cycle k and the next landing position in cycle k+1. Finally, (iv) is the thrust and attitude manager, which transforms the results from the solver in (iii) into command inputs for the low-level controller (v). The detailed implementation of the controller is as follows.

[0100] Landing status prediction

[0101] The high-level hopping controller loop is executed once per hopping cycle. Starting from the vertex of cycle k, the total thrust of the hopping rotorcraft is nominally set to zero, and the unpowered robot follows the Figure 3A The trajectory shown. According to the current position p(t) and speed at time stamp t Time to landing and Determined to be The landing position and speed are

[0102]

[0103]

[0104] During the descent, the robot's attitude is controlled with minimized angular velocity and resultant thrust, allowing the motion to be considered as a free fall starting from a height z(t)-l0.

[0105] Altitude control and next landing position

[0106] Based on the landing set point attitude z b (t LD )=R(t LD )e3 and the calculated landing speed use The support phase dynamics (Eq. 6 and Eq. 7) are forward integrated using Eq. 8 and Eq. 9 to produce the liftoff state R(t TO )and Immediately after takeoff (detected by a significant change in axial acceleration), the underlying controller (v) (described in Materials and Methods) rapidly re-orients the robot to an upright orientation (z b =e3) to minimize horizontal thrust. Therefore, the landing position of cycle k+1 is completely determined by the lateral component of the lift-off velocity ( ) and the time the robot spends in the air phase. This flight time varies depending on the set point altitude because aerial maneuvers are divided into powered ascent (PA) and unpowered projection (PJ) ( Figure 3A). For the following equation, by briefly generating a size of ∑f i = mg of vertical thrust to ensure that the jump height set point z is reached d :

[0107]

[0108] in, is the vertical lift-off speed, z d Indicates the relative jumping height. The former is when the vertical lift-off speed is not enough for the robot to passively reach the set point, and the latter is when the jump height without any thrust assistance exceeds z d During the powered flight phase, the thrust of the propellers balances the weight and the aircraft maintains its upward velocity. The rest of the trajectory is a projectile with a duration of:

[0109]

[0110] The first term refers to the remaining time the robot spends ascending, and the second term refers to the free fall. Finally, the landing position of cycle k+1 is iteratively updated as

[0111]

[0112] The results of equations 11-15 verify that the landing position of the next cycle (k+1) is mainly determined by the landing posture z of the current cycle. b (t LD )Sure.

[0113] Landing attitude calculation and air trajectory planning

[0114] According to the estimated current landing position p(t LD )| k , the controller uses Equation 15 to iteratively search for the landing attitude that minimizes the predicted position error for the next landing,

[0115]

[0116] Under no-slip conditions subject to the ground friction coefficient μ (Note S4)

[0117] arccos(e3·z b (t LD ))| k ,arccos(e3·z b (t TO ))| k <tan -1 μ (17)

[0118] According to pd The set point and the current state of the robot, the error Can be scaled down to zero or a specific value, which indicates whether the robot can reach the desired position in a single or multiple steps.

[0119] Thrust and attitude manager

[0120] Determine the landing attitude z according to Equation 16 b (t LD ), which is then implemented by the bottom controller as the robot falls (v). To adjust the jump height, after taking off, the robot is quickly redirected to an upright position and the resulting thrust is kept constant at ∑f i =mg duration Δt PA , as described by Equation 13. This action injects energy into the system to compensate for any losses. Afterwards, the robot remains upright until the landing position of the next jump cycle is predicted again by (i).

[0121] Planning strategy for trajectory tracking

[0122] Unlike flying robots that can continuously stabilize any control errors, the cyclic nature of bouncing motion allows only one corrective action per cycle. The robot's actions to change its landing posture while falling only affect the landing position in the next cycle. Therefore, in order to track the predetermined trajectory, under the assumption that In the case of d Select the robot in t LD | k+1 This consideration eliminates inherent delays, allowing the robot to more accurately track time-varying trajectories. Nevertheless, the complexity of the achievable trajectory is inherently limited by the frequency of the bounces.

[0123] Bounce testing and model validation

[0124] To validate the identified parameters and derived dynamic model, preliminary controlled jumping experiments were performed using the developed controller. As detailed in the Materials and Methods section, the landing states of 130 consecutive jumps were recorded ( and θ LD ). The experiment uses the designed model to calculate the rotation of the fuselage Δψ and the take-off angle θ. TO Predict takeoff status and compare the prediction results with Figure 2C The measurement results presented in the comparison are compared (due to the power climb can not be accurately measured ). The measured results are highly consistent with the predicted results, where Δψ and θ TOThe root mean square error (RMSE) is only 1.0 and 1.6°. The agreement between the model predictions and the measurements verifies that the derived equations and associated assumptions are suitable for capturing the stance-phase dynamics of the hop rotorcraft.

[0125] Next, the tracking performance was evaluated using circular and step trajectories. For the circular trajectory, the robot was instructed to move around a circle with a radius of 1.20 m at a constant height (0.60 m) in 0.2 ms. -1 The step trajectory requires the robot to maintain a jump height of 0.75m and move horizontally up to 2m multiple times within 40 seconds. Three repeated tests are performed for each trajectory. The resulting trajectory is shown in Figure 4 As shown in A and B, the trajectory tracking experiment in the bouncing mode ( Figure 4 A in FIG shows a reference circular trajectory and an achieved circular trajectory, Figure 4 (B in Figure 1 shows the reference and implemented step trajectories). Tracking performance was determined by calculating the root mean square error (RMSE) of three repeated tests: the RMSE for landing position was 16 cm for the circular trajectory and 49 cm for the step trajectory. For jump height, the RMSEs were 4.1 cm and 4.8 cm, respectively. Figure 4 Figure B shows that the amplified error in the step trajectory is caused by the inability to respond quickly to significant changes in the desired trajectory. These results show that the proposed controller can achieve accurate trajectory tracking with small altitude errors and moderate landing errors, even in the case of large inter-step displacements and lack of control authority during the air phase.

[0126] Jumping agility

[0127] Next, experiments were conducted to investigate the relationship between the robot's jumping height and frequency, and to calculate its jumping agility, which is defined as the robot's periodic average vertical velocity v = 2hf (the definition of jumping agility proposed here is different from the vertical jumping agility defined in (31). Vertical jumping agility refers to the vertical climbing speed). The developed position controller was used to command the robot to jump in place for more than 60 seconds. The test was divided into seven segments, each corresponding to a different jumping height ranging from 0.59m to 1.63m. In each segment, the robot jumped at a constant height for at least six cycles ( Figure 16 ). The time period of one bounce cycle of each system is then measured and plotted against the corresponding height (see Figure 5A The plot includes the model-predicted time periods, which can be broken down into the time the robot spends in the support phase (t in Eq. S12 in Note S3). SP =t TO -t LD), the time spent in the power climb phase (Δt in Equation 13 PA ), and the time spent in the ballistic phase (Δt in Eq. 14 PJ ). In addition, we also identified the ballistic limit (31), which occurs when the robot spends negligible time in the support phase and the entire flight phase is ballistic.

[0128] like Figure 5A As shown, the measured duration is approximately 100 ms longer than the model prediction. This discrepancy is primarily due to the model ignoring the thrust generated by the robot's descent for posture control, which prolongs the descent. The model prediction is 40 ms longer than the ballistic limit, corresponding to the time the robot spends in the stance phase. Therefore, we can infer that these two factors together extend the robot's bounce duration compared to the theoretical limit.

[0129] Jumping agility is calculated as the product of height and frequency. Due to the short stance phase time (<45 ms), the jump gyroplane achieved a jumping agility of 2.38 m / s at h = 1.63 m, which is 30% higher than the 1.83 m / s achieved by the Salto-1P (stance phase time exceeds 120 ms) (31, 32) and other jumping robots at 1.25 m. Figure 5B and Table S2). In summary, the hopping gyroplane exploits the natural dynamics of elastically retractable legs with high stiffness to minimize ground contact time (see Note S3), thereby achieving high agility due to the reduced stance phase time during hopping.

[0130] Coordinated hybrid movement for agile maneuvers

[0131] Strategically combining hopping and flight can uniquely enhance maneuverability and agility, as hopping mode can generate bursts of acceleration for flight. By instantaneously switching to hopping mode for a single jump during flight, a monopedal robot can generate instantaneous high acceleration through ground support forces. Using the developed hopping model, the takeoff direction is regulated by the landing attitude. This maneuver helps the robot decelerate, accelerate while hovering, or make sharp turns, thereby providing enhanced agility despite a limited thrust-to-weight ratio (e.g., 1.2).

[0132] The first maneuver demonstrates the use of springy legs and ground support forces to accelerate and then decelerate the robot in flight. Figure 6A and Figure 6B As shown, the robot is initially commanded to hover. To accelerate forward, the bounce mode is activated and the robot enters free fall (in Figure 6B Once touching down at a pitch angle of 14°, the passive support phase dynamics induce a forward velocity of 1.14 ms. -1and the time spent in SP is less than 45ms of pulse takeoff, resulting in 26.0ms -2 lateral SP acceleration (calculate landing and takeoff speeds and SP acceleration as detailed in Note S5). Includes the descent period (e.g. Figure 6B and Figure 10 The shaded mark in the figure shows 0.50s), and the average lateral acceleration is 2.2ms. -2 After taking off, the robot continued to fly and reached a time of more than 1.99ms before performing the second jump. -1 The forward speed was reduced to 0.05ms, allowing the aircraft to land at a pitch angle of 19°. -1 The lateral speed of the sudden stop is 43.5ms. -2 lateral SP deceleration and 3.3ms -2 The average deceleration (including Figures 6A-6F and Figure 10 The 0.52 s falling period is marked in the figure).

[0133] Next, agility is demonstrated by making a sharp turn. The robot uses the ground to quickly change its direction of travel by 90 degrees, such as Figure 6C and Figure 6D As depicted in . -1 The robot changes its flight path in 0.54s (from falling to completing SP) by leg-assisted right turn. -1 The lateral speed of landing is more than 1.23ms -1 The post-jump speed of Figure 11 This is equivalent to 44.4ms -2 lateral SP acceleration (in 45ms) and 4.2ms -2 The large SP acceleration produces a sharp right-angle trajectory, rather than Figure 6C When blending is implemented to suddenly reverse the direction of flight, higher acceleration is achieved ( Figure 12 ). A jump with a pitch angle of 28° at landing is fully flipped in 0.55s (from falling to completing SP), from 1.79ms -1 The lateral landing speed to the opposite direction is 1.46ms -1 The speed after the jump is equivalent to 72.3ms -2 lateral SP acceleration (in 45ms) and 6.9ms -2 The average lateral acceleration.

[0134] To further push the limits of agility, hybrid jumps on walls and inclined surfaces were implemented. Non-horizontal surfaces expand the range of non-slip landing and take-off angles (Note S4). This effectively increases the achievable lateral acceleration. In the experiment, the robot was able to jump in over 4 ms. -1 The robot flew towards the wall at a speed of 1.8m. In the 0.54s or 1.8m before reaching the surface, the attitude controller redirected the robot for landing. The robot landed at a tilt (pitch) angle of 57° and a speed of 3.6ms. -1 Landing speed on the wall ( Figure 6E and 6F as well as Figure 14 ). Wall jumping reverses the robot's lateral velocity in 45ms to 2.68ms. -1 After the bounce, the robot then spends 0.43s accelerating toward another slope (30°) and performs a second jump within 0.63s (from falling to completing SP), thus reducing the flight time from 3.9ms to -1 The deceleration was to end the maneuver in a hover. The average lateral acceleration during these two periods was 11.4ms. -2 and 5.7ms -2 , and the lateral SP acceleration reaches 139.8ms -2 and 66.6ms -2 .

[0135] The results show that hop-fly propulsion is capable of achieving average and instantaneous lateral accelerations that are remarkable compared to its thrust-to-weight ratio of only 1.2. The hop-rotor can achieve instantaneous and average accelerations exceeding 14g and 1.2g by using ground support forces and elastic legs for intermittent hopping. This is significantly higher than the accelerations reported for other micro aerial robots with similar or higher thrust-to-weight ratios (56, 57, 67). Hybrid propulsion is particularly advantageous for robots with limited thrust power (e.g., small, lightweight platforms) because it allows these robots to perform fast and demanding maneuvers that would otherwise be impossible.

[0136] Self-stabilizing bouncing via active pneumatic stabilizers

[0137] According to the proposed bouncing dynamics model, the robot's takeoff velocity during a jump directly depends on the landing attitude and landing velocity. This means that velocity measurements are required as feedback to stabilize the robot. To reduce the robot's dependence on sensors and external measurements, an actuated pneumatic stabilizer is proposed to interact with the airflow to stabilize the robot. The strategy that enables the robot to jump into position without position or velocity feedback involves a method based on the robot's velocity during the fall phase. Adjust landing angle θ LD This is achieved by properly balancing the rotational torques generated by the attitude controller and the stabilizers.

[0138] Pneumatic stabilizer

[0139] 7A to 7D An example detachable active aerodynamic stabilizer and Poincare map are shown. Figure 7A A robot 700 is shown equipped with an example pneumatic stabilizer 710 , according to an embodiment. Figure 7B yes Figure 7A An enlarged view of portion C in the middle to show details of the stabilizer 710. Figure 7C It is a graph showing the relationship between landing speed, landing attitude, and takeoff speed. Figure 7D shows a plot as θ z | k and φ| k The landing speed angle θ as a function of z According to θ z | k+1 / θ z | k Poincare map of the evolution of . The dots represent the landing states recorded during the bounce stability test. Black, gray, and white represent measurements when only the attitude controller is active, only the pneumatic stabilizer is active, or both mechanisms are active. Figure 7A and Figure 7B As shown, the detachable aerodynamic stabilizer 710 of the jump rotorcraft includes three horizontally hinged aerodynamic surfaces 712 and weighs 4.9 grams. Three cables 713 (dashed lines) are installed between the bottom of the three aerodynamic surfaces 712 and the end of a crank (i.e., cable mount 716) on a drive unit (e.g., a servo motor 714 (H-King282AS)). The three cables 713 are installed so as to pass through five cable guides 717 (each cable passes through three cable guides 717). These aerodynamic surfaces 712 can be made rigid by the drive unit pulling the cables 713, or allowed to swing freely in response to airflow when the cables 713 are released. Tightening the cables 713 tightly brings the bottom of the aerodynamic surfaces 712 into close proximity with the three cable guides 717 and activates the stabilizer 710, allowing the aerodynamic surfaces 712 to withstand aerodynamic loads and generate torque to guide the robot's posture based on airflow. Conversely, releasing the cables 713 deactivates the stabilizer 710, thereby allowing the three aerodynamic surfaces 712 to rotate freely about the hinges, avoiding the generation of aerodynamic forces and torques.

[0140] Damper-Mediated Stability

[0141] The stabilizer is activated only during descent while bouncing. The stabilizer uses the upward airflow to generate torque, which is achieved by aligning the robot's main axis parallel and opposite to its translational velocity (i.e.: ) to rotate the robot's posture and reduce the landing angle θTD At the same time, the posture controller applies the torque generated by the thrusters to make the robot upright. b →z w =e3. Due to competition, the robot's main axis z when landing b Pointing perpendicular to the axis and the velocity vector ( ) between (see Figure 7C By adjusting control gains and stabilizer configurations, the jump dynamics can be stabilized without velocity measurements. In other words, the jump rotorcraft gains the ability to operate in realistic environments using only feedback from its onboard inertial sensors.

[0142] To demonstrate the stability of the damper assistance, we numerically construct the Poincare map assuming a constant bounce height of 0.5 m. The landing state is chosen as the fixed point of the limit cycle. Under the influence of the attitude controller and the pneumatic stabilizer, the vector z w 、z b and Coplanar. Angle between landing speed and vertical (See Figure 7C ) indicates that in the case of stable bouncing, the horizontal velocity should be close to zero during repeated bouncing. z In addition, it is defined as the robot's main axis z b Vertical to landing (see Figure 7C ,when is right; and when The landing attitude φ with a sign angle between θ and θ will also affect the takeoff state and the subsequent landing state. z Any combination of and φ predicts the next landing location as described in Materials and methods.

[0143] The Poincare map plots the value of the bounding box for different θ values ​​at a specific bounce height. z | k and φ| k θ z | k+1 / θ z | k , where k represents the bounce period ( Figure 7D and Figure 14 ). The mapping reveals the stable region (θ z | k+1 / θ z | k <1), the condition for the convergent bounce velocity is established. It is worth noting that the black dashed line in the Poincare map corresponds to φ| k= 0, indicating a scenario where the attitude controller is dominant and the robot always lands in an upright orientation. On the other hand, the dashed line indicated by “Stabilizer Only” depicts a scenario where the stabilizer is dominant and the landing velocity and attitude are aligned (θ z | k =φ| k These dashed lines lie near the boundaries of the stable region, indicating that relying on either strategy alone will not yield sufficiently robust stability. However, the Poincare map exhibits significant overlap between the stable region and the region between the dashed lines. By adjusting the control gains and stabilizer configuration, the interaction between the controller and the mechanism stabilizes the bounce velocity and posture during repeated jumps without the need for velocity measurements.

[0144] Bounce stability test

[0145] To confirm the insights from the Poincare analysis, three sets of experiments were conducted to evaluate the performance of the jumping robot under each individual control strategy (attitude control and pneumatic stabilizer) and a combination of these strategies. For each set of experiments, the robot began jumping after falling from approximately 75 cm. The jumping trajectory was tracked to determine the robot's attitude and velocity during the landing phase.

[0146] When utilizing only the attitude controller (dashed line denoted by “controller only”), the robot is expected to consistently land in an upright orientation or φ = 0, but the horizontal bounce velocity or θ is not guaranteed. z The experimental results confirm this ( Figure 7D ), indicating that the robot can diverge at a horizontal speed of θ z | k+1 / θ z | k >1 before jumping 3-5 cycles.

[0147] It is predicted that relying on the stabilizer alone (the attitude controller is active only in the CP, i.e., when the robot is ascending) will shrink θ z The difference between φ and θ does not directly reduce θ z The experiment once again verified this ( Figure 7D ). Model prediction results (θ z =φ) and the results reflect the limited effectiveness of the pneumatic stabilizers, which depends on the size and the time the robot spends descending. Overall, the robot is poorly stable and crashes after 6-10 bounce cycles.

[0148] In contrast, experiments integrating both the attitude controller and the stabilizer produced highly robust hops, as expected in theory. The robot performed well in multiple consecutive hops ( Figure 7DThe robot maintained a near-zero horizontal velocity component and a near-upright posture in the 3×3-m field without position and velocity feedback, achieving more than 56 bounces in 45 seconds.

[0149] Live bouncing demonstration

[0150] To further demonstrate the robustness and reliability of the stabilization strategy, three field tests were conducted in different environments, including stairs, corridors, and outdoor terrain. In each test, the operator commanded the controller a desired landing attitude, but the actual landing attitude depended on both the attitude setpoint and the pneumatic stabilizers, as described previously. The adjusted desired landing attitude produced a deviation that guided the robot to bounce in the prescribed direction. The control scheme allowed the hopping rotorcraft to ascend / descend a flight of stairs, navigate in narrow corridor spaces, and traverse rough terrain. Through these field experiments, it was verified that the active stabilizer achieved stable and resilient mobility without the need for vision or additional sensors for velocity feedback.

[0151] As described above, embodiments of the present invention provide a hybrid jumping-flying robot (jumping gyroplane) that combines jumping and flying capabilities to achieve high-performance locomotion. Its passive telescopic legs distinguish it from existing biomimetic jumping robots that rely on latched or latchless elastic drives because it does not require triggers, stance phase drives, or variable mechanical advantages, making it mechanically simpler and more reliable. The thrust-based drive of the passive telescopic legs allows fine-tuning of the jumping height and gives the jumping gyroplane superior jumping agility, surpassing the most advanced jumping robots. The short stance phase achieved due to the lack of drive in the stance phase allows for a higher jumping frequency, resulting in its high agility. The robot achieved a maximum speed of 2.38 m / s at a jumping height of 1.63 m, exceeding the highest agility reported for jumping robots (including the Salto-1P (31, 32, 68)) ( Figure 5B The use of thrust allows for fine-tuning of jump height. Experiments have demonstrated jumps from 0.6 to 1.6 m, demonstrating a wide range of jump heights.

[0152] The hoprotor's ability to fly and hop facilitates rapid changes in speed and direction. The robot's jumping ability can be exploited to mitigate damage from collisions with walls or the ground by employing jumping maneuvers. The integration of attitude control and aerodynamic stabilizers establishes the robot's hopping control autonomy. Poincare analysis and experiments demonstrate that the attitude controller and aerodynamic stabilizers work synergistically to stabilize the hoprotor's hopping dynamics. Without external feedback, the robot can achieve over 56 consecutive jumps at near-zero velocity and land upright, demonstrating the value of integrating attitude control and aerodynamic surfaces.

[0153] Crucially, the hoprotor's passive leg design can be easily adapted to conventional rotorcraft. By simply adding elastic legs and varying the controls, a standard quadcopter can be transformed into a hopping robot, unlocking new performance frontiers through hybrid locomotion. Overall, the hoprotor represents an improved platform that transcends the limitations of either aerial or ground locomotion alone, demonstrating the potential of integrating flight and hopping capabilities.

[0154] Battery life and performance

[0155] Unlike in aerial mode, the hop gyro generates thrust intermittently rather than continuously during hop mode. This mode of operation provides the opportunity to significantly extend the operating time of the hop gyro while reducing power consumption. To evaluate the endurance, continuous hopping tests were performed using a fully charged 250mAh single lithium-ion battery (8.3 grams). The robot bounced continuously for more than 1246 seconds (20.8 minutes). With a 650mAh lithium-ion battery (16.8 grams), the endurance increased to more than 3052 seconds (50.9 minutes). However, the total mass of the robot with the high-capacity battery (43.1 grams) exceeded the maximum take-off weight for flight (42.0 grams). The battery voltage recorded on board during the test is as follows Figure 17 B. Notably, the proposed ground locomotion method shows a four- to eight-fold improvement in endurance compared to a baseline quadcopter (Crazyflie 2.1 with reflective markings but no legs, 32.1 g), which hovered for only 379 seconds on a 250mAh battery.

[0156] The lack of reliable onboard current sensors and weight constraints make it impractical to directly measure the robot's operating power consumption. Despite this, the motor duty cycle is used as a metric to compare flight operations with ground operations. This is because the robot needs to continuously generate T≈mg when hovering, while it only briefly generates T=mg when bouncing after takeoff. The duty cycle of the aircraft is defined as D=(1 / T)∫ T ∑(f i / mg)dt, D = 1 is obtained for the baseline quadcopter flight. In the endurance test, the hop rotorcraft spent more than 85% of the time in the ballistic and support phases and performed attitude control with minimum thrust (outside the power phase ∑f i <0.11 mg, see Figure 17 A). For these reasons, the overall duty cycle for 1246 seconds is only 0.28, representing a more than threefold improvement in efficiency and endurance. In comparison, hybrid quadcopter robots PogoDrone (43) and LEO (53) save only 20% and 44% of power respectively by hopping and walking compared to flying, with duty cycles exceeding 0.5.

[0157] Materials and methods

[0158] Experimental setup and measurement results.

[0159] Ten motion capture cameras (e.g., OptiTrack Prime13w) were used to capture the 3×3×2.5-m 3 Experiments were conducted in a field. Attitude measurements were used for both control and real-world data measurements. High-level controllers (including hopping and flight controllers) were implemented in Python on a ground computer and executed at 100 Hz. A custom attitude controller was implemented onboard and operated at 1 kHz. The robot and ground station communicated via a radio module (e.g., the Bitcraze Crazyradio PA) via the Crazyflie Python API.

[0160] Drop test for parameter identification.

[0161] Since the support phase dynamics captured by Equations 6 and 7 are subject to some unknown lumped physical parameters (i.e., f c / m, and l p (l0 = 22 cm is a design parameter), so a drop test was designed to identify these model parameters based on the axial dynamics of the robot (Eq. 6) before applying the equations to predict and control the bouncing motion.

[0162] Figure 8A The drop test setup is schematically presented in FIG. A robotic gripper can be provided (or manufactured) to grasp the robot via a cable and release the robot when triggered. The end of the cable passes through the CoM of the aircraft to ensure that the robot is in an upright orientation. A high-speed camera (e.g., MotionBLITZ EoSens mini 2) captures the robot's trajectory at a speed of 1,000 frames per second, covering the landing point. Both the gripper and the camera can be controlled by the same computer. Figure 8A The system is schematically shown in Figure 6. Feature points on the robot are identified and tracked between frames using a Kanade-Lucas-Tomasi tracker (69). The two-dimensional trajectory is reconstructed by calculating the geometric centers of the tracked feature points. Figure 8B An example diagram of a hop rotorcraft in stance phase with tracking features is shown.

[0163] The test was conducted at three drop heights: 0.68, 0.82, and 0.95 m, with four drops at each height. The height of the robot in the free-fall experiment is represented by twelve reconstructed trajectories, as shown in Figure 2. Figure 8CAs shown in the figure, for the drop heights of 0.68, 0.82, and 0.95 m, the robot spent 32.0 ± 0.7 ms, 32.5 ± 0.5, and 33.0 ± 0.7 ms in the support phase. The leg contraction l0-l(t) was calculated from the data to Figure 8D Contraction versus acceleration is plotted in . The results show two linear trend lines with a vertical offset and the same gradient. The lower and upper lines correspond to leg compression and leg retraction, respectively. The clear and even spacing between the downstroke acceleration and the upstroke acceleration (deep and shallow) reflects energy loss in the form of Coulomb friction or elastic hysteresis. This yields the elastic force model proposed in Equation 4. The least squares method was applied to estimate the model parameters. The best-fit linear model ( Figure 8D The solid line in the figure yields k / m = 5.00 × 10 3 s -2 、f h / m=12.7m / s 2 and l p =1.97cm.

[0164] The identified parameters listed in Table S1 confirm that the weight of the robot is negligible compared to the force of the pre-stretched elastic body, such as kl p / mg≈10.

[0165] Low-level controls for flying, bouncing, and hybrid maneuvers.

[0166] The same set of equations is applied to determine the rotor commands for flight and to adjust the robot's attitude during the air hop phase. To achieve a given attitude, a proportional-integral-derivative controller (55) is first implemented to calculate the required torque τ at the body center p,d .

[0167] According to the operation requirements, the target thrust size T d It can be zero, mg or a specific value. To evaluate the force distribution between the four rotors, we define f = [f1,f2,f3,f4] T and the 4×4 configuration matrix A for power allocation

[0168] [τ p T] T =Af (18)

[0169] To ensure that even T d =0, there is also f i ≥0, the following pose priority assignment (similar to (57)) is used to calculate f.

[0170]

[0171] For f i ≥0 and τ p,d =τp

[0172] Although the resultant thrust production may not be correctly set to T d , but this ensures that the torque (τ p,d =τ p ), and when the desired thrust and torque may lead to motor saturation, especially for T d Unpowered ejection is set to zero, minimizing the thrust error (TT d ).

[0173] Model validation.

[0174] The robot was commanded to bounce at different height setpoints ranging from 0.5 to 0.7 m and to translate laterally from 0 to 1 m per step for over 90 seconds. The trajectory was recorded. The data was processed to obtain the landing state and takeoff state. The landing and takeoff timestamps were identified from the CoM position. The transformation velocity ( ) and posture state (z b (t LD ), z b (t TO )). Since in practice, these four vectors may not be completely coplanar, such as Figure 2A As modeled in , the rotation axis e ψ Calculated as the unit normal vector of the best-fit plane:

[0175]

[0176] The average value of the objective function in Equation 20 is 0.8°, indicating minimal misalignment. ψ After the rotation plane, the angle θ of each jump is obtained LD , Δψ and θ TO Based on data from 130 jumps in 90 seconds, covering a wide area of ​​landing conditions ( and 0°<θ LD <20°).

[0177] Poincare maps for bounce stability analysis.

[0178] The constructed Poincare map assumes a constant jump height z d Therefore, the vertical landing speed at cycle k is given by Determine. Given a landing attitude φ| k and landing speed angle θ z | k , in vector z w 、z b (t LD )| kand coplanar with the axis of rotation e ψ Under the assumption of orthogonality, calculate the landing angle θ LD | k =|φ| k -θ z | k |. Take-off state z b (t TO ) k | and is obtained from Equations 8 and 10. After takeoff, the robot briefly accelerates in the upright direction before entering the ballistic trajectory (PJ) to compensate for the energy loss (PA). The horizontal velocity remains constant during the flight. This means that the horizontal velocity at takeoff in cycle k is equal to the horizontal velocity at landing in cycle k+1. The vertical landing velocities at cycles k+1 and k are related to the jump height z d The landing speed angle θ is the same as the specified speed. z | k+1 is the direction of the landing velocity relative to the vertical. This allows for any θ z | k and φ| k Calculate θ z | k+1 or θ z | k+1 / θ z | k , which allows the Poincare map to describe the jump period θ z The stability of Figure 7D and Figure 15).

[0179] Supplementary Notes

[0180] Moment of inertia (Note S1)

[0181] After landing, considering the position of the rotation axis on the ground, the moment of inertia of the robot relative to the ground contact point is obtained by the parallel axis theorem.

[0182] I=I cm +ml 2 diag(1,1,0) (S1)

[0183] Among them, I cm =diag(I x ,I y ,I z For micro quadcopters (Bitcraze, Crazyflie 2.1), I x ,I y ,I z ≈2g·cm 2, and for l0=0.22m and m=27g, ml 2 ≈1×10 4 g·cm 2 That is to say, thanks to the long-leg design, ml 2 The term dominates. Therefore, when the yaw rotation is minimized, the robot can be treated as a point mass (rather than a rigid body).

[0184] Simplification of support phase dynamics (Note S2)

[0185] When the spring force dominates the weight of the robot, the motion of the robot in the support phase is described by Equation 5. Considering the non-slip ground contact point as the origin of the auxiliary inertial reference frame, the position of the CoM is given by the leg vector l(t)z b Description. Axial dynamics and angular dynamics correspond to l(t) and z b (t) movement.

[0186] Starting with angular motion, assume that the landing is around z b The angular rate of is minimized by the attitude controller. The initial angular momentum of the support phase is determined by the angular velocity (perpendicular to z b , as described in Landing Transition) designation, as Figure 2B In addition, due to the external force (z b f e ) does not contribute to any torque, so the angular momentum (magnitude and direction) of the robot remains unchanged. The rotation axis is constrained to e ψ The result is or

[0187]

[0188] To derive the axial dynamics, use the leg vector to replace Eq. Expressed as d / dt(l(t)z b (t)). Since the leg axis z b (t) According to the angular velocity Evolution, so And Equation 5 becomes

[0189]

[0190] To extract the axial dynamics, the b Obtain the projection of Equation S3.

[0191]

[0192] The term represents the centrifugal acceleration caused by rotation.

[0193] Finally, by comparing with f e / m comparison to consider The importance of pre-stretching was used to fabricate the prototype. As the identified parameters listed in Table S1, f e / m>kl p / m=96ms -2 .on the other hand, The upper limit of can be estimated based on the robot's landing speed. For a jump height of h = 1m, If the landing angle θ LD About or less than 20° (such as Figure 2C The angular velocity is and Since the centrifugal acceleration is one order of magnitude smaller than the contribution of the elastic body, the effect on f can be neglected. e The dependence of f from Equation 4 is e After merging, Equation S4 simplifies to Equation 6.

[0194] Solution of the support phase dynamics (Note S3)

[0195] Due to simplifications in Note S2, the support phase dynamics are separated into axial and angular dynamics. The axial motion is captured by an unforced ordinary linear differential equation. The response of the system is obtained analytically.

[0196] Given the initial conditions at landing, t = t LD As the initial timestamp, we get

[0197] l(t LD )=l0 and

[0198] On the downstroke During this period, the term in Equation 6 = -1, the solution is

[0199]

[0200] in, By solving i(t MD ) = 0 to find the time when the leg is fully contracted. This yields:

[0201]

[0202] and

[0203]

[0204] This condition becomes the initial state for the next phase, in which the leg recoils The solution of Equation 6 during this time period is

[0205]

[0206] Then, by targeting l(t TO ) = 10 Solve equation S6 to find the takeoff time. This yields

[0207]

[0208] and

[0209]

[0210] Therefore, the total time spent in the support phase is

[0211]

[0212] Its upper limit is

[0213] That is, the maximum support phase time is inversely proportional to the square root of the stiffness k. At the same time, equation S11 provides the knowledge required to calculate the takeoff speed. An example diagram of the entire support phase l(t) is shown in Figure 9 shown.

[0214] According to Equation 7, once l(t) is determined, we can perform a positive integration of the angular dynamics to determine Δψ:

[0215]

[0216] where the expression for l(t) is taken from Equations S6 and S9.

[0217] Friction Limitation (Note S4)

[0218] The derived model describing the dynamics of the SP relies on the no-slip assumption. This may not hold in extreme maneuvers when the friction coefficient μ is low. b The vertical component of the force becomes the ground support force, and the lateral component should not exceed the friction limit. b ) is limited to less than tan -1 μ, can prevent slipping. Since this angle is LD or t TO is maximized, so this requires

[0219] ψ(t LD ) and ψ(t TO )≤tan -1 μ (S15)

[0220] Because the bank angle is greatest during landing or takeoff.

[0221] Measurement of acceleration during the stance phase (Note S5)

[0222] Due to the limited sampling rate (≈100 Hz) and spatial resolution (≈1 mm) of the motion capture system, it is impossible to accurately capture the short stance phase (t SP <45ms, please refer to the drop test Figures 8A to 8D To accurately estimate the acceleration during the stance phase, some simplifying assumptions were made and the estimation problem was transformed into an optimization problem.

[0223] First, the recorded robot positions are examined in a short period before and after the jump, and the trajectory is divided into three phases: the support phase sandwiched between the air phase, and the air phase is characterized by the pre-jump period and the post-jump period. Conservatively assuming that the support phase time t SP =t TO -t LD The time between landing and takeoff is 45ms, but the exact landing timestamp and takeoff timestamp are unknown.

[0224] When the robot is subjected only to constant vertical acceleration (usually g is a free fall), assuming the trajectory of the robot before and after the jump ( ) is a parametric function of time. Under this assumption, the following expressions for the robot position and velocity can be derived:

[0225]

[0226]

[0227] Among them, v LD and v TO are the landing and takeoff speeds to be determined, and

[0228]

[0229]

[0230] Among them, s LD and s TO The landing and take-off locations are yet to be determined.

[0231] In order to take into account the possible occurrence of a due to attitude control and altitude control before landing and after takeoff LD and a TO With the deviation of g, we simultaneously search for the unknown parameter Θ = {a LD ,a TO ,vLD ,v TO ,s LD ,s TO This is achieved by performing a least squares regression on the robot's measured and expected trajectory in the air before and after the support phase, focusing on the period immediately before the support phase (t LD -Δt <t<t LD ) and after the support phase (t TO <t<t TO +Δt) for a short time interval.

[0232] Assume that the length of the support phase is t SP =t TO -t LD , given a specific time window length Δt, then at t LD -Δt to t LD With t TO to t TO The measured trajectory of the robot between +Δt should follow equations S18 and S19. Based on this principle, t LD It can be estimated by the following formula

[0233]

[0234] where the sum is the data points from each time range. Δt = 0.4 s was chosen to ensure that enough data points (≈80) were included to determine the 15 unknowns. Increasing Δt may not produce an improved fit because the acceleration may not be constant over longer periods due to propulsive thrust. Once the optimal parameters are determined, Equations S16 and S17 can be used to estimate the landing and takeoff speeds. This method allows the calculation of speeds without taking numerical derivatives, which can be sensitive to noise in the measurements and the choice of low-pass filter cutoff frequency.

[0235] Figure 8A is a schematic diagram of the experimental setup for the drop test used for parameter identification; Figure 8B is a diagram of the robot and tracking features from high-speed video; Figure 8C shows the height of the robot in the free-fall experiment, where the dark and light curves represent the descending and ascending phases (downstroke and upstroke); Figure 8D The relationship between the vertical acceleration and the compressed length of the robot during the support phase of the fall is shown. Figure 9 Example trajectories of leg contractions l(t) are shown. The dark solid and light solid lines represent the analytical solutions for the downstroke and upstroke l(t), respectively. The dashed line represents the expanded solution.

[0236] Figure 10 The trajectory of the robot with mixed travel of longitudinal acceleration and deceleration is shown. Figure 11 The trajectory of the robot's mixed travel with 90° turns is shown. Figure 12 A trajectory of mixed travel with a U-turn is shown. Figure 13 A trajectory of mixed travel with a non-horizontal surface is shown. Figure 14 shows the Poincare map, which depicts the z | k and φ| k The landing speed angle θ as a function of z According to θ z | k+1 / θ z | k Evolution of: Figure 14 Figure A shows the prediction for a jump height of 0.4 m; Figure 14 Figure B shows the prediction for a jump height of 0.6 m; Figure 14 Figure C shows the prediction for a jump height of 0.7 m; Figure 14 D in FIG. 5 shows the prediction for a jump height of 0.8 m.

[0237] Figure 15A and Figure 15B The robot's trajectories are shown for three scenarios during the passive stability test: stable bouncing (implemented using pneumatic stabilizers and a posture controller), bouncing using only the posture controller, and bouncing using only the pneumatic stabilizer. The stable bouncing scenario was achieved by implementing both the pneumatic stabilizer and the posture controller. The four different pattern curves represent four replicates. Figure 16 Shows the height of the robot in the agility evaluation. Figure 17 Shows the results from the endurance test: Figure 17 A in FIG shows the height of the robot when it bounces and the corresponding motor command; and Figure 17 Figure B shows the onboard battery voltage of the robot when jumping and flying.

[0238] [Table S1: Parameters for identification of the gyroplane]

[0239]

[0240] [Table S2: Jump height, frequency, and jumping agility of reported jumping robots]

[0241]

[0242]

[0243] According to an embodiment of the present invention, the hybrid jumping-flying robot seamlessly integrates a micro quadcopter with passive telescopic legs, overcomes the limitations of traditional jumping mechanisms that rely on support phase leg drive, and greatly simplifies the complexity of the mechanical structure. Through dynamic analysis, a thruster-based jumping control method was developed to stabilize and control the position of the robot during continuous jumping. This unique design and driving strategy allows for adjustable jumping height, short support phase duration, and position controllability. Compared with conventional jumping mechanisms or jumping robots, the hybrid jumping-flying robot achieves highly reliable controllability and jumping agility with a simple mechanism.

[0244] In flight mode, the robot functions as a conventional micro aerial vehicle, allowing stable hovering and agile maneuvering. In addition, thanks to the passive legs, the robot can perform coordinated hybrid jumping and flying motions by performing intermittent in-flight jumps. For example, during high-speed flight, the robot uses ground contact or the environment to generate instantaneous bursts of acceleration and bounces to slow down, turn, or accelerate, which significantly improves agility beyond just flying. Having jumping legs also improves the robot's endurance. In jumping mode, the robot generates thrust intermittently, rather than continuously as during flight mode. When the robot does not need to stay in the air, this operating mode provides an opportunity to significantly extend the robot's operating time and reduce power consumption. Compared to flight, jumping mode can extend the operating time by four times.

[0245] To achieve stable hopping using only onboard sensors, the robot is equipped with active pneumatic stabilizers as a separate component. The stabilizers influence landing attitude and stabilize hopping velocity and attitude without the need for external feedback or vision. The resulting hybrid hopping-flight robot offers unprecedented versatility when navigating complex environments.

[0246] Some embodiments of the present invention provide a hybrid jumping-flying robot comprising a micro quadcopter attached to a telescopic leg having an elastic element. The telescopic leg comprises an upper section and a lower section connected by a guide wheel assembly to allow vertical translation. Pre-stretched rubber bands are used as elastic elements (elastomers). The design according to some embodiments of the present invention enables elastic force to dominate gravity and decouples the robot's dynamics from gravity orientation, which simplifies jumping dynamics and achieves controlled jumping travel.

[0247] Some embodiments of the present invention provide a model-based hopping controller capable of controlling a robot's takeoff velocity and landing position, thereby enabling trajectory tracking and complex hybrid maneuvers. The controller can be configured to numerically solve for the robot's landing attitude based on a dynamic model of the robot during hopping. The controller can be configured to control the robot's landing position and takeoff velocity in three dimensions.

[0248] Compared with existing flying robots, effective position control using ground reaction forces through elastic legs achieves superior jumping agility.

[0249] The hybrid hopping-flying robot can carry a variety of sensors for environmental monitoring. However, its unique hopping motion enhances the robot's agility, improves its efficiency, and extends its operating time by more than four times. Furthermore, due to the simple mechanical structure of the telescopic legs, the design can also be installed as an add-on component on conventional quadcopters, giving them hopping motion capabilities.

[0250] According to embodiments of the present invention, the robot's combined jumping and flight capabilities achieve both mechanical simplicity and dynamic efficiency. Through its hybrid motion, the robot transcends the limitations of either aerial or terrestrial motion alone, allowing it to navigate complex environments with ease and enhanced agility. Its jumping and flight capabilities enable rapid changes in direction, making it more versatile than traditional aerial robots.

[0251] The robot's passive telescopic leg design allows it to perform high-performance locomotion without the need for triggers, support-phase actuation, or variable mechanical advantage. This makes it mechanically simpler and more reliable than other biomimetic jumping robots that rely on latches or latch-free elastic actuation.

[0252] The robot surpasses state-of-the-art jumping robots, achieving a maximum speed (jumping agility) of 2.38 m / s at a jumping height of 1.63 m. Its thrust-based drive allows fine-tuning of jumping height, and its short stance phase enables a higher jumping frequency, resulting in extraordinary agility.

[0253] Unlike in aerial mode, the robot generates thrust intermittently during hopping mode, extending its operating time and reducing power consumption. This feature allows the robot to achieve a four-fold increase in endurance compared to a baseline quadcopter, making it more energy-efficient for long-duration missions.

[0254] The robot's passive leg design can be easily integrated into conventional rotorcraft, enabling a standard quadcopter to be transformed into a hopping robot with simple additions and control changes. This adaptability unlocks new performance frontiers through hybrid locomotion and broadens the potential applications of both aerial and ground robots.

[0255] It should also be understood that where the methods and systems of the present invention are implemented entirely or in part by a computing system, any suitable computing system architecture may be utilized. This would include stand-alone computers, networked computers, dedicated or non-dedicated hardware devices. Where the terms "computing system" and "computing device" are used, these terms are intended to include, but are not limited to, any suitable arrangement of computers or information processing hardware capable of performing the functions described.

[0256] Those skilled in the art will understand that the embodiments described and / or illustrated herein may be varied and / or modified to provide other embodiments of the invention. Therefore, the embodiments described and / or illustrated herein should be considered in all respects to be illustrative and not restrictive. Example optional features of some embodiments of the invention are provided in the overview and description. Some embodiments of the invention may include one or more of these optional features (some of which are not specifically shown in the accompanying drawings). Some embodiments of the invention may lack one or more of these optional features (some of which are not specifically shown in the accompanying drawings). Although some embodiments relate to human point clouds, it should be understood that the method / framework of the present invention can be applied to other point clouds (not limited to human point clouds).

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Claims

1. A robot comprising: Aerial unit; a passive leg mechanism operably coupled to the aerial unit; as well as A controller is configured to control the operation of the aerial unit so that the robot is operable in at least a flying mode and a bouncing mode.

2. The robot according to claim 1, wherein: The controller is configured to control operation of the aerial unit such that the robot alternates between the flying mode and the bouncing mode during operation.

3. The robot according to claim 1, wherein: The passive leg mechanism consists of only a single telescopic leg device.

4. The robot according to claim 3, wherein: The single telescopic leg device comprises: an upper leg section secured to the aerial unit; a lower leg section movably connected to the upper leg section via one or more connectors; and An elastic mechanism is operably coupled between the upper leg section and the lower leg section.

5. The robot according to claim 1, wherein: The controller is configured to predict a landing position of the robot in the bouncing mode.

6. The robot according to claim 1, wherein: The controller is configured to determine a landing position of a next bounce cycle of the robot based on a landing posture of a current bounce cycle of the robot.

7. The robot according to claim 1, wherein: The aerial unit includes a mini drone or a micro drone.

8. The robot according to claim 7, wherein: The aerial unit includes a micro quadcopter.

9. The robot according to claim 4, wherein: The telescopic leg device also includes one or more guide wheel groups, each of which is operably coupled between a corresponding one of the one or more connectors and the lower leg section to limit the movement of the lower leg section to translation only and reduce friction.

10. The robot according to claim 4, wherein: The lower leg section includes a foot for contacting the ground or environment.

11. The robot according to claim 10, in, The lower leg section includes a first hook for supporting a portion of the elastic mechanism; and Wherein, at least one of the connectors comprises a second hook for supporting another part of the elastic mechanism.

12. The robot according to claim 4, wherein: The elastic mechanism comprises one or more elastic elements.

13. The robot according to claim 12, wherein: The one or more elastic elements are mounted between the upper leg section and the lower leg section such that the one or more elastic elements are tensioned to provide an elastic force operable to exceed the weight of the robot.

14. The robot according to claim 4, wherein: The length measured from the lowermost end of the lower leg section to the center of mass CoM of the robot is at least twice the wheelbase length of the aerial unit.

15. The robot according to claim 1, further comprising: A stabilizer is operable to interact with the airflow to stabilize the robot.

16. The robot according to claim 15, wherein: The stabilizer is configured to control landing attitude and stabilize bounce speed and attitude without external feedback or vision.

17. The robot according to claim 15, wherein: The stabilizer includes one or more horizontally articulated aerodynamic surfaces.

18. The robot according to claim 17, wherein: The one or more horizontally articulated aerodynamic surfaces are driven by a cable arrangement connected to a drive unit.

19. The robot according to claim 18, wherein: The one or more horizontally articulated aerodynamic surfaces are arranged to become rigid when the cable arrangement is actuated, and to oscillate freely in response to airflow when the cable arrangement is deactuated.

20. The robot according to claim 1, wherein: The controller is configured to: Predicting the landing position and speed of the robot in the current bounce cycle k; Determine the take-off posture and take-off speed of the robot for the current bounce cycle k based on the predicted landing position and speed of the current bounce cycle k, the pre-specified landing position, and the bounce height set point of the next bounce cycle k+1; Determining the expected landing posture of the current bounce cycle k to achieve the determined take-off posture and take-off speed of the robot in the current bounce cycle k; as well as The robot is stabilized and the landing position of the next bounce cycle k+1 is controlled by adjusting the landing posture of the current bounce cycle k.

21. The robot according to claim 20, wherein: The controller is configured to: The landing position for the next hop cycle k+1 is determined based on the lateral component of the takeoff velocity, which is affected by the landing attitude, and the amount of time the robot spends in the air phase.

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