Rolling-walking compound motion control method and equipment for double-wheel-foot robot

Abstract

The invention belongs to the related technical field of mobile robots, and discloses a rolling-walking composite motion control method and device for a double-wheel-foot robot, and the method comprises the steps: (1) simplifying the rolling motion of wheels of the double-wheel-foot robot into the sliding motion of a sliding block; (2) constructing a system kinetic equation of the double-wheel-foot robot based on the simplified kinetic model; constructing a constraint equation based on the contact state of the two legs and the ground; discretizing the system kinetic equation, the cost function and the constraint equation, and converting model prediction control problems corresponding to the system kinetic equation, the cost function and the constraint equation into nonlinear problems for numerical solution so as to complete leg motion planning; (3) calculating the rotation speed of the wheel based on the leg motion planning result; and (4) based on the rotation speed of the wheels and the leg motion planning result, a whole-body control algorithm is adopted to calculate and obtain moment instructions of leg joints and the wheels. According to the invention, the state space dimension is reduced, and the wheel-ground contact constraint is simplified.

Description

Technical Field

[0001] The present invention belongs to the technical field related to mobile robots, and more specifically, relates to a rolling-walking composite motion control method and device for a two-wheeled legged robot. Background Art

[0002] Each wheeled leg of the two-wheeled legged robot is provided with a driving wheel at its end. The wheel can contact the ground to generate a rolling motion, and the two legs can also be alternately lifted to generate a walking motion. The rolling-walking composite motion can combine the advantages of fast wheeled motion speed, high energy efficiency, and strong terrain adaptability of legged motion. However, the structure of the two-wheeled legged robot is complex, and the motion of the leg joints and wheels is coupled, which poses challenges to the design of the motion planning and control algorithms of the robot.

[0003] Currently, the existing motion planning and control algorithms for two-wheeled legged robots focus on the jumping motion and rolling motion of the two-wheeled legged robots. For example, Patent CN119065253 discloses a trajectory planning method and device for a two-wheeled legged robot, which constructs a dynamic model describing the core dynamic characteristics of the robot's balanced state, and obtains the target trajectory through two steps of preliminary trajectory optimization and target trajectory optimization, improving the speed tracking performance of the two-wheeled legged robot and the robustness of the controller. However, this method is based on a two-dimensional model on the neutral plane and cannot plan the walking motion, and the applicable scenarios are limited. For example, Patent CN118605588 discloses a motion control method and device for a two-wheeled legged robot's standing long jump, which realizes the standing long jump control without motion decoupling by respectively planning the variation functions of the nominal leg length of the robot and the deflection angle of the robot's center of mass over time. This method can pass through terrains such as steps, but has limitations such as large landing impact and long adjustment distance. Among them, the two-wheeled legged robot does not have symmetry along the neutral plane in the rolling-walking composite motion, is a complex dynamic system with both discrete touchdown events and continuous state variables, and has highly non-linear characteristics, resulting in a high planning dimension and complex control of the robot. The planning and control methods based on symmetric models or continuous dynamics are incompetent. Summary of the Invention

[0004] In view of the above defects or improvement requirements of the prior art, the present invention provides a rolling-walking composite motion control method and device for a two-wheeled legged robot, aiming to solve the problems of high planning dimension and complex control of existing robots.

[0005] To achieve the above object, according to one aspect of the present invention, a rolling-walking composite motion control method for a two-wheeled legged robot is provided, and the steps are as follows:

[0006] (1) Simplify the rolling motion of the wheels of the two-wheeled legged robot into the sliding motion of a slider to obtain a simplified dynamic model;

[0007] (2) Calculate the body acceleration of the two-wheeled and two-legged robot based on the simplified dynamic model, and then construct the system dynamic equation of the two-wheeled and two-legged robot based on the body acceleration; at the same time, construct the constraint equation based on the contact state between the two legs of the two-wheeled and two-legged robot and the ground; then, discretize the system dynamic equation, cost function and constraint equation, and transform the model predictive control problem corresponding to the system dynamic equation, cost function and constraint equation into a nonlinear problem for numerical solution to complete the leg motion planning;

[0008] (3) Through pure rolling constraint, calculate the rotational speed of the wheels based on the optimal body attitude, rotational speed, translational speed, leg joint angles and angular velocities obtained in the leg motion planning;

[0009] (4) Based on the rotational speed of the wheels and the leg motion planning results, use the whole-body control algorithm to calculate the torque commands of the leg joints and wheels.

[0010] Further, based on the rotational speed of the wheels and the optimal body attitude, position, rotational speed, translational speed, leg joint angles, angular velocities, and three-dimensional contact forces between the robot and the ground obtained from the leg motion planning, use the whole-body control algorithm to calculate the torque commands of the leg joints and wheels.

[0011] Further, the mathematical expression of the simplified dynamic model is:

[0012]

[0013] Among them, q is the generalized coordinate including the position, attitude of the robot body and leg joint angles, M(q) is the inertia matrix corresponding to the generalized coordinate, is the nonlinear term in dynamics, τ j is the joint torque, S is the torque selection matrix, F l and F r respectively correspond to the three-dimensional contact forces between the left leg and the right leg and the ground.

[0014] Further, the acceleration of the robot body obtained by solving the simplified dynamic model is:

[0015]

[0016] The system dynamic equation is:

[0017]

[0018] x consists of the translational speed, rotational speed, spatial position, attitude of the robot body and leg joint angles; u consists of the three-dimensional contact forces between the two-wheeled and two-legged robot and the ground and the leg joint angular velocities.

[0019] Further, the constraint equations include the grounded leg constraint, the swinging leg constraint, and the friction cone constraint; the grounded leg constraint includes a motion constraint, that is:

[0020]

[0021] where v ci is the velocity vector of the end of the grounded leg, is the normal vector of the contact plane Λ between the wheel part and the ground, is the normal vector of the single-leg plane Π;

[0022] The swinging leg constraint includes a motion constraint. The end of the swinging leg follows a preset reference velocity v z,ref (t) in the z direction, that is:

[0023]

[0024] where v fi is the velocity vector of the end of the swinging leg, is the direction vector of the Z axis of the world coordinate system, and v z,ref (t) is the preset reference velocity.

[0025] Further, for the motion tracking of the touchdown point, in the x direction, the touchdown point has no acceleration, and in the z direction, the touchdown point has a centripetal acceleration pointing to the wheel center, that is:

[0026]

[0027] where [r] x , [r] y and [r] z respectively represent the values of the three-dimensional vector r in the x, y, and z directions; is the acceleration of the i-th touchdown point in the world coordinate system, Express this acceleration in the ground coordinate system {D}. Based on the pure rolling assumption, this acceleration is zero in the x direction and provides centripetal acceleration in the z direction; the instantaneous angular velocity of the touchdown point includes two parts, namely the rotational angular velocity ω calf,y of the calf and the angular velocity of the wheel joint motor. The centripetal acceleration is obtained through the formula a = ω 2 r.

[0028] Further, for the motion tracking of the wheel center of the grounded leg, the motion of the wheel center E is tracked using a PD control law, that is:

[0029]

[0030] a e,des =(v e,des (t) - v e,des(t - Δt)) / Δt

[0031]

[0032] wherein, is the acceleration of the wheel center E in the world coordinate system, and J E is the Jacobian matrix at the wheel center E, which maps the joint space velocity to the velocity of the wheel center E. During a control period, the desired velocity v e,des is differentiated to obtain the desired acceleration a e,des . Finally, the magnitude of the x - component of the acceleration of the wheel center E in the world coordinate system is calculated through the PD control law to achieve the motion tracking of the leg end.

[0033] Furthermore, considering the centripetal acceleration tracking when the robot rotates or turns, when the bipedal wheeled robot rotates or turns, the robot has centripetal acceleration in the y - direction, and the y - components of the accelerations of the left and right legs when touching the ground in the ground coordinate system and are calculated by the following formulas respectively:

[0034]

[0035] wherein, ω b,z is the instantaneous angular velocity of the bipedal wheeled robot, v b,x is the instantaneous linear velocity of the bipedal wheeled robot along the forward direction, and d is the lateral offset width from the centroid of the bipedal wheeled robot's body to the ground contact point.

[0036] The present invention also provides a rolling - walking composite motion control system for a bipedal wheeled robot. The system includes a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, it executes the rolling - walking composite motion control method for the bipedal wheeled robot as described above.

[0037] The present invention also provides a computer - readable storage medium. The computer - readable storage medium stores machine - executable instructions. When the machine - executable instructions are called and executed by the processor, the machine - executable instructions cause the processor to implement the rolling - walking composite motion control method for the bipedal wheeled robot as described above.

[0038] Generally speaking, compared with the prior art by the above - conceived technical solution of the present invention, the rolling - walking composite motion control method and device for the bipedal wheeled robot provided by the present invention mainly have the following beneficial effects:

[0039] 1. In the trajectory planning, the wheel part is simplified as a slider for processing in the motion control method, which reduces the state - space dimension, simplifies the wheel - ground contact constraint, improves the calculation efficiency, and reduces the solution time.

[0040] 2. In trajectory tracking, the motion task requirements of the robot's body and legs are comprehensively considered to ensure the body balance and overall dynamic stability of the two-wheeled foot robot during movement.

[0041] 3. The present invention also considers the centripetal acceleration of the robot to optimize the body posture and joint torque in the whole-body control algorithm, improving the stability of the robot during rapid rotation or turning.

[0042] 4. The entire motion control algorithm performs real-time online operations, has robustness, and improves the passing ability of the two-wheeled foot robot in complex terrains. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 is a flowchart of a rolling-walking composite motion control method for a two-wheeled foot robot provided by the present invention;

[0044] Figure 2 is a schematic structural diagram of the two-wheeled foot robot related to the present invention;

[0045] Figure 3 is a schematic diagram of the rolling-walking composite motion of the two-wheeled foot robot;

[0046] Figure 4 is a schematic diagram of the wheel-ground contact of the grounded leg of the two-wheeled foot robot;

[0047] Figure 5 is a schematic diagram of the motion of the two-wheeled foot robot during turning. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0048] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0049] The present invention provides a rolling-walking composite motion control method for a two-wheeled foot robot. The control method includes two parts: composite motion trajectory planning and composite motion trajectory tracking. In composite motion trajectory planning, the rolling motion of the wheels is simplified to the sliding motion of sliders, the dynamic model of the robot is simplified, and a model predictive control algorithm is used to plan the body pose and speed of the robot, the angles and angular velocities of the leg joints, and the ground reaction force.

[0050] The two-wheeled foot robot includes a body and two wheel legs, where L and R represent the left leg and the right leg respectively. Each leg consists of a thigh, a calf, and a wheel part. The body is connected to the thigh through a thigh joint, the thigh is connected to the calf through a knee joint, and the calf is connected to the wheel part through a wheel joint. Each leg has three rotational degrees of freedom, and the structures of the two legs are exactly the same. Take an arbitrary right-handed coordinate system as the world coordinate system {A}, and let the origin of the base coordinate system {B} coincide with the geometric center of the body. The X-axis of the base coordinate system is parallel to the torso, the Z-axis is perpendicular to the base and points upward, and the Y-axis is determined according to the right-hand rule. Sensors are installed on the body to calculate the attitude and position information of the robot body, and sensors are installed at the rotational joints of all legs to obtain joint angle and speed information.

[0051] For the rolling-walking compound motion of the two-wheeled foot robot, during the motion, the driving wheels at the ends of the two legs of the two-wheeled foot robot can contact the ground and perform rolling motion, or can be lifted upward under the control of the leg joints to complete the leg-lifting motion. The two motions of the two legs occur simultaneously for a period of time, which is the rolling-walking compound motion. The rolling motion is a special case of the rolling-walking compound motion. In this motion mode, the driving wheels at the ends of the two legs of the two-wheeled foot robot are always in contact with the ground and perform rolling motion.

[0052] The calculation formula for the rolling ratio of the rolling-walking compound motion is:

[0053]

[0054] where, T roll and T walk are respectively the time lengths of single-leg rolling and lifting in one cycle. At least one leg is in the rolling state at each moment, and the rolling ratio ρ≥0.5. When ρ = 1, the rolling-walking compound motion is simplified to the rolling motion.

[0055] Please refer to Figure 1 , Figure 2 and Figure 3 , the control method mainly includes the following steps:

[0056] Step 1, simplify the rolling motion of the wheels of the two-wheeled foot robot into the sliding motion of a slider to obtain a simplified dynamic model.

[0057] In this simplified dynamic model, the rolling motion of the wheels is ignored, the wheels are simplified to sliders, and the rolling motion of the wheels is simplified to the sliding motion of a slider. Define the ground coordinate system {X D , Y D , Z D}, where X D , Z D are respectively the horizontal forward direction and the vertical lifting direction of the two-wheeled foot robot, and the Y D direction is determined by the right-hand screw rule, XD Y D is the horizontal plane; then the foot-end slider can slide on the ground along the forward direction, and the mathematical expression of the simplified dynamic model is as follows:

[0058]

[0059] where q is the generalized coordinate including the position, attitude of the robot body and the leg joint angles, M(q) is the inertia matrix corresponding to the generalized coordinate, is the non-linear term in dynamics, τ j is the joint torque, S is the torque selection matrix, F l and F r correspond to the three-dimensional contact forces of the left leg and the right leg with the ground respectively. The liftoff and touchdown of the two legs are reflected in the dynamic model as whether the foot-end contact forces F l and F r are zero or not.

[0060] In one embodiment, a simplified dynamic model of rolling-walking composite motion is constructed. In this embodiment, the generalized coordinates selected include the body position, attitude and leg joint angles. The base position is expressed as the relative coordinate of the origin of the base coordinate system {B} with respect to the origin of the world coordinate system {A}, and is represented in the world coordinate system {A}, denoted as , the base attitude is expressed as the rotation Euler angles from the world coordinate system {A} to the base coordinate system {B}, denoted as , that is, after the world coordinate system {A} rotates by γ angle around its own Z axis, then rotates by β angle around its own Y axis, and finally rotates by α angle around its own X axis, the base coordinate system {B} can be obtained. The leg joint angles are expressed as: , which are the thigh joint angle, knee joint angle of the left leg, thigh joint angle and knee joint angle of the right leg in sequence. Finally, they are combined into the generalized coordinates of dynamics The generalized coordinate velocity includes the angular velocity, linear velocity of the body and the angular velocity of the leg joints,

[0061] By solving the dynamic equation, the acceleration of the body can be obtained:

[0062]

[0063] where is the inertia matrix associated with the robot body, which is the upper left 6×6 sub-matrix of the overall inertia matrix M(q), is the associated inertia matrix of the coupling between the body and the legs, which is the upper right 6×4 sub-matrix of the overall inertia matrix M(q). In this embodiment, simplify Without considering the influence of leg acceleration on the body, the simplified body acceleration formula is obtained as follows:

[0064]

[0065] Step 2: Calculate the body acceleration of the bipedal wheeled robot based on the simplified dynamic model, and then construct the system dynamic equation of the bipedal wheeled robot based on the body acceleration; meanwhile, construct a constraint equation based on the contact state between the two legs of the bipedal wheeled robot and the ground; then, discretize the system dynamic equation, cost function, and constraint equation, and transform the model predictive control problem corresponding to the system dynamic equation, cost function, and constraint equation into a nonlinear problem for numerical solution to complete the leg motion planning.

[0066] In this embodiment, the model predictive control algorithm is used for leg motion planning. Among them, the body acceleration of the bipedal wheeled robot is calculated based on the simplified dynamic model, and then the system dynamic equation of the bipedal wheeled robot is constructed based on the body acceleration. Specifically, according to the simplified dynamic equation of the rolling-walking composite motion of the bipedal wheeled robot, by selecting the state vector x and the input vector u, the system dynamic equation can be obtained:

[0067]

[0068] Preferably, x consists of the translational velocity, rotational velocity, spatial position, attitude of the robot body, and leg joint angles; u consists of the three-dimensional contact forces between the bipedal wheeled robot and the ground and the leg joint angular velocities.

[0069] Among them, by solving the simplified dynamic model and ignoring the influence of leg acceleration on the body acceleration, the acceleration of the robot body can be obtained as:

[0070]

[0071] The cost function includes the process cost and the terminal cost. Select the observation interval with a duration of T starting from the current moment to respectively describe the cumulative error between the state vector and the input vector and the reference value during the process of this observation interval and the terminal error still existing at the end moment of the observation interval, that is:

[0072]

[0073] Construct a constraint equation based on the contact state between the two legs of the bipedal wheeled robot and the ground. The constraint equation includes the grounded leg constraint, the swinging leg constraint, and the friction cone constraint. In the composite motion, the contact state between the two legs of the bipedal wheeled robot and the ground is determined by the set contact timing, and it is necessary to apply constraints on the velocity and contact force of the end of the grounded leg and the end of the swinging leg respectively according to the contact state.

[0074] The contact timing can be automatically updated at a certain period or manually triggered to change. When the legs constraint is always in the state of touching the ground, the two-wheeled foot robot is in the rolling mode. When switching between the state of touching the ground and the swinging state at a certain period, it is in the rolling-walking composite motion mode.

[0075] The ground contact leg constraint includes a motion constraint, that is:

[0076]

[0077] Among them, v ci is the velocity vector at the end of the ground contact leg, is the normal vector of the contact plane Λ between the wheel part and the ground, is the normal vector of the single-leg plane Π.

[0078] The friction cone constraint restricts the horizontal component of the contact force at the end of the ground contact leg to be less than the maximum frictional force to avoid uncontrolled slipping, that is:

[0079]

[0080] Among them, μ s is the friction coefficient of the contact surface, f ci,x , f ci,y and f ci,z are respectively the three components of the contact force at the end of the ground contact leg. f ci,x and f ci,y are in the contact surface, and f ci,z is perpendicular to the contact surface.

[0081] The swinging leg constraint includes a motion constraint. The end of the swinging leg follows a preset reference velocity v z,ref (t) in the z direction, that is:

[0082]

[0083] Among them, v fi is the velocity vector at the end of the swinging leg, is the direction vector of the Z axis of the world coordinate system, and v z,ref (t) is the preset reference velocity.

[0084] In a specific embodiment, first, the system dynamics equation is constructed; in this example, the state vector x consists of the translational velocity, rotational velocity, spatial position, attitude of the robot body, and leg joint angles. The system input u consists of the three-dimensional contact force between the two-wheeled foot robot and the ground and the leg joint angular velocity, that is:

[0085]

[0086] The attitude of the body is represented by the rotational Euler angles. The reciprocal of the Euler angles with respect to time has the following relationship with the angular velocity of the body:

[0087]

[0088] Combining the above body acceleration formula, the system dynamics equation is obtained as:

[0089]

[0090] Then, a cost function is constructed. The cost function consists of two parts, the process cost function L(x(t), u(t), t) and the terminal cost function Φ(x(T)), that is:

[0091]

[0092] In this embodiment, the process cost function L(x(t), u(t), t) consists of the second norm of the state vector error weighted by Q and the second norm of the input vector error weighted by R, that is:

[0093]

[0094] The terminal cost function Φ(x(T)) is the second norm of the state vector error at time T at the end of an observation interval weighted by Q T That is:

[0095]

[0096] Secondly, a constraint equation is constructed. In this example, the constraint equation includes a grounded leg constraint, a swinging leg constraint, and a friction cone constraint.

[0097] The grounded leg constraint includes a motion constraint. As Figure 3 shown, in the motion constraint, the slider at the end of the foot of the grounded leg can instantaneously advance and slide on the ground. There is no velocity of the slider at the end in the normal vector of the contact plane between the wheel and the ground. At the same time, based on the no-side-slip assumption, there is no velocity of the slider at the end in the normal vector of the single-leg plane, that is:

[0098]

[0099] where, v ci is the velocity vector at the end of the grounded leg, is the normal vector of the contact plane Λ between the wheel and the ground, is the normal vector of the single-leg plane Π.

[0100] The friction cone constraint restricts the horizontal component of the contact force at the end of the grounded leg to be less than the maximum friction force to avoid uncontrolled slipping, that is:

[0101]

[0102] where μ s is the friction coefficient of the contact surface, and f ci,x , f ci,y and f ci,z are respectively the three components of the contact force at the end of the touchdown leg, and f ci,x and f ci,y are within the contact surface, and f ci,z is perpendicular to the contact surface.

[0103] The swing leg constraint includes a motion constraint. The end of the swing leg follows a preset reference velocity v z,ref (t) in the z direction. In this embodiment, the motion of the swing leg in the forward direction has no reference, and the motion in this direction is automatically inspired by the model predictive control algorithm, that is:

[0104]

[0105] where, v fi is the velocity vector of the end of the swing leg, is the direction vector of the Z axis of the world coordinate system, and v z,ref (t) is the preset reference velocity.

[0106] Step 3, through the pure rolling constraint, calculate the rotational speed of the wheel based on the optimal body attitude, rotational speed, translational speed, leg joint angles and angular velocities obtained in the leg motion planning.

[0107] Through the pure rolling constraint, calculate the reference rotational speed of the wheel joints of both legs. Calculate the rotational speed of the wheel joints under the assumption of pure rolling contact between the wheel and the ground, that is:

[0108]

[0109] where, is the wheel speed, and r EC is the vector radius from the wheel center to the contact point, is the velocity of the wheel center E in the world coordinate system.

[0110] Step 4, based on the rotational speed of the wheel and the optimal body attitude, position, rotational speed, translational speed, leg joint angles, angular velocities, and three-dimensional contact force between the robot and the ground obtained from the leg motion planning, use the whole body control algorithm to calculate the torque commands of the leg joints and the wheels.

[0111] In the process of calculating the torque commands of the leg joints and wheels using the whole-body control algorithm, specific task objectives are constructed. For a two-wheeled biped robot to achieve composite motion, it is necessary to coordinate the motion objectives of the body, the motion objectives of the two legs, and the objectives of the contact forces between the robot and the ground. Specifically, the composite motion of a two-wheeled biped robot requires coordinating the dynamic constraints of the robot's body, the pure rolling constraint of the wheels, the zero-force constraint of the swinging leg, the joint torque limit constraint, the friction cone constraint, the body acceleration tracking, the contact force tracking of the grounded leg, the end motion tracking of the swinging leg, the touchdown point motion tracking, and the centripetal acceleration tracking of the robot.

[0112] Please refer to Figure 4 , considering the touchdown point motion tracking, the acceleration of the i-th touchdown point in the world coordinate system is:

[0113]

[0114] In the x-direction of the ground coordinate system, there is no acceleration at the touchdown point, that is:

[0115]

[0116] where, [r] x , [r] y and [r] z represent the values of the three-dimensional vector r in the x, y, and z directions respectively.

[0117] In the z-direction of the ground coordinate system, the touchdown point has a centripetal acceleration pointing to the wheel center, that is:

[0118]

[0119] where, is the acceleration of the i-th touchdown point in the world coordinate system, Express this acceleration in the ground coordinate system {D}. Based on the pure rolling assumption, this acceleration is zero in the x-direction and provides centripetal acceleration in the z-direction, r o is the wheel radius. The instantaneous angular velocity of the touchdown point consists of two parts, namely the rotational angular velocity ω calf,y of the calf and the angular velocity of the wheel motor. The centripetal acceleration can be obtained through the formula a = ω 2 r.

[0120] Within a control period, perform differential processing on the desired velocity v e,des to obtain the desired acceleration as:

[0121] a e,des =(v e,des (t) - v e,des (t - Δt)) / Δt

[0122] The motion of the wheel center E is tracked using a PD control law, i.e.:

[0123]

[0124] where J E is the Jacobian matrix at the wheel center E, and the desired velocity v e,des is differentiated within one control period to obtain the desired acceleration a e,des . Finally, the magnitude of the x-component of the acceleration of the wheel center E in the ground coordinate system is calculated through the PD control law to achieve the motion tracking of the wheel center of the grounded leg.

[0125] For the motion tracking of the wheel center of the grounded leg, the motion of the wheel center E is tracked using a PD control law, i.e.:

[0126]

[0127] where is the acceleration of the wheel center E in the world coordinate system, J E is the Jacobian matrix at the wheel center E, which maps the joint space velocity to the velocity of the wheel center E and the desired velocity v e,des is differentiated within one control period to obtain the desired acceleration a e,des . Finally, the magnitude of the x-component of the acceleration of the wheel center E in the world coordinate system is calculated through the PD control law to achieve the motion tracking of the end of the leg.

[0128] Consider the centripetal acceleration tracking when the robot rotates or turns. When the bipedal wheeled robot rotates or turns, the robot has a centripetal acceleration in the y direction, and the y-components of the accelerations of the left and right legs when they touch the ground in the ground coordinate system and are calculated by the following formulas respectively:

[0129]

[0130] where ω b,z is the instantaneous angular velocity of the bipedal wheeled robot, v b,x is the instantaneous linear velocity of the bipedal wheeled robot along the forward direction, and d is the lateral offset width from the centroid of the bipedal wheeled robot's body to the touchdown point.

[0131] In a specific embodiment, please refer to Figure 5 . For the centripetal acceleration tracking constraint of the robot, when the bipedal wheeled robot rotates, the robot has a centripetal acceleration in the y direction, i.e.:

[0132]

[0133] where and are the x-components of the accelerations of the left and right legs when touching the ground in the world coordinate system, ω b,z is the instantaneous angular velocity of the bipedal wheeled robot, v b,x is the instantaneous linear velocity of the bipedal wheeled robot along the forward direction, and d is the lateral offset width from the centroid of the bipedal wheeled robot body to the touchdown point.

[0134] In the whole-body control algorithm, specific task objectives are constructed. All tasks correspond to an equation or an inequality mathematically:

[0135] A i x wbc = b i

[0136] C i x wbc < d i

[0137] Among them, x wbc is the decision variable. In this example, the decision variables include the body and joint accelerations, contact forces, and all joint torques, that is The task is described as an equality constraint, inequality constraint, or least squares objective of the decision variable, that is w i = A i x wbc - b i . Combining all the tasks of the least squares objective according to the weights, the following quadratic programming problem is obtained:

[0138]

[0139] Solving this quadratic programming problem can obtain the optimal decision vector x wbc , and the last six digits of this vector are the joint torques of the 6 active joints of the bipedal wheeled robot.

[0140] In this example, in order to compensate for uncertainties, for the leg joints, the control torque is obtained by superimposing the PD control term and the feedforward force term, that is:

[0141]

[0142] For the wheels, the control torque is obtained only by superimposing the speed term and the feedforward force term, that is:

[0143]

[0144] Among them, q i,des and are the expected joint angles and speeds obtained in the composite motion planning, q i,est and are the estimated joint angles and velocities obtained through motor feedback. The calculated τ i i.e., the joint control torque.

[0145] The present invention also provides a rolling-walking composite motion control system for a two-wheeled and two-legged robot. The system includes a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, it performs the rolling-walking composite motion control method for the two-wheeled and two-legged robot as described above.

[0146] The present invention also provides a computer-readable storage medium. The computer-readable storage medium stores machine-executable instructions. When the machine-executable instructions are called and executed by a processor, the machine-executable instructions cause the processor to implement the rolling-walking composite motion control method for the two-wheeled and two-legged robot as described above.

[0147] Those skilled in the art can easily understand that the above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A rolling-walking composite motion control method for a two-wheeled foot robot, characterized in that: The steps are: (1) Simplify the rolling motion of the wheels of the two-wheeled robot into the sliding motion of the slider to obtain a simplified dynamic model; (2) The body acceleration of the two-wheeled leg robot is calculated based on the simplified dynamic model, and then the system dynamics equation of the two-wheeled leg robot is constructed based on the body acceleration; at the same time, the constraint equation is constructed based on the contact state between the two legs of the two-wheeled leg robot and the ground; then, the system dynamics equation, cost function and constraint equation are discretized, and the model predictive control problem corresponding to the system dynamics equation, cost function and constraint equation is converted into a nonlinear problem for numerical solution to complete the leg motion planning; (3) The rotation speed of the wheel is calculated based on the optimal body posture, rotation speed, translation speed, leg joint angle and angular velocity obtained in the leg motion planning through pure rolling constraint; (4) Based on the rotation speed of the wheels and the leg motion planning results, the whole-body control algorithm is used to calculate the torque instructions of the leg joints and wheels.

2. The rolling-walking composite motion control method of a two-wheeled foot robot according to claim 1, characterized in that: Based on the optimal body posture, position, rotation speed, translation speed, leg joint angle, angular velocity, and three-dimensional contact force between the robot and the ground obtained from the wheel rotation speed and leg motion planning, the torque instructions of the leg joints and wheels are calculated using the whole-body control algorithm.

3. The rolling-walking composite motion control method of a two-wheeled foot robot according to claim 1, characterized in that: The mathematical expression of the simplified kinetic model is: Among them, q is the generalized coordinate containing the robot's body position, posture and leg joint angles, and M(q) is the inertia matrix corresponding to the generalized coordinate. is the nonlinear term in dynamics, τ j is the joint torque, S is the torque selection matrix, F l and F r They correspond to the three-dimensional contact forces between the left leg and the right leg and the ground respectively.

4. The rolling-walking composite motion control method of a two-wheeled foot robot as claimed in claim 3, characterized in that: By solving the simplified dynamic model, the acceleration of the robot body is obtained as: The system dynamics equation is: x is composed of the robot's body translational velocity, rotational velocity, spatial position, posture and leg joint angles; u is composed of the three-dimensional contact force between the two-wheeled robot and the ground and the leg joint angular velocity.

5. The rolling-walking composite motion control method of a two-wheeled foot robot according to claim 1, characterized in that: The constraint equations include the ground contact leg constraint, the swing leg constraint and the friction cone constraint; the ground contact leg constraint includes the motion constraint, namely: Among them, v ci is the velocity vector of the contact leg tip, is the normal vector of the wheel contact plane Λ, is the normal vector of the single-leg plane Π; The swing leg constraint contains a motion constraint where the end of the swing leg follows a pre-set reference velocity v in the z direction. z,ref (t), that is: Among them, v fi is the velocity vector at the end of the swing leg, is the Z-axis direction vector of the world coordinate system, v z,ref (t) is the preset reference speed.

6. The rolling-walking composite motion control method of a two-wheeled foot robot according to any one of claims 1 to 5, characterized in that: The motion tracking of the touchdown point shows that in the x direction, the touchdown point has no acceleration, and in the z direction, the touchdown point has a centripetal acceleration pointing to the wheel center, that is: Among them, [r] x , [r] y and [r] z Respectively represent the values ​​of the three-dimensional vector r in the x, y and z directions; is the acceleration of the ith touchdown point in the world coordinate system, The acceleration is expressed in the ground coordinate system {D}. Based on the pure rolling assumption, the acceleration is zero in the x direction and provides centripetal acceleration in the z direction. The instantaneous angular velocity of the touchdown point consists of two parts: the rotational angular velocity ω of the lower leg. calf,y Angular velocity of the wheel joint motor By the formula a = ω 2 r is the centripetal acceleration.

7. The rolling-walking composite motion control method of a two-wheeled foot robot according to any one of claims 1 to 5, characterized in that: The wheel center movement tracking of the ground contact leg, the movement of the wheel center E is tracked using the PD control rate, that is: a e,des =(v e,des (t)-v e,des (t-Δt)) / Δt in, is the acceleration of the wheel center E in the world coordinate system, J E is the Jacobian matrix at the wheel center E, mapping the joint space velocity to the velocity of the wheel center E, In one control cycle, the desired speed v e,des Perform differential processing to obtain the expected acceleration a e,des Finally, the x-component of the acceleration of the wheel center E in the world coordinate system is calculated through the PD control rate to achieve leg end motion tracking.

8. The rolling-walking composite motion control method of a two-wheeled foot robot according to any one of claims 1 to 5, characterized in that: Consider the centripetal acceleration tracking of the robot when rotating or turning. When the two-wheeled robot rotates or turns, the robot has centripetal acceleration in the y direction. The y component of the acceleration in the ground coordinate system when the left and right legs touch the ground is and The calculation formulas are: Among them, ω b,z is the instantaneous angular velocity of the two-wheeled robot, v b,x is the instantaneous linear velocity of the two-wheeled robot along the forward direction, and d is the lateral offset width from the centroid of the two-wheeled robot to the touchdown point.

9. A rolling-walking composite motion control system for a two-wheeled foot robot, characterized in that: The system includes a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, the rolling-walking composite motion control method of the two-wheeled leg robot according to any one of claims 1 to 8 is executed.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores machine-executable instructions. When the machine-executable instructions are called and executed by the processor, the machine-executable instructions prompt the processor to implement the rolling-walking composite motion control method of the two-wheeled leg robot according to any one of claims 1-8.

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