Vibration compensation device and method for aerial work platform carrying robot system

Abstract

The embodiment of the invention provides a device and a method for improving the vibration compensation of an aerial work platform carrying robot (BLMR) system. The device can reduce the cost and improve the operation precision and safety of the BLMR at the same time. Aerial work platforms typically include scalable, large scale, variable stiffness structures that are affected by complex non-linear static deformations and vibrations induced by dynamic movement / gust. This vibration may be compensated at an end effector of the robot by a Jacobian matrix-based vibration compensation JVCI process via the IMU. The output of the JVCI process may depend on IMU feedback and may be combined with other vibration damping techniques, including various feed-forward techniques.

Description

[0001] Cross - reference to related applications

[0002] This disclosure claims priority to U.S. Provisional Application No. 63 / 615,786, filed on December 29, 2023, entitled "Boom - Lift - Mounted Robot System with Vibration Compensation and Variable Stiffness", the entire content of which is incorporated herein by reference. Technical Field

[0003] The following description generally relates to a boom - lift - mounted robot (BLMR) system with variable stiffness and telescoping capabilities, and more particularly, to apparatus and methods for determining and compensating for vibrations occurring in a BLMR system. Background Art

[0004] Boom lifts are commonly used in various industries to provide safe and efficient access to elevated work areas. Recently, the concept of a boom - lift - mounted robot (BLMR) has been proposed, which combines a boom lift with an industrial robot to facilitate increased levels of construction automation. Thus, robots can be used to perform tasks traditionally carried out by human workers, such as construction, cleaning, inspection, or maintenance. Summary of the Invention

[0005] This disclosure describes a vibration compensation apparatus and method for a boom - lift - mounted robot system, and a boom - lift - mounted robot system.

[0006] One aspect of the present disclosure provides a vibration compensation apparatus including: at least one processor; and at least one memory storing executable instructions that, when executed by the at least one processor, facilitate performance of operations including: receiving inertial measurement unit (IMU) data from an IMU device of a boom - lift - mounted robot (BLMR) system, where the IMU device is located near an end of a boom of a boom lift that supports a robotic device including an end - effector; performing a Jacobian - based vibration compensation in the IMU (JVCI) process configured to compensate for vibrations exhibited at the end - effector of the robotic device, where the JVCI process receives a JVCI input including the IMU data and generates a JVCI output indicative of vibrations caused; and updating the motion of the robotic device based on the JVCI output to compensate for vibrations exhibited at the end - effector.

[0007] Another aspect of the present disclosure provides a vibration compensation method, which includes: receiving inertial measurement unit (IMU) data from an IMU device of a boom-mounted robotic system (BLMR) on an aerial work platform, where the IMU device is located near the end of a boom of the aerial work platform that supports a robotic device including an end effector; performing a Jacobian-based vibration compensation in the IMU (JVCI) process, which is configured to compensate for vibrations exhibited at the end effector of the robotic device, where the JVCI process receives a JVCI input including the IMU data and generates a JVCI output indicative of the vibrations; and updating the motion of the robotic device based on the JVCI output to compensate for the vibrations exhibited at the end effector.

[0008] Another aspect of the present disclosure provides a boom-mounted robotic system (BLMR) on an aerial work platform, which includes: an aerial work platform; a robotic device mounted on the aerial work platform; and a vibration compensation device configured to implement any one of the vibration compensation methods provided in another aspect of the present disclosure. BRIEF DESCRIPTION OF THE DRAWINGS

[0009] Many aspects, embodiments, objects, and advantages of the embodiments of the present disclosure will become more apparent when considered in conjunction with the following detailed description, in which like reference numerals in the following drawings always refer to like parts, where:

[0010] Figure 1 Several different types of aerial work platforms according to some embodiments of the present disclosure are shown;

[0011] Figure 2 An exemplary boom-mounted robotic system (BLMR) on an aerial work platform according to some embodiments of the present disclosure is shown, where vibrations in the aerial work platform may cause uncontrolled movement of the robotic end effector.

[0012] Figure 3 A schematic block diagram of an integrated vibration compensation scheme according to some embodiments of the present disclosure is shown, which can combine multiple techniques including feedforward and feedback techniques;

[0013] Figure 4 A schematic diagram of an exemplary prototype BLMR system according to some embodiments of the present disclosure is shown;

[0014] Figure 5 Exemplary static deformation distribution diagrams in the operational and joint spaces according to some embodiments of the present disclosure are shown;

[0015] Figure 6AA graph showing the reference trajectory and IK results of the end effector of a BLMR system over time according to some embodiments of the present disclosure;

[0016] Figure 6B A graph showing the variation of the open-loop BLMR end effector tracking error over time according to some embodiments of the present disclosure, including with and without static deformation compensation;

[0017] Figure 7A A graph showing an example natural frequency distribution of a BLMR in different telescopic states according to some embodiments of the present disclosure;

[0018] Figure 7B A graph showing an example Nyquist plot of a closed-loop system with different telescopic lengths according to some embodiments of the present disclosure;

[0019] Figure 8A A graph showing various examples of the variation of the tracking error of the end effector of a BLMR over time without compensation, using TVIS technology, using JVCI technology, and their combination, according to some embodiments of the present disclosure;

[0020] Figure 8B A graph showing an example spectrogram of the variation of the tracking error of a BLMR over frequency without compensation, using TVIS technology, JVCI technology, and their combination, according to some embodiments of the present disclosure;

[0021] Figure 9 A schematic block diagram showing an example device according to some embodiments of the present disclosure that can utilize JVCI technology, possibly in combination with other technologies, to compensate for vibrations exhibited in a BLMR system;

[0022] Figure 10 A schematic block diagram showing additional aspects or elements of an example device according to some embodiments of the present disclosure that can utilize JVCI technology to compensate for vibrations exhibited in a BLMR system;

[0023] Figure 11 A schematic diagram showing an exemplary method according to some embodiments of the present disclosure that can utilize JVCI technology (possibly in combination with other technologies) to compensate for vibrations exhibited in a BLMR system;

[0024] Figure 12 A schematic diagram showing an exemplary method according to some embodiments of the present disclosure that can provide additional aspects or elements related to utilizing JVCI technology to compensate for vibrations exhibited in a BLMR system; and

[0025] Figure 13FIG. 0 shows an example block diagram of a computer operable to execute according to some embodiments of the present disclosure. DETAILED DESCRIPTION

[0026] The subject matter of the present disclosure will now be described with reference to the drawings, where like reference numerals are always used to denote like elements. For purposes of explanation, numerous specific details are set forth in the following description in order to provide a thorough understanding of the subject matter of the present disclosure. However, the subject matter of the present disclosure is clearly practicable without these specific details. In other instances, well-known structures and devices are shown in block diagram form in order to facilitate the description of the subject matter of the present disclosure.

[0027] As described above, due to rapid urbanization, labor shortages, safety issues, and potential applications in extraterrestrial habitats, construction robots are increasingly being used in the modern construction industry. In various construction tasks such as site preparation (e.g., underground structure preparation, above-ground structure preparation, etc.), construction surface operations are a labor-intensive and time-consuming process, which is often characterized by the need for maintenance. Due to dynamic environmental disturbances, interaction forces, and diverse exterior wall layouts, achieving automation of construction surface operations poses significant challenges. In addition, aerial work platforms typically include large telescopic variable-stiffness structures that are vulnerable to complex non-linear static deformations and vibrations induced by dynamic motion / gusts. These problems impede the precise and safe operation of BLMRs.

[0028] To address these challenges, representative construction surface operation automation platforms have been proposed, including quadcopters, exterior wall robots, and climbing robots. Most exterior wall robots add robotic arms to a gondola. Exterior wall robots are typically a low-cost automation solution but are usually limited to flat walls without balconies or similar obstacles. Climbing robots are designed for non-destructive evaluation tasks such as low-load detection. Quadcopters can quickly fly over unstructured terrain but have limited payloads and short endurance times. To address the above challenges, recent research has proposed combining industrial robots with aerial work platforms, which can represent a general construction surface operation platform.

[0029] PRELIMINARY REFERENCE Figure 1 , Figure 1 FIG. 18 shows several different types of aerial work platforms 102 according to some embodiments of the present disclosure. For example, aerial work platform 102A is an example of a scissor lift. Aerial work platform 102B is an example of a vertical mast lift. Aerial work platform 102C is an example of an articulated lift. Aerial work platform 102D is an example of a telescopic lift. Aerial work platform 102E is an example of a telescopic articulated lift.

[0030] The aerial work platform 102 (e.g., aerial work platforms 102A - 102E or other suitable types of aerial work platforms) is the most commonly used aerial platform and can be effectively deployed to adapt to complex building surface environments and tasks. As Figure 1 shown, the aerial work platform 102 is currently operated by construction workers to reach a specified height for maintenance, cleaning, repair, and inspection work. The aerial work platform 102 is classified into scissor lifts, vertical mast aerial work platforms, telescopic lifts, articulated lifts, and related hybrid combinations according to the structural telescopic type. Among the exemplary types of the aerial work platform 102, scissor lifts and vertical mast lifts only provide vertical movement and are relatively easy to control. These two types of aerial work platforms 102 are usually used for low-altitude lifting.

[0031] Telescopic lifts and their variants can provide the potential to cover a wide range of operating heights. In addition, telescopic lifts are the most representative platforms for potential aerial work platform-mounted robot (BLMR) automation. However, due to the extendable long arm, telescopic lifts may be severely affected by vibrations. The variable stiffness characteristics of the extendable long arm have been widely observed in different applications (e.g., cranes, aerial ladders, and space structures). Due to mobile and external gust disturbances, the telescopic movement of the long arm generates variable-frequency structural vibrations, which may pose a challenge to the existing control technologies of robot-mounted devices that rely on precise positioning and / or precise movement of the end effector. To study these vibration characteristics, in the remaining part of this disclosure, the telescopic lift is selected as a representative example of the aerial work platform. However, it should be understood that the technologies of this disclosure can be applied to any type of aerial work platform 102.

[0032] Therefore, to achieve the automation of building surface operations, this disclosure studies the vibration compensation of the aerial work platform-mounted robot (BLMR) system. Through the feedback of the inertial measurement unit, the static deformation compensation and the vibration compensation based on the Jacobian matrix are systematically combined to solve the typical telescopic problems of the BLMR affected by static and vibration dynamics. To verify these methods, a BLMR prototype was designed and constructed, and the telescopic amount of the BLMR prototype affected by static errors and vibration characteristics was determined through experiments. By comparing the vibration compensation method proposed in this disclosure with the time-varying input shaping method, it is shown that the vibration compensation method proposed in this disclosure enhances its tracking performance under the vibration of the BLMR caused by movement.

[0033] Preliminary reference Figure 2 , Figure 2An exemplary boom-mounted robotic (BLMR) system 200 in accordance with some embodiments of the present disclosure is shown, where vibrations in the boom may cause uncontrolled movement of the robotic end effector. It is readily understood that the BLMR system 200 may include a boom 202 (e.g., any type of boom 102 or other suitable type of boom). The boom 202 may include a telescoping end 204 that may be adapted to carry a robot 206. The robot 206 may include an end effector 208. The end effector 208 may also be referred to as an End-Of-Arm Tooling (EOAT) element, and the end effector 208 may be a device attached to the end of a robotic arm. The end effector 208 may represent the part of the robot that interacts with the environment and performs tasks such as grasping, manipulating, or handling objects. The end effector 208 may serve as the "business end" of the robot, enabling it to perform specific operations.

[0034] Accordingly, the end effector 208 can vary widely depending on the application or task requirements. For example, the end effector 208 may include or represent a fixture for grasping or holding an object, a welding tool such as an electrode for arc welding or other metal joining processes, a spraying system for dispensing fluids such as a nozzle or a pump, or other specialized tools for, e.g., cutting, grinding, drilling, etc.

[0035] However, the vibrations exhibited in the BLMR system 200 can have an adverse effect on the position of the end effector 208 and / or cause uncontrolled movement of the end effector 208, which can have a negative impact on the operations being performed by the robot 206. Many techniques have been studied to compensate for these vibrations.

[0036] For example, early studies on the mitigation of structural vibrations in boom structures utilized feedforward methods. For example, the use of input shaping control methods has been proposed to suppress the vibrations of the boom. These methods have been further extended to Commandless Input Shaping Technique (CIST) to mitigate vibrations during the unloading process. Other techniques considered involve the development of a dual-mode zero-vibration input shaper that suppresses end-point vibrations considering multiple modes. To account for model uncertainties and disturbances, some techniques employ a combination of feedforward CIST and feedback to suppress vibrations. However, the above-mentioned methods have limited effectiveness in mitigating vibrations because they do not consider the significant issue of the vibration characteristics of parameter variations.

[0037] Recent research has focused on vibration compensation of structural frequencies that vary with different configurations. For example, considering telescopic booms, some techniques can rely on Time-Varying Input Shapers (TVIS) to reduce vibrations in aerial work platform systems. To enhance the robustness of vibration compensation methods, feedback control can also be introduced to mitigate vibrations in aerial work platform systems. Other solutions can be based on dynamic models established with modal parameters, associated with a PD (Proportional plus Derivative) controller through feedback measured by the rotational angle of each segment to reduce vibrations. Additionally, some techniques have established an infinite-dimensional model of telescopic elevators and utilized an observer-based state feedback controller that incorporates information from strain gauges and gyroscopes. This can be further combined with other techniques where the state feedback controller is based on an Euler-Bernoulli arm model with feedforward control to mitigate vibrations in telescopic boom elevators. However, these methods either require modal parameters or are only applicable to certain types of configurations.

[0038] Robot-based vibration compensation methods are relatively mature but are mainly applicable to scenarios where the robot is mounted on a fixed base. Some techniques use feedforward and classical feedback control in combination with state estimation and use angular velocity sensors and acceleration sensors for state estimation to reduce vibrations. Other techniques have proposed a neural network compensation sliding mode controller with a two-dimensional arm model to reduce vibrations in a dual-inertia system with a variable-length flexible load. To reduce vibrations, iterative learning input shaping based on accelerator feedback and adaptive finite impulse response input shaping using strain gauges have been proposed. However, these robot-based vibration compensation methods are limited in the BLMR scenario because they are either applicable to rotary joints or target repeatable operations.

[0039] Recently, feedback control methods based on laser tracker devices (e.g., laser tracker device 220) have been proposed to mitigate the vibrations of BLMRs. However, directly using the measurements of the laser tracker device as feedback is both expensive and prone to potential laser beam blockage when performing complex tasks. Therefore, the present disclosure proposes a new feedback method that combines static deformation compensation and dynamic vibration compensation through feedback from an Inertial Measurement Unit (IMU) 210 to address vibration problems and / or challenges related to telescoping. Compared with other solutions, the method proposed in the present disclosure can utilize a robotic manipulator (e.g., robot 206) and the IMU 210 installed at the end 204 of a general telescopic arm structure for an aerial work platform 202, and can perform vibration compensation using robotic operations, without being limited by the type of joints of the telescopic arm structure, without restrictions on the type of robotic manipulator installed at the end (with sufficient redundancy), and without the need to know the modal parameters in advance during automated building surface operations.

[0040] In this regard, the technology of the present disclosure can generally relate to a feedback vibration compensation method that proposes Jacobian matrix-based vibration compensation JVCI feedback via an Inertial Measurement Unit (IMU) 210 to account for telescoping-dependent vibrations in a general BLMR-type structure, and the JVCI feedback has a linear parameter varying system stability proof.

[0041] Furthermore, a typical telescopic BLMR (e.g., BLMR 200) integrated with an electrical control system can be designed and constructed to capture telescoping-dependent vibration characteristics. Thus, as will be further detailed below, compared with time-varying input shaping methods, the technology proposed in the present disclosure can be verified through experiments on multi-dimensional analysis of vibrations to demonstrate enhanced tracking accuracy and vibration mitigation effects.

[0042] More specifically, the present disclosure will be organized by section below for better understanding. In this regard, the first section provided below relates to the vibration compensation of BLMR 202, including static deformation compensation, time-varying input shaping methods, and Jacobian matrix-based vibration compensation via the IMU with an attached stability proof. The second section provided subsequently discusses the design and experimental case studies of BLMRs to evaluate the technology of the present disclosure. Finally, there is a conclusion section.

[0043] Vibration Compensation of Exemplary BLMR

[0044] Regarding the kinematics of telescopic BLMRs, consider the configuration of a general BLMR (e.g., BLMR 200) that combines n a electric / pneumatic cylinders and has n rFor a robotic arm with joints, the telescopic amount d of the actuator of the aerial work platform can be defined as:

[0045]

[0046] where are respectively the telescopic amounts of n a electric / pneumatic cylinders.

[0047] The robotic joint q can be defined as:

[0048]

[0049] where are respectively n r joints.

[0050] And, the overall BLMR state h can be defined as:

[0051]

[0052] As Figure 2 shown, define the inertial coordinate system attached to the ground the body-fixed coordinate system attached to the end 204 and the body-fixed coordinate system attached to the end effector 208 of the robotic arm can define the connection point p of the aerial work platform carrying the robot t (d), and the position p of the end effector of the robot e (d,q). The rotational Euler angles (following ZYX rotation) of the end effector 208 can be given by The state velocity of the BLMR200 connected by the Jacobian matrix J to the velocity and angular velocity of the end effector is, for example:

[0053]

[0054] where z can be the unit vector {0 0 1} along the local Z direction for a rotational joint T or the zero vector {0 0 0} for a prismatic joint T , can be the rotation matrix from the coordinate system corresponding to the i-th actuator to the ground coordinate system . The forward kinematics is given by formula (4). It should be noted that, due to the combination of the degrees of freedom (DOFs) of the aerial work platform and the robot, the state of the BLMR200 is usually greater than six degrees of freedom. Therefore, the corresponding inverse kinematics may be redundant and cannot be uniquely determined. The inverse kinematics Q is a standard quadratic programming problem with linear constraints and is given by the following formula:

[0055]

[0056] Among them, δh, δp e , and δθ e can be local perturbations around the state, and W can be a positive definite weight matrix. In addition to the Jacobian matrix of the robotic end effector 208, the Jacobian matrix at the end 204 of the aerial work platform may also be important or crucial because it takes into account significant deviations due to the flexure of the long arm. To account for the non-linear static deformation, a laser tracker device 220 can be used to measure the static error at the end 204 as shown in Figure 2 and is defined as Utilizing the low-frequency characteristics of the deformation, a static deformation profile can generate the compensated aerial work platform actuator input δd, given by the following formula:

[0057]

[0058] Among them, can be the right pseudo-inverse of J t . The static deformation compensation S(d) can be given by the formula

[0059] d = d r + δd, (7)

[0060] Among them, d r can represent the desired telescopic amount of the aerial work platform actuator.

[0061] Regarding the Jacobian matrix-based vibration compensation via the feedback of the IMU 210, due to the flexibility of the aerial work platform 202, the movement of the BLMR 200 introduces vibrations into the end effector 208. Figure 3 A comprehensive compensation scheme including different controllers is shown in

[0062] Now turning to Figure 3 , Figure 3 The schematic block diagram 300 shown in shows a comprehensive vibration compensation scheme according to some embodiments of the present disclosure, which can combine multiple techniques including feedforward techniques and feedback techniques.

[0063] As shown in the figure, as part of the feedforward element, one or more TVIS techniques 302, BLMR IK techniques 304, and static deformation compensation techniques 306 can be employed. It can be understood that static deformation can be compensated with a deformation distribution map to improve the trajectory accuracy, which will be described in further detail below. Additionally, one or more JVCI techniques 320 that can be achieved through feedback can be used to account for vibrations. The JVCI technique 320 can include joint space compensation allocation techniques 308, band-pass filter techniques 310, and extended Kalman filter (EKF) techniques 312. Therefore, the JVCI technique 320 can be used to reconfigure some of the feedforward techniques 302, 304, and / or 306.

[0064] In the feedforward vibration mitigation method for vibration characteristics dependent on scalability, some TVIS techniques 302 can effectively mitigate vibrations dependent on scalability. For example, assume that the natural frequency ω n (d) and damping ratio ξ(d) of the BLMR200 can be non-linear functions of the arm extension. When implementing TVIS, the natural frequency and damping ratio are scheduled over time, and the time-varying input shaping filter I(t) can be

[0065]

[0066] where u(t) can be a pulse signal. From Equation (9), T I (t) and L(t) can be the time-varying time shifts and ratios between pulses,

[0067]

[0068] The reference trajectory p r (t) of the end effector can be convolved with the time-varying input shaping filter I(t) to obtain the corrected reference trajectory

[0069]

[0070] To mitigate the vibration problem in real time without the natural frequency and damping ratio of the BLMR, a vibration compensation technique based on the Jacobian matrix via the IMU, such as the JVCI technique 320, is proposed. As Figure 2 shown, to compensate for these vibrations, assume that the IMU210 is attached to the bottom of the end 204 of the aerial work platform, but other arrangements are of course possible. This arrangement stems from the fact that the extendable long arm of the aerial work platform helps to accurately capture the flexibility of the main structure, while the robotic manipulator arm is significantly stiffer and is assumed to follow rigid body motion. A position controller with an actuator having a P-PI structure can disadvantage the overall state of the BLMR Vibration at the end 204 can be expected to be compensated for by a robotic manipulator.

[0071] q = q r + Δq, (11)

[0072] where q r can be the desired robotic joint input and Δq can be the incremental joint motion for compensating vibration. Thus, the dynamic contributions of the joints can be established. Assume that the vibration structural mode depends on the telescopic state d of the actuator of the aerial work platform, so the dynamic system is modeled as a linear parameter varying system, defined as G o (s; d), where s can be the Laplace variable and the multi-dimensional variable d can be the slowly varying parameter that determines the local vibration characteristics. The input and output of the system can be the joint motion q i (t) and the acceleration a(t) and angular velocity ω(t) from IMU measurements,

[0073]

[0074] where Q(s), A t (s) and Ω t (s) are the Laplace transforms of q i (t), a(t) and ω(t).

[0075] The vibration of the end 204 can be reconstructed by the extended Kalman filter (EKF) technique 312 and IMU 210 measurements. The body-fixed coordinate system can be related to the inertial coordinate system by a ZYX Euler angle rotation (defined as ). The velocity of the end 204 can be given by . The dynamic model of the IMU can be defined as,

[0076]

[0077] where C(θ t ) can be defined as,

[0078]

[0079] and, R(θ t ) can be defined as,

[0080]

[0081] where s κ = sin(κ) and c κ = cos(κ) (κ = φ, θ, ψ). The given dynamic model of the IMU is used to predict and can be defined as

[0082]

[0083] where L can be an observer matrix. By estimating the body-fixed coordinate system after the band-pass filter system G b (s) the end vibration δp t is defined as

[0084]

[0085] where R T (θ) represents the rotation matrix from the inertial coordinate system to the body-fixed coordinate system G b (s) can be used to eliminate drift, while and P t (s) are the Laplace transforms of the estimated end position and the reference end position p t respectively. It can be assumed that the response speed of the industrial robot 204 is faster than that of the aerial work platform 202. High-frequency vibrations can be compensated by the robot manipulator, and even if there are large vibrations at the end 204, the vibrations of the end effector 208 can be reduced. Based on the criteria of minimum joint movement and minimum change in the center of mass, an optimized configuration method for reducing the vibrations of each joint is proposed. The vibration δp of the end 204 t can be compensated by solving the joint space compensation distribution H(q) through the incremental joint movement δq t This optimization problem is defined as

[0086]

[0087] where w1 and w2 are weights, J r is the Jacobian matrix of the robot manipulator, δp c is the change in the center of mass of the robot, defined as

[0088]

[0089] where f m (·) is used to calculate the center of mass of the robot manipulator. After solving this optimization problem, the incremental joint movement is given by

[0090] Δq = K c δq t , (20)

[0091] where K c is the feedback gain. Substituting δpt The incremental movement assigned to each joint affects the vibration performance because the dynamic contributions of the joints may be different. An optimized allocation method based on Equation (18) is proposed to reduce the vibration caused by each joint.

[0092] The feedback stability of some JVCI technologies 320 may highly depend on K c The design. The EKF technology 312 and the robot joint space compensation allocation technology 308 can be linearized into G e (s;d) and G a (d). The vibration at the end is usually significantly faster than its nominal motion (e.g., the planned trajectory with only d). Therefore, the stability of the system is analyzed in the conventional linear parameter varying (LPV) system coordinate system with d as the scheduling parameter.

[0093] For example, the overall open-loop system is defined as:

[0094] G(s;d) = K c G a (d)G b (s)G e (s;d)G o (s;d). (21)

[0095] The stability of the system can be guaranteed by the generalized Nyquist theorem for a multiple-input multiple-output (MIMO) system, where G(jω f ;d) can be obtained through experimental measurement. Let P ol be the number of open-loop unstable poles in the open-loop MIMO transfer function matrix G(s;d). In some cases, the closed-loop system is stable if and only if the Nyquist plot of det(I + G(s;d)) encircles the origin P ol times in the counterclockwise direction and does not cross the origin. For a conventionally open-loop stable BLMR system, this theorem requires that det(I + G(s;d)) does not encircle the origin.

[0096] BLMR Prototype Experiment

[0097] As Figure 4 shown, in order to verify the technologies and / or methods proposed in the present disclosure, in terms of design and hardware configuration, a scaled-down BLMR prototype was designed and constructed by combining a telescopic lift and a collaborative robot.

[0098] Figure 4Shows a schematic diagram of an exemplary prototype BLMR system according to some embodiments of the present disclosure. In this exemplary configuration, two joints of the aerial work platform are driven by two electromechanical cylinders (EMCs) driven by motors. An IMU is installed at the end of the aerial work platform, with an acceleration resolution of 0.0002g and an angular velocity resolution of 0.01° / s, for real-time feedback. The robotic joints, electromechanical cylinders, and IMU are all under real-time control and perception through a communication protocol with a sampling rate of 1 kHz. As Figure 2 shown, the vibration or deformation is measured by a laser tracker device, and its distance resolution can be 50 μm. The detailed specifications of the BLMR prototype are listed in Table I.

[0099]

[0100] Table I

[0101] As Figure 4 shown, regarding kinematic modeling, in the schematic diagram of the prototype BLMR system 400, the triangle 402 represents the initial configuration of the BLMR. In the initial configuration, the length of each side of the triangle 402 can be represented as e 10 , e 20 and e 30 . To simplify the calculation, the motion d1 can be converted to the rotation q d1 of the link 401,

[0102]

[0103] In a given motion range, there is a mapping relationship between d1 and q d1 , and q d1 can be converted to d1,

[0104]

[0105] The variable set can be rewritten as,

[0106]

[0107] The detailed Denavit - Hartenberg (DH) coordinate system of the BLMR is as Figure 4 shown, and the DH table is shown in Table II below. The overall transformation matrix from the ground to the end - effector coordinate system can be given by

[0108] T = T1T2T3T4T5T6T7T8T9T 10 T 11 . (25)

[0109] The position of the end - effector is,

[0110] p e = Tl, (26)

[0111] where l is the tool in the end - effector coordinate system. The Jacobian matrix J can be

[0112]

[0113] where z1 = {001} T for a revolute joint, and z0 = {000} T for a prismatic joint.

[0114] i <![CDATA[α i-1 > <![CDATA[a i-1 > <![CDATA[d i > <![CDATA[θ i > 1 0 0 <![CDATA[l1]]> 0 2 π / 2 0 0 <![CDATA[π / 2+q d1 > 3 π / 2 0 <![CDATA[l2]]> π / 2 4 0 0 <![CDATA[d2]]> 0 5 0 0 <![CDATA[l3]]> 0 6 π / 2 0 <![CDATA[l4]]> <![CDATA[π / 2+q1]]> 7 -π / 2 0 0 <![CDATA[q2 - π / 2]]> 8 0 <![CDATA[l5]]> 0 <![CDATA[q3]]> 9 -π / 2 0 <![CDATA[l6]]> <![CDATA[q4]]> 10 π / 2 0 0 <![CDATA[π / 2+q5]]> 11 -π / 2 0 0 <![CDATA[π+q6]]>

[0115] Table II

[0116] To improve the positioning accuracy of the end - effector, first, the static deformation compensation technology is utilized. When the robot stands at the end, the EMC telescopic amounts d1 and d2 are sampled at intervals of 50 mm to form a sampling grid, where d1 ranges from 0 to 400 mm and d2 ranges from 0 to 700 mm. As Figure 5 shown, the static deformation distribution map of the end of the aerial work platform can be automatically generated by using a laser tracker and through the designed software.

[0117] Figure 5 Shows an exemplary static deformation distribution map 500 in the workspace and joint space according to some embodiments of the present disclosure. It should be noted that such deformation is usually a smooth non - linear function. Therefore, even for the high - dimensional deformation distribution map of a large aerial work platform with more degrees of freedom and uncertain loads, the adaptive mesh - generation technology and surrogate models can be used to reduce the required number of samples. The deformations in the X - direction and Z - direction and their total deformation are plotted in both the workspace and joint space. They are respectively defined as and Generally, the deformation is mainly caused by the moment generated by the payload gravity relative to the base. The deformation distribution map in the workspace shows that the deformation is mainly concentrated in the Z - direction and increases as the aerial work platform extends further in this direction. The deformation distribution map in the joint space shows that as the aerial work platform extends and the moment increases, the influence of the telescopic amount d2 on the deformation is greater.

[0118] To verify the effectiveness of the static deformation compensation, the BLMR moves along a 1 - m lifting trajectory with speed and acceleration limitations ( Figure 6A the dashed line in

[0119]

[0120] The corresponding initial joint positions are,

[0121]

[0122] Using Equation (5), the corresponding EMC trajectory d and the robot trajectory are calculated and plotted in Figure 6A .

[0123] Now referring to Figure 6A , Figure 6A Figure 600A shows the curves of the reference trajectory of the end effector of the BLMR system over time and the IK (Inverse Kinematics) results according to some embodiments of the present disclosure, demonstrating the reference trajectory of the end effector of the BLMR system over time and the IK results according to some embodiments of the present disclosure.

[0124] Here, the variation of the z-axis rotation is shown (e.g., curve 602). Assuming d 1r (e.g., curve 604) and d 2r (e.g., curve 606) are the reference motions of two EMCs, while q 2r , q 3r , and q 5r (e.g., curves 608, 610, and 612 respectively) are the reference motions of the robot joints, while the other joints q 1r , q 4r and q 6r are held at zero. The tracking errors e x and e z of the end effector in the X and Z directions are captured using a laser tracker, and these errors are recorded with and without static deformation compensation and shown in Figure 6B .

[0125] Now referring to Figure 6B , Figure 6B Figure 600B shows the graph of the open-loop BLMR end effector tracking error over time according to some embodiments of the present disclosure, including with and without static deformation compensation. According to some embodiments of the present disclosure, the tracking error of the BLMR end effector over time in the open loop, including the cases with static deformation compensation (e.g., curve 620) and without static deformation compensation (e.g., curve 622).

[0126] As the EMCs expand and contract, the deviation between the uncompensated trajectory and the reference trajectory increases. Table III below shows the steady-state error (SSE) and root mean square error (RMSE) of the trajectory with and without static deformation compensation. Although there are fluctuations due to the flexibility of the BLMR, static deformation compensation improves the motion accuracy. Current static deformation compensation schemes have limitations and may not be able to completely eliminate the SSE. A static deformation distribution map and cubic interpolation method can be used to estimate the deformation at each point. When constructing the static deformation distribution map, the robot is fixed at the end of the BMLR, and different configurations of the industrial robot also affect the deformation of the aerial work platform.

[0127]

[0128] Table III

[0129] For the vibration compensation of the BLMR prototype 400, a similar tracking experiment can be used to evaluate the feedforward trajectory generation method of the TVIS technique 302, the feedback control method of the proposed JVCI technique 320, and the effectiveness of their combination in reducing the vibration caused by the movement of the BLMR. The TVIS technique requires continuous updating of the natural frequency and damping ratio of the BLMR. Similar to the sampling grid of the deformation distribution map, a laser tracker device can be used to capture the impulse response to obtain the natural frequency and damping ratio distribution map of the BLMR system. For the BLMR and general telescopic arm systems, the first bending mode is the main one. Given the first bending mode, the damping ratio can be calculated based on the first few resonance peaks and valleys.

[0130]

[0131] where Y 2k-1 and Y 2k can be the peak and valley in the oscillatory impulse response. The difference in damping ratio observed at different telescopic states is usually small. As the number of peak and valley combinations used to calculate the damping ratio increases, the average value tends to 0.0387, which can be applied throughout the telescopic space. Using this damping ratio, the natural frequency distribution map can be calculated from the resonance of the impulse response. As Figure 7A shown, the frequency maps of the workspace and joint space are represented by and respectively.

[0132] Now turning to Figure 7A , Figure 7A shows an example natural frequency distribution map 700A of the BLMR in different telescopic states according to some embodiments of the present disclosure.

[0133] Different from the uniform damping ratio, the natural frequency distribution shows variations, especially in the telescoping direction of the telescoping amount d2. As the BLMR reaches a farther or higher position, the natural frequency decreases. The parameters of TVIS can be estimated by the cubic interpolation of the frequency distribution map.

[0134] In addition, the feedback control method JVCI technology 320 can adjust the vibration in the XZ plane, so three joints q2, q3, and q5 can be used to compensate for the vibration of p. t According to the acceleration and angular velocity resolution of the IMU, the state function and the measurement covariance matrix in the EKF can be set to diag{0.01, 0.01, 0.01, 0.001, 0.001, 0.001, 0.1, 0.1, 0.1} and diag{0.01, 0.01, 0.01}, respectively.

[0135] The Jacobian constraint δp in formula (18) t = J r δq t may be undetermined, which provides room for optimization. The undetermined constraint can be used to reduce the optimization variables to only δq t5 , thus transforming the problem into an unconstrained optimization. This may reduce the computational amount and enable the optimization formula (18) to achieve real-time solution. To consider their different nominal values, the coefficients w1 and w2 can be set to 1 and 5×10^6, respectively. The vibration δp t can be assigned to the industrial robot according to formula (18).

[0136] Since the change in the telescoping length is slow enough compared to the structural dynamics, if the JVCI feedback control is stable at all telescoping lengths, the stability of the LPV system can be guaranteed. The overall open-loop system G o (s; d) from the robot joints q2, q3, and q5 to the end vibration can be identified under different telescoping states, and d1 and d2 can be sampled at intervals of 125 mm and 250 mm, respectively. The m-th d1 sample and the n-th d2 sample can be defined as d mn , thus forming a sampling grid. Sinusoidal reference signals with different frequencies and amplitudes can be sent to q2, q3, and q5 to measure the corresponding a(t) and ω(t) responses.

[0137] This sequence also forms a set of frequency response functions (FRFs) G o (jω f ; d mn ), where ω fIt can be the measurement frequency. Each measured FRF can correspond to a point in the sampling grid of d. The relevant FRF can be used to construct the overall open-loop LPV transfer function according to Equation (21). The closed-loop stability of the LPV system can be verified using the generalized Nyquist theorem. Figure 7B shows the Nyquist plots of the closed-loop systems with different gains in different telescopic states

[0138] Now refer to Figure 7B , Figure 7B , which shows FIG. 700B of an example of the Nyquist of a closed-loop system with different telescopic lengths according to some embodiments of the present disclosure, including a closed-loop system G mn with different telescopic lengths d c of the Nyquist plot of (s). For better visualization, the sampling interval of the gain K can be set to 10. To ensure the stability of the system, the point 702 located at the respective origin should be outside the encirclement. According to this rule, the gain K c is set to 40 in the experiment. c

[0139] After the parameters are determined, the TVIS technique 302, the JVCI technique 320, and their combinations can be applied to the BLMR. The tracking errors e x and e z in the X and Z directions are as Figure 8A shown.

[0140] Now turning to Figure 8A , which shows FIG. 800A of various examples of the tracking error of the end effector of the BLMR varying with time without compensation, using the TVIS technique, using the JVCI technique, and their combinations, according to some embodiments of the present disclosure. Figure 8A It is divided into three time periods, including a first time period 802 from 0 to about 3 seconds (s), a second time period 804 from about 3 seconds (s) to about 10 seconds (s), and a third time period 806 greater than about 10 seconds (s).

[0141] To evaluate the performance, in addition to the peak values of the fast Fourier transform (FFT) of the vibration signals at the start (e.g., the first time period 802) and the end (e.g., the third time period 806) as shown in Figure 8A , the convergence time of the residual vibration is also considered, which can be defined as the time when the vibration amplitude is less than about 0.05 mm after the BLMR stops moving. The average vibration reduction percentage R can be defined as,

[0142]

[0143] wherein, A c1 and A c2 can be the compensation peaks at the start and end, respectively; A u1 and A u2 can be the uncompensated peaks at the start and end, respectively, and these peaks are as Figure 8B shown.

[0144] Now referring to Figure 8B , Figure 8B FIG. 800B shows an example spectrogram of the tracking error of the BLMR varying with frequency without compensation, using TVIS technology, JVCI technology, and combinations thereof, according to some embodiments of the present disclosure. Figure 8B The left portion of Figure 8A gives a first graph 808 representing the first time period 802 in Figure 8A , while the right portion provides a second graph 810 representing the third time period 806 in

[0145] The detailed comparison results are shown in Table IV. It can be observed that all vibration compensation methods reduce the vibration in the uncompensated example 820 to some extent. Compared with TVIS compensation 822, the performance of JVCI compensation 824 is enhanced because the former takes into account the interference from the real-time movement of the robot. TVIS compensation 822 depends to a large extent on the accuracy of the mapping of the natural frequency and damping ratio. In addition, constructing such a mapping using a smaller grid increases the cost. Therefore, TVIS compensation 822 is usually used to compensate for the vibration generated during the telescopic movement trajectory of the aerial work platform, and is ineffective in static scenarios where the aerial work platform is not moving. The combination 826 of JVCI and TVIS further improves the tracking performance, indicating that this combination is a promising method for vibration damping in aerial work platform devices. This shows the potential of combining JVCI technology 320 with TVIS technology 302 (e.g., as Figure 3 shown), to achieve enhanced performance and reduced costs by using a rough (e.g., lower cost) mapping of the natural frequency and damping ratio.

[0146]

[0147] Table IV

[0148] Referring to Figure 9 , Figure 9 ​​​​FIG. 0 shows a schematic block diagram of an example apparatus 900 according to some embodiments of the present disclosure. The example apparatus 900 may utilize the JVCI technique 320 (possibly in combination with other techniques such as, for example, the TVIS technique 302, the SDC technique 306, etc.) to compensate for vibrations exhibited in the BLMR systems 200, 400. The apparatus 900 may include all or part of the elements described in detail in connection with the BLMR systems 200, 400. For example, in certain embodiments, the apparatus 900 may communicate (e.g., wired or wirelessly) with one or more elements of the BLMR systems 200, 400. In some embodiments, the BLMR systems 200, 400 may include the apparatus 900. The apparatus 900 may include a processor 902 that may be specifically configured to interface with the BLMR systems 200, 400 and / or for vibration compensation. The apparatus 900 may further include a memory 904 that stores executable instructions that, when executed by the processor 902, may facilitate the performance of operations.

[0149] The processor 902 may be a hardware processor having structural elements known to be associated with a processing unit or circuit. The various operations of the processor 902 are represented by functional elements shown in the figures herein, and these functional elements may require, for example, specialized instructions stored in the memory 904 and / or the vibration compensation apparatus 906. Together with these specialized instructions, the processor 902 and / or the vibration compensation apparatus 906 may be a specialized apparatus. Further examples of the memory 904 and the processor 902 may be referred to Figure 13 . It should be understood that the apparatus 900 or the computer 1302 may represent a server device or a client device and may be used to implement one or more of the Figure 9 systems, devices, or components shown and described in connection with the other figures disclosed herein.

[0150] Reference Figure 2 and Figure 9, at step 908, device 900 may receive IMU data 910. The IMU data may be received from any suitable IMU, such as IMU 210 of BLMR system 200. Thus, the IMU may be located near the end (e.g., end 204) of the arm of an aerial work platform (e.g., aerial work platform 202) that supports a robotic device (e.g., robotic device 206) including an end effector (e.g., end effector 208). Specifically, the IMU may be any suitable electronic device that can measure or report the specific force and angular rate of an object, and sometimes also measure or report the orientation of the object using a combination of accelerometers, gyroscopes, magnetometers, or similar devices. The IMU may consist of any sensors that can work together and typically provide motion data (e.g., IMU data 910) of the subject in a time series format. For example, the IMU data may include acceleration data 910A (e.g., linear, angular, etc.), angular velocity data 910B (e.g., rotational rate, etc.), or other suitable data, such as orientation data (e.g., pitch, roll, yaw, etc.).

[0151] At step 912, device 900 may perform a JVCI process 914 (e.g., JVCI technique 320). The JVCI process 914 may be configured to compensate for vibrations exhibited at the end effector (e.g., end effector 208) of the robotic device. In this regard, as shown in step 916, the JVCI process 914 may include receiving and / or utilizing a JVCI input 918. The JVCI input 918 may include IMU data 910 (e.g., acceleration 910A, angular velocity 910B, etc.), which represents real-time feedback related to BLMR system vibrations.

[0152] In some embodiments, the JVCI input data 918 may further include BLMR joint data 918A. The BLMR joint data represents an optimal dynamic allocation with a stability proof of the BLMR system having a linear parameter varying system (e.g., G(s;d)). As previously described, the linear parameter varying system may be a function of the Laplace variable and the distance variable, where the Laplace variable is applicable to the Laplace transform and the distance variable indicates the telescopic state of the aerial work platform arm in at least one dimension (e.g., X, Y, Z, etc.).

[0153] As shown in step 920, in response to the JVCI input 918, the device 900 can generate a JVCI output 922. The JVCI output 922 can indicate movement due to vibrations exhibited by the BLMR system. At step 924, based on the JVCI output 922, the device 900 can update the movement of the robotic device 206 to compensate for vibrations exhibited by the end effector. Thus, although the end effector of the robotic device 206 is subject to vibrations that would otherwise negatively impact its accuracy and / or positioning, it can still maintain a higher level of accuracy for the current task.

[0154] Now turning to Figure 10 , Figure 10 FIG. 1000 is a schematic block diagram showing additional aspects or elements of an exemplary device in accordance with some embodiments of the present disclosure, which exemplary device can utilize JVCI techniques to compensate for vibrations exhibited in a BLMR system.

[0155] At step 1002, the device 900 can use an Extended Kalman Filter (EKF) 1004. For example, as part of the JVCI process 914, the device 900 can determine or reconstruct vibrations based on the IMU data 910 through the EKF 1004. The EKF 1004 can include all or part of the detailed EKF techniques 312 associated with Figure 3 As described above, the EKF 1004 can represent a mathematical algorithm for estimating the state of a non - linear dynamic system from noisy measurements. Traditional Kalman filters can only handle linear systems, while the EKF 1004 can handle non - linear systems. The EKF 1004 can use a first - order Taylor series expansion to approximate the non - linear system so that it can handle non - linear systems. In this regard, the EKF 1004 can employ a state - transition model that represents the mathematical representation of the system dynamics, describing how the state evolves over time; a measurement model that represents the mathematical representation of how the system state is observed through measurements; and linearization, in order to approximate the non - linear system by linearizing the state - transition and measurement models around the current estimate of the state.

[0156] Optionally, at step 1006, as part of the JVCI process 914, the device 900 can relate the coordinate system of the robotic device 206 (e.g., coordinate system 212T, coordinate system 212E, etc.) to the ground coordinate system of the BLMR system (e.g., coordinate system 212G) based on three - dimensional Euler angle rotations.

[0157] At step 1008, the apparatus 900 may further perform a Static Deformation Compensation (SDC) process 1010. The SDC process 1010 may be configured to compensate for static deformations associated with the BLMR system. In some embodiments, as shown in step 1012, the SDC process 1010 may include determining a deformation distribution map (e.g., see Figure 5 ) based on measurements from a laser tracker device (e.g., laser tracker device 220).

[0158] At step 1014, the apparatus 900 may perform a TVIS process 1016. The TVIS process 1016 may be configured to compensate for vibrations of the aerial work platform based on the natural frequency and damping ratio of the BLMR system, which may include incorporating all or part of the TVIS technique 302 detailed in Figure 3 or elsewhere herein. For example, as shown in step 1018, the apparatus 900 may determine or receive the natural frequency and damping ratio of the BLMR system. At step 1020, the apparatus 900 may compensate for vibrations of the aerial work platform based on the natural frequency and damping ratio (e.g., in a feed-forward manner).

[0159] As previously described, in some embodiments, e.g., in certain deployments of the BLMR system, the JVCI output 922 may be used alone to compensate for vibrations. In other embodiments, the JVCI output 922 may be combined with other techniques to further improve vibration compensation. For example, at step 1022, the apparatus 900 may combine the JVCI output 922 (e.g., real-time feedback) with certain feed-forward techniques, such as the outputs from the SDC process 1010 and / or the TVIS process 1016.

[0160] Exemplary Method

[0161] Figure 11 and 12 respectively illustrate various exemplary methods 1100 and 1200 related to the subject matter of the present disclosure. For simplicity of explanation, these methods are shown and described as a series of steps. It should be understood and appreciated that the subject matter of the present disclosure is not limited to the order of the steps, as some steps may occur in a different order and / or concurrently with the actions shown and described herein. For example, those skilled in the art will understand and appreciate that the methods may alternatively be represented as a series of related states or events, such as in a state diagram. Additionally, not all of the steps shown are necessary to implement the methods of the present disclosure. Further, it should be further understood that the methods herein and throughout the present disclosure are capable of being stored on a manufacture to facilitate transporting and transferring these methods to a computer.

[0162] Now refer toFigure 11 , Figure 11 illustrates an exemplary method 1100 that can utilize JVCI technology (possibly in combination with other technologies) to compensate for vibrations exhibited in a BLMR system, according to some embodiments of the present disclosure. Although method 1100 describes a complete method, in some embodiments, method 1100 may include steps of one or more 1200 methods, as shown by A inserted in the figure.

[0163] At step 1102, a device including at least one processor may receive inertial measurement unit (IMU) data from an IMU device of an aerial work platform-mounted robot (BLMR) system. The IMU device may be located near the end of an aerial work platform arm that supports a robotic device including an end effector.

[0164] At step 1104, the device may perform a JVCI process for vibration compensation based on the Jacobian matrix of the IMU. The JVCI process is configured to compensate for vibrations exhibited at the end effector of the robotic device. The JVCI process receives JVCI inputs including IMU data. In response, the device may generate JVCI outputs indicative of the vibrations.

[0165] At step 1106, based on the JVCI outputs, the device may update the position of the end effector to compensate for the vibrations. Method 1100 may terminate or continue with the insertion of A, which will be described in further detail in Figure 12 connection.

[0166] Now turning to Figure 12 , Figure 12 illustrates an exemplary method 1200. According to some embodiments of the present disclosure, the exemplary method 1200 may provide additional aspects or elements related to utilizing JVCI technology to compensate for vibrations exhibited in a BLMR system.

[0167] At step 1202, a device including at least one processor may reconstruct vibrations based on IMU data and an extended Kalman filter (EKF).

[0168] At step 1204, the device may associate the coordinate system of the robotic device with the ground coordinate system of the BLMR system based on three-dimensional Euler angle rotations.

[0169] At step 1206, the device may perform a static deformation compensation (SDC) process, which is configured to compensate for static deformations associated with the BLMR system. In some embodiments, the SDC process may generate outputs that can be combined with the JVCI outputs, and the combined outputs may be used to compensate for vibrations.

[0170] Exemplary Operating Environment

[0171] To provide additional context for the various embodiments described in this disclosure, Figure 13 and the following discussion is intended to briefly and generally describe a suitable computing environment 1300 in which various embodiments of the embodiments described in this disclosure can be implemented. Although the above embodiments have been described in the general context of computer-executable instructions that can run on one or more computers, those skilled in the art will recognize that the embodiments can also be implemented in combination with other program modules and / or as a combination of hardware and software.

[0172] Generally, program modules include routines, programs, components, data structures, etc. that perform specific tasks or implement specific abstract data types. In addition, those skilled in the art will understand that various methods can be practiced with other computer system configurations, including single-processor or multi-processor computer systems, microcomputers, mainframe computers, Internet of Things (IoT) devices, distributed computing systems, and personal computers, handheld computing devices, microprocessor-based or programmable consumer electronics, etc., each of which can be operatively coupled to one or more associated devices.

[0173] Embodiments of the embodiments shown in this disclosure can also be implemented in a distributed computing environment where certain tasks are performed by remote processing devices linked through a communication network. In a distributed computing environment, program modules can be located in local and remote memory storage devices.

[0174] Computing devices typically include various media, which can include computer-readable storage media, machine-readable storage media, and / or communication media, where the use of these two terms in this disclosure is different, as follows. Computer-readable storage media or machine-readable storage media can be any available storage media accessible by a computer, including volatile media and non-volatile media, removable media and non-removable media. By way of example and not limitation, computer-readable storage media or machine-readable storage media can be implemented in combination with any method or technology for storing information, such as computer-readable or machine-readable instructions, program modules, structured data, or unstructured data.

[0175] A computer-readable storage medium may include, but is not limited to, random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other storage technologies, compact disc read-only memory (CD-ROM), digital versatile disc (DVD), Blu-ray disc (BD) or other optical disc storage, magnetic cassettes, magnetic tape storage or other magnetic storage devices, solid state drives or other solid state storage devices, or other tangible and / or non-transitory media that can be used to store the desired information. In this regard, the terms "tangible" or "non-transitory" as applied to storage, memory or computer-readable media in the present disclosure should be understood to exclude only propagating transitory signals per se as modifiers, and do not relinquish the right to all standard storage, memory or computer-readable media that are not only propagating transitory signals per se.

[0176] A computer-readable storage medium can be accessed by one or more local or remote computing devices, e.g., via an access request, query, or other data retrieval protocol, for various operations on information stored on the medium.

[0177] A communication medium typically embodies computer-readable instructions, data structures, program modules or other structured or unstructured data in the form of data signals, such as a modulated data signal (e.g., a carrier wave or other transmission mechanism), and includes any information delivery or transport medium. The term "modulated data signal" refers to a signal that has one or more of its characteristics set or changed in such a manner as to encode information in one or more signals. By way of example, and not limitation, communication media include wired media such as a wired network or direct-wired connection, and wireless media such as acoustic, RF, infrared and other wireless media.

[0178] Referring again to Figure 13 , an example environment 1300 for implementing various embodiments of the aspects described in the present disclosure includes a computer 1302 that includes a processing unit 1304, a system memory 1306, and a system bus 1308. The system bus 1308 couples system components including, but not limited to, the system memory 1306 to the processing unit 1304. The processing unit 1304 can be any of a variety of commercially available processors. Dual microprocessors and other multiprocessor architectures can also be used as the processing unit 1304.

[0179] The system bus 1308 can be any of several types of bus structures, which can be further interconnected to a memory bus (with or without a memory controller), a peripheral bus, and a local bus using any of various commercially available bus architectures. The system memory 1306 includes a ROM 1310 and a RAM 1312. The basic input / output system (BIOS) can be stored in non-volatile memory, such as ROM, erasable programmable read-only memory (EPROM), EEPROM, where the BIOS contains basic routines that help transfer information between components within the computer 1302, such as during startup. The RAM 1312 can also include high-speed RAM, such as static RAM for caching data.

[0180] The computer 1302 also includes an internal hard disk drive (HDD) 1314 (e.g., EIDE, SATA), one or more external storage devices 1316 (e.g., a floppy disk drive (FDD) 1316, a memory stick or flash drive reader, a memory card reader, etc.), and an optical disc drive 1320 (e.g., which can read from or write to a CD-ROM disc 1322, a DVD, a BD, etc.). Although the internal HDD 1314 is illustrated as being within the computer 1302, the internal HDD 1314 can also be configured for external use in a suitable chassis (not shown). Additionally, although not shown in the environment 1300, solid state drives (SSDs) can be used in addition to or in place of the HDD 1314. The HDD 1314, the external storage devices 1316, and the optical disc drive 1320 can be connected to the system bus 1308 via an HDD interface 1324, an external memory interface 1326, and an optical disc drive interface 1328, respectively. The interface 1324 for external drive implementation can include at least one or both of the universal serial bus (USB) and the Institute of Electrical and Electronics Engineers (IEEE) 1394 interface technology. Other external drive connection technologies are also within the scope of the embodiments described in this disclosure.

[0181] The drives and their associated computer-readable storage media provide non-volatile storage of data, data structures, computer-executable instructions, etc. For the computer 1302, the drives and storage media are adapted to store any data in an appropriate digital format. Although the above description of computer-readable storage media refers to various types of storage devices, those skilled in the art should understand that other types of storage media that are computer-readable, whether currently existing or developed in the future, can also be used in the exemplary operating environment, and any such storage media can contain computer-executable instructions for performing the methods described herein.

[0182] Many program modules can be stored in the drive and RAM 1312, including an operating system 1330, one or more application programs 1332, other program modules 1334, and program data 1336. All or part of the operating system, application programs, modules, and / or data can also be cached in the RAM 1312. The systems and methods described in this disclosure can be implemented using various commercial operating systems or combinations of operating systems.

[0183] Computer 1302 can optionally include emulation technology. For example, a hypervisor (not shown) or other intermediate program can simulate the hardware environment of the operating system 1330, and the simulated hardware can optionally be different from the hardware shown in Figure 13 In such an embodiment, the operating system 1330 can include one VM of multiple virtual machines (VMs) hosted on the computer 1302. Additionally, the operating system 1330 can provide a runtime environment for the application programs 1332, such as a Java runtime environment or a.NET framework. The runtime environment is a consistent execution environment that allows the application programs 1332 to run on any operating system that includes the runtime environment. Similarly, the operating system 1330 can support containers, and the application programs 1332 can be in the form of containers, which are lightweight, independent executable software packages that include, for example, code, runtime, system tools, system libraries, and application settings.

[0184] Furthermore, the computer 1302 can enable a security module, such as a Trusted Platform Module (TPM). For example, for the TPM, the boot component hashes the next boot component in a timely manner and waits for the result to match a security value before loading the next boot component. This process can occur at any layer in the code execution stack of the computer 1302, for example, applied to the application execution level or the operating system (OS) kernel level, thus achieving security at any code execution level.

[0185] A user can input commands and information into the computer 1302 through one or more wired / wireless input devices, such as pointing devices like the keyboard 1338, touch screen 1340, and mouse 1342. Other input devices (not shown) can include microphones, infrared (IR) remote controls, radio frequency (RF) remote controls or other remote controls, joysticks, virtual reality controllers and / or virtual reality headsets, game pads, styluses, image input devices such as cameras, gesture sensor input devices, visual motion sensor input devices, emotion or face detection devices, biometric input devices such as fingerprint or iris scanners, etc. These and other input devices are typically connected to the processing unit 1304 through an input device interface 1344, which can be coupled to the system bus 1308, but can be connected through other interfaces, such as parallel ports, IEEE 1394 serial ports, game ports, USB ports, IR interfaces, BLUETOOTH interfaces, etc.

[0186] The monitor 1346 or other types of display devices can also be connected to the system bus 1308 through an interface, such as a video adapter 1348. In addition to the monitor 1346, the computer typically includes other peripheral output devices (not shown), such as speakers, printers, etc.

[0187] The computer 1302 can operate in a network environment, using a logical connection through wired and / or wireless communication to one or more remote computers, such as the remote computer 1350. The remote computer 1350 can be a workstation, server computer, router, personal computer, portable computer, microprocessor-based entertainment device, peer device, or other common network nodes, and typically includes many or all of the elements described with respect to the computer 1302, although for the sake of brevity, only the memory / storage device 1352 is shown. The described logical connections include wired / wireless connections to a local area network (LAN) 1354 and / or a larger network, such as a wide area network (WAN) 1356. Such LAN and WAN network environments are common in offices and companies and facilitate enterprise-wide computer networks, such as intranets, all of which can be connected to a global communication network, such as the Internet.

[0188] When used in a LAN network environment, the computer 1302 can be connected to the LAN 1354 through a wired and / or wireless communication network interface or adapter 1358. The adapter 1358 can facilitate wired or wireless communication with the LAN 1354, and the LAN 1354 can also include a wireless access point (AP) arranged thereon for communicating with the adapter 1358 in a wireless mode.

[0189] When used in a WAN network environment, computer 1302 may include a modem 1360, or may be connected to WAN 1356 through other devices for establishing communication on WAN 1356, such as through the Internet. Modem 1360 may be internal or external, and a wired or wireless device, and may be connected to system bus 1308 through input device interface 1344. In a network environment, program modules described with respect to computer 1302 or portions thereof may be stored in remote memory / storage device 1352. It should be understood that the network connections shown are examples, and other methods for establishing communication links between computers may be used.

[0190] When used in a LAN or WAN network environment, computer 1302 may access a cloud storage system or other network-based storage systems instead of the external storage device 1316 as described above. Generally, the connection between computer 1302 and the cloud storage system may be established through LAN 1354 or WAN 1356, for example, through adapter 1358 or modem 1360, respectively. When connecting computer 1302 to an associated cloud storage system, external storage interface 1326 may, with the help of adapter 1358 and / or modem 1360, manage the storage provided by the cloud storage system in the same way as other types of external storage. For example, external storage interface 1326 may be configured to provide access to cloud storage sources as if these sources were physically connected to computer 1302.

[0191] Computer 1302 may operate to communicate with any wireless device or entity operatively configured for wireless communication, such as printers, scanners, desktop and / or portable computers, portable data assistants, communication satellites, any device or location associated with a wirelessly detectable tag (such as kiosks, newsstands, store shelves, etc.) and telephones. This may include Wi-Fi (Wireless Fidelity) and Bluetooth wireless technologies. Thus, the communication may be a predefined structure like a traditional network, or just an ad hoc communication between at least two devices.

[0192] Wi-Fi, or Wireless Fidelity, allows you to connect to the Internet from your couch at home, your bed in a hotel room, or a conference room at work without wires. Wi-Fi is a wireless technology similar to that used in cell phones, enabling devices such as computers to send and receive data indoors and outdoors, anywhere within the range of a base station. Wi-Fi networks use radio technologies named IEEE 1102.11 (a, b, g, n, etc.) to provide secure, reliable, and fast wireless connections. Wi-Fi networks can be used to connect computers to each other, to the Internet, and to wired networks (using IEEE802.3 or Ethernet). Wi-Fi networks operate at a data rate of 54Mbps (802.11a) and / or in the 2.4GHz radio band at 11Mbps (802.11b), 54Mbps (802.11g) data rate, or up to 600Mbps (802.11n) data rate in the unlicensed 5GHz radio band, or with products that include both bands (dual-band), so the network can provide real-world performance similar to that of the basic "10BaseT" wired Ethernet used in many offices.

[0193] As used in this disclosure, the term "processor" can substantially refer to any computing processing unit or device, including but not limited to a single processor with software multithreading execution capabilities; a multi-core processor with software multithreading execution capabilities; a multi-core processor employing hardware multithreading technology; a parallel platform; and a parallel platform with distributed shared memory in a single machine or multiple machines. Additionally, a processor can refer to an integrated circuit, a state machine, an application-specific integrated circuit (ASIC), a digital signal processor (DSP), including a field-programmable gate array (FPGA), a programmable logic controller (PLC), a complex programmable logic device (CPLD), discrete gate or transistor logic, discrete hardware components, or any combination thereof designed to perform the functions described herein. A processor can utilize nanoscale architectures, such as but not limited to molecular and quantum dot-based transistors, switches, and gates, to optimize space usage or enhance the performance of user devices. A processor can also be implemented as a combination of computing processing units. One or more processors can be used to support a virtualized computing environment. A virtualized computing environment can support one or more virtual machines representing a computer, a server, or other computing devices. In such a virtualized virtual machine, components such as processors and storage devices can be virtualized or logically represented. In one aspect, when a processor executes instructions to perform an "operation", this can include the processor directly performing the operation and / or facilitating, guiding, or cooperating with another device or component to perform the operation.

[0194] In this disclosure specification, terms such as "data storage", "data memory", "database", "cache", and any other information storage components substantially related to the operation and function of components refer to "memory components" or entities embodied in "memory" or components containing memory. It should be understood that the memory components or computer-readable storage media described herein can be volatile memory or non-volatile storage, or can include both volatile and non-volatile memory. By way of illustration and not limitation, non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM, electrically erasable ROM (EEPROM), or flash memory. Volatile memory can include random access memory (RAM), which serves as an external cache memory. By way of illustration and not limitation, RAM has many forms, such as synchronous RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDR SDRAM), enhanced SDRAM (ESDRAM), synchronous DRAM, and direct Rambus RAM (DRRAM). In addition, the memory components of the systems or methods of this disclosure are intended to include, but not be limited to, including these and any other suitable types of memory.

[0195] The illustrated aspects of this disclosure can be implemented in a distributed computing environment where certain tasks are performed by remote processing devices linked through a communication network. In a distributed computing environment, program modules can be located in local and remote memory storage devices.

[0196] The above systems and processes can be embodied in hardware, such as a single integrated circuit (IC) chip, multiple ICs, application-specific integrated circuit (ASIC), etc. In addition, the order in which some or all of the process blocks appear in each process should not be considered restrictive. Instead, it should be understood that some process blocks can be executed in various orders, which are not all the orders that can be explicitly stated in this disclosure.

[0197] As used in this disclosure, the terms "component", "module", "system", "interface", "cluster", "server", "node", etc. generally intend to refer to computer-related entities, combinations of hardware, hardware and software, software, or entities related to an operating machine with one or more specific functions. For example, a component can be, but is not limited to, a processor, a processor, an object, an executable file, an execution thread, computer-executable instructions, a program, and / or a process running on a computer. By way of illustration, an application running on a controller and the controller can both be components. One or more components can reside in a process and / or an execution thread, and a component can be located on one computer and / or distributed between two or more computers. As another example, an interface can include input / output (I / O) components and associated processor, application, and / or API components.

[0198] In addition, various embodiments can be implemented as a method, apparatus, or article of manufacture using standard programming and / or engineering techniques to produce software, firmware, hardware, or any combination thereof to control a computer to implement one or more aspects of the subject matter of this disclosure. An article of manufacture can include a computer program accessible from any computer-readable device or computer-readable storage / communication medium. For example, a computer-readable storage medium can include, but is not limited to, magnetic storage devices (e.g., hard disks, floppy disks, magnetic strips...), optical disks (e.g., compact discs (CDs), digital versatile discs (DVDs)...), smart cards, and flash memory devices (e.g., cards, sticks, key drives...). Of course, those skilled in the art will recognize that many modifications can be made to this configuration without departing from the scope or spirit of the various embodiments.

[0199] In addition, the words "example" or "exemplary" as used in this disclosure are intended to be used as examples, instances, or illustrations. Any aspect or design described as "exemplary" in this disclosure is not necessarily to be construed as preferred or advantageous over other aspects or designs. Instead, the use of the word "exemplary" is intended to represent a concept in a concrete way. As used in this disclosure, the term "or" is intended to mean inclusive or "and not exclusive". That is, unless otherwise specified or the context clearly indicates, "X employs A or B" is intended to mean any natural inclusive permutation. That is, if X employs A; X employs B; or X employs both A and B simultaneously, then in any of the above cases, "X employs A or B" is satisfied.

[0200] The foregoing includes examples of the present disclosure. Of course, for purposes of describing this specification, it is not possible to describe every conceivable combination of components or methods, but one of ordinary skill in the art will recognize that many further combinations and permutations of this specification are possible. Accordingly, this specification is intended to embrace all such alterations, modifications, and variations that fall within the spirit and scope of the appended claims. In addition, to the extent that the term "comprising" is used in the detailed description or claims, such term is intended to be inclusive in a manner similar to the term "including" and when used as a transitional word in a claim, is to be interpreted as "including".

Claims

1. A vibration compensation device, comprising: at least one processor; as well as at least one memory storing executable instructions that, when executed by the at least one processor, facilitate performance of operations including: Receiving inertial measurement unit (IMU) data from an IMU device of a BLMR system of a robot mounted on an aerial work platform, wherein the IMU device is located near an end of an aerial work platform arm supporting a robotic device including an end effector; executing a Jacobian-based vibration compensation JVCI process via an IMU, the JVCI process configured to compensate for vibrations exhibited at the end effector of the robotic device, wherein the JVCI process receives a JVCI input comprising the IMU data and generates a JVCI output indicative of vibrations caused by the vibrations; as well as Based on the JVCI output, the motion of the robotic device is updated to compensate for the vibration exhibited at the end effector.

2. The vibration compensation device according to claim 1, wherein: The IMU data includes acceleration measurements of the vibrations and angular velocity measurements of the vibrations.

3. The vibration compensation device according to claim 1, wherein: The JVCI input also includes BLMR joint data representing an optimal dynamic allocation with stability proof of the BLMR system based on a linear parameter variation system.

4. The vibration compensation device according to claim 3, wherein: The linear parameter variation system is a function of a Laplace variable and a distance variable, wherein the Laplace variable is suitable for Laplace transformation and the distance variable represents the telescopic state of the aerial work platform arm in at least one dimension.

5. The vibration compensation device according to claim 1, wherein: The JVCI process also includes reconstructing the vibration based on the IMU data and an extended Kalman filter.

6. The vibration compensation device according to claim 1, wherein: The JVCI process also includes relating the coordinate system of the robotic device to the ground coordinate system of the BLMR system based on three-dimensional Euler angle rotations.

7. The vibration compensation device according to claim 1, wherein: The operations include executing a static deformation compensation (SDC) process configured to compensate for static deformation associated with the BLMR system.

8. The vibration compensation device according to claim 7, wherein: The SDC process includes determining a deformation profile based on measurements from a laser tracker device.

9. The vibration compensation device according to claim 1, wherein: The operations also include executing a time varying input shaper (TVIS) process configured to compensate for vibrations of the aerial work platform based on a natural frequency of the BLMR system and a damping ratio of the BLPR system.

10. The vibration compensation device according to claim 9, wherein: The TVIS process includes determining the natural frequency and the damping ratio.

11. The vibration compensation device according to claim 9, wherein: The operations also include combining an output of the TVIS process with the JVCI output to determine a combined vibration compensation output, and using the combined vibration compensation output to update joint motion of the BLMR system.

12. A vibration compensation method, comprising: Receiving inertial measurement unit (IMU) data from an IMU device of a BLMR system of a robot mounted on an aerial work platform, wherein the IMU device is located near an end of an aerial work platform arm supporting a robotic device including an end effector; executing a Jacobian-based vibration compensation JVCI process via an IMU, the JVCI process configured to compensate for vibrations exhibited at the end effector of the robotic device, wherein the JVCI process receives a JVCI input comprising the IMU data and generates a JVCI output indicative of vibrations caused by the vibrations; as well as Based on the JVCI output, the motion of the robotic device is updated to compensate for the vibration exhibited at the end effector.

13. The vibration compensation method according to claim 12, wherein: The IMU data includes acceleration measurements of the vibrations and angular velocity measurements of the vibrations.

14. The vibration compensation method according to claim 12, wherein: The JVCI input also includes BLMR joint data representing an optimal dynamic allocation with stability proof of the BLMR system based on a linear parameter variation system.

15. The vibration compensation method according to claim 14, wherein: The linear parameter variation system is a function of a Laplace variable and a distance variable, wherein the Laplace variable is suitable for Laplace transformation and the distance variable represents the telescopic state of the aerial work platform arm in at least one dimension.

16. The vibration compensation method according to claim 12, wherein: Executing the JVCI process further includes reconstructing the vibration based on the IMU data and an extended Kalman filter.

17. The vibration compensation method according to claim 12, wherein: Executing the JVCI process further includes associating a coordinate system of the robotic device with a ground coordinate system of the BLMR system based on a three-dimensional Euler angle rotation.

18. The vibration compensation method according to claim 12, wherein: Performing the operations includes executing a static deformation compensation (SDC) process configured to compensate for static deformation associated with the BLMR system.

19. The vibration compensation method according to claim 18, wherein: Performing the SDC process includes determining a deformation profile based on measurements of a laser tracker device.

20. The vibration compensation method according to claim 12, wherein: Performing the operations further includes executing a time varying input shaper (TVIS) process configured to compensate for vibrations of the aerial work platform based on a natural frequency of the BLMR system and a damping ratio of the BLPR system.

21. The vibration compensation method according to claim 20, wherein: Executing the TVIS process includes determining the natural frequency and the damping ratio.

22. The vibration compensation method according to claim 20, wherein: Performing the operations further includes combining an output of the TVIS process with the JVCI output to determine a combined vibration compensation output, and using the combined vibration compensation output to update joint motion of the BLMR system.

23. A BLMR system for an aerial work platform equipped robot, the BLMR system comprising: Aerial work platforms; A robot device mounted on the aerial work platform; as well as A vibration compensation device, configured to implement the vibration compensation method according to any one of claims 12-22.

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