A cooperative control method for a multi-redundant robotic arm system under complex actuator failure.

Abstract

The present invention provides a method for collaborative control of a multi-redundant manipulator system under a complex actuator failure, including: design of a manipulator motion constraint algorithm, wherein the manipulator motion constraint algorithm adopts an asymptotically optimal RRT* algorithm and is composed of collision detection, trajectory planning, and forward and inverse dynamics; design of a dynamic model of a multi-redundant manipulator system under a complex actuator failure; design of a distributed event-triggered state observer, wherein the distributed event-triggered state observer includes a communication topology, an event triggering mechanism, and a distributed observer; design of an adaptive compensation controller, wherein the adaptive compensation controller is implemented by a backstepping method, a feedback controller is obtained by constructing a Lyapunov function of a closed-loop system, and a Nussbaum function and a virtual control law are introduced. The present invention can effectively eliminate the influence of complex failures on the actuator and ensure the normal and stable operation of the equipment.

Description

Technical Field

[0001] The present invention relates to the field of multi-redundant mechanical arm motion control, and in particular to a multi-redundant mechanical arm system collaborative control method under complex actuator failure. Background Art

[0002] The robotic arm is a typical multi-input and multi-output strongly coupled complex system, and its industrial application has a history of more than 60 years. Today, with the continuous development of intelligent technology, artificial intelligence technologies such as image recognition and deep learning have been widely used in the field of robotic arms, making the application scenarios of robotic arms gradually penetrate from traditional industrial fields to service industries: the Da Vinci surgical robot jointly developed by IBM, MIT and Heartport can replace doctors in the medical field to perform surgical treatment on patients; the seven-degree-of-freedom redundant robotic arm Panda developed by Franka Emika is equipped with high-precision force sensors, providing researchers with a reliable development platform.

[0003] Compared with a single robot, a multi-redundant robot system has greater flexibility, stronger reliability and higher operating efficiency, and can complete more complex tasks. However, due to the complexity of the structure, the kinematic and dynamic analysis of the multi-redundant robot system becomes more cumbersome and complex. At the kinematic level, the calibration of the base coordinate system of the multi-redundant robot system requires the relative position of each robot, and the motion trajectory planning of the multi-redundant robot system is more complex than that of a single robot. In other words, when performing complex collaborative tasks, the multi-redundant robot system must consider the relative motion constraints between the collaborative robots in addition to the posture constraints of each robot, which makes the kinematic analysis more difficult. At the dynamic level, since the multi-redundant robot system is a mechanical system with highly redundant degrees of freedom, this feature makes the coupling relationship of the robot more complex, and the dynamic parameters of different configurations of the robot in the system will also be different, which makes the traditional single robot control algorithm cannot be directly applied to the multi-redundant robot system. Therefore, it is necessary to deeply analyze the kinematic and dynamic properties of the multi-redundant robot system and establish a mathematical model that can describe the dynamic characteristics of the entire collaborative system in order to achieve efficient collaborative control goals.

[0004] In actual working conditions, the actuators of the multi-redundant manipulator system are always in operation, which makes them the most prone to failure in the system. Common actuator failures include stuck, partial failure, oscillation, and noise interference. Unlike network attacks at the network layer, actuator failures are very common at the physical layer, usually due to equipment aging and abnormal operation. The actuator of the manipulator is the drive motor. When the actuator fails, the actual torque applied to the actuator is unknown. In addition to the rated torque provided by the manipulator motor, the actual torque is also affected by the fault. Actuator failure will change the operation trajectory of the manipulator, thus failing to achieve the expected control target. At present, most studies generally consider the following two types of actuator failures: one is the partial failure of the actuator, and the other is the stuck failure of the actuator. The common method to solve the above faults is to design an adaptive compensation law to eliminate the impact of the fault on the actuator to ensure the normal operation of the equipment. This method does not require a fault diagnosis and isolation unit, can avoid the influence of fault diagnosis errors, and ensure the real-time performance of the system. However, as described earlier, the actuator failure in the study did not take into account the situation that the control direction is unknown. The oscillation and reversal of the drive motor will cause a sudden change in the control direction. In addition, the multi-redundant robotic arm system is a typical multiple-input multiple-output (MIMO) system, which requires the design of a more appropriate adaptive compensation control law to ensure the stability of the system. It can be seen that in the case of more complex actuator failures, it is particularly important to develop an adaptive compensation control algorithm suitable for the MIMO system.

[0005] On the other hand, in early studies, multi-robot systems usually assume real-time continuous communication. However, in actual situations, each intelligent agent is equipped with an embedded microprocessor with limited energy. Therefore, it is of great significance to realize functions such as information collection, communication with neighboring areas, and generation of control signals to drive the system under limited energy and communication resources. For multi-redundant robot systems, traditional control is executed in a periodic manner, namely the so-called time-triggered control, which is based on the theory of sampled data systems, is predictable and easy to implement. However, from the perspective of resource utilization, time-triggered control periodically executes control tasks, which wastes resources such as computing and device energy. In addition, if the sampling period is relatively small, a large number of redundant sampling signals will be released to the shared communication network with limited bandwidth, which will inevitably cause network congestion. Therefore, event-triggered control has attracted the attention of more and more scholars. The so-called event-triggered control means that whether the control task is executed is determined by the event trigger condition given in advance, rather than according to the time situation. If the trigger condition is met at a certain moment, it means that the event is triggered and the control task is executed immediately. Compared with the time-triggered control mechanism, the event-triggered control scheme can reduce the use of computing resources, battery device energy and communication resources. In fact, some experiments have proved that event-triggered control methods can effectively reduce the number of control tasks executed, thereby significantly saving communication resources while ensuring the performance of the closed-loop system. Summary of the invention

[0006] In view of this, the present invention provides a method for collaborative control of a multi-redundant robotic arm system under complex actuator failure, comprising the following steps:

[0007] S1. Design of robot motion constraint algorithm. The robot motion constraint algorithm adopts the asymptotically optimal RRT* algorithm, which consists of collision detection, trajectory planning and forward and inverse dynamics.

[0008] S2. Design of dynamic model of multi-redundant manipulator system under complex actuator failure;

[0009] S3. Design of a distributed event-triggered state observer, wherein the distributed event-triggered state observer includes a communication topology, an event triggering mechanism, and a distributed observer;

[0010] S4. Adaptive compensation controller design. The adaptive compensation controller is implemented by backstepping method. The feedback controller is obtained by constructing the Lyapunov function of the closed-loop system, and the Nussbaum function and virtual control law are introduced.

[0011] The beneficial effects brought by the technical solution provided by the present invention are:

[0012] At the kinematic level, the present invention considers the position constraints of the robot itself and the relative motion constraints between multiple robot arms, and uses the RRT* algorithm to allow the robot to find obstacle avoidance paths online; at the dynamic level, the present invention designs an adaptive compensation control algorithm based on the Nussbaum function to solve the impact of complex actuator failures on the multi-redundant robot arm system, ensure the stability of the entire closed-loop system, and introduce an event trigger mechanism to save communication resources. The present invention can effectively eliminate the impact of complex failures on actuators, improve the robustness of the multi-redundant robot arm system, and ensure the normal and stable operation of the equipment. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] The present invention will be further described below with reference to the accompanying drawings and embodiments, in which:

[0014] Figure 1 It is a framework diagram of an implementation scheme of a method for cooperative control of a multi-redundant manipulator system under complex actuator failure of the present invention;

[0015] Figure 2 It is a communication topology structure of a multi-redundant mechanical arm system proposed by a method for cooperatively controlling a multi-redundant mechanical arm system under a complex actuator failure of the present invention;

[0016] Figure 3 It is a schematic diagram of the process of reselecting the parent node by the asymptotically optimal RRT* algorithm proposed in the collaborative control method of a multi-redundant manipulator system under a complex actuator failure of the present invention;

[0017] Figure 4 It is a schematic diagram of the process of rewiring random trees using the asymptotically optimal RRT* algorithm proposed in the collaborative control method of a multi-redundant manipulator system under complex actuator failure of the present invention;

[0018] Figure 5 It is a distributed observer position estimation curve proposed by a method for cooperative control of a multi-redundant manipulator system under complex actuator failure of the present invention;

[0019] Figure 6 It is a distributed observer speed estimation curve proposed by a method for cooperative control of a multi-redundant manipulator system under complex actuator failure of the present invention;

[0020] Figure 7 It is a position curve of a multi-redundant manipulator system event-triggered collaborative control system under a complex actuator failure of the present invention;

[0021] Figure 8 It is a speed curve of a multi-redundant manipulator system event-triggered collaborative control system under a complex actuator failure of the present invention;

[0022] Fig. 9It is a position error curve of a multi-redundant manipulator system event-triggered collaborative control system under a complex actuator failure of the present invention;

[0023] Fig.10 It is a speed error curve of a multi-redundant manipulator system event-triggered collaborative control system under a complex actuator failure of the present invention;

[0024] Fig.11 It is a demonstration diagram of the RRT* algorithm proposed in the collaborative control method of a multi-redundant robotic arm system under complex actuator failure in the present invention in three-dimensional space. DETAILED DESCRIPTION

[0025] To make the objectives, technical solutions and advantages of the present invention more clear, the embodiments of the present invention will be further described below with reference to the accompanying drawings.

[0026] A method for collaborative control of a multi-redundant robotic arm system under complex actuator failures comprises the following steps:

[0027] S1. Design of robot arm motion constraint algorithm. The robot arm motion constraint algorithm adopts the asymptotically optimal RRT* algorithm, which consists of collision detection, trajectory planning and forward and inverse dynamics, specifically:

[0028] Specifically:

[0029] S11, the initial point of the robot is used as the root node x init , from which branches begin to form;

[0030] S12. Generate a random point x in the robot's "configuration" space rand ;

[0031] S13, traverse the points in the tree and find the distance from x rand The nearest point x near ;

[0032] S14, from x near To x near The direction grows at a certain step length. If there is no obstacle, the grown branches and endpoints are added to the tree, recorded as x new ,

[0033] The collision conditions are:

[0034] x0-r0-l<x new,x <x0+r0+l

[0035] y0-r0-l<x new,y <y0+r0+l

[0036] z0-r0-l<x new,z <z0+r0+l

[0037] Among them, (x0, y0, z0) are the coordinates of the center of the spherical obstacle, r0 is the sphere diameter, and l is the expanded size of the obstacle after expansion processing;

[0038] S15, at the newly generated node x new A "region" with a radius of r is defined nearby, and the nodes in the region are used as x new Parent node alternatives

[0039] S16, calculate all x in this way init arrive The cost and to x new The cost and the minimum cost are selected As x new Parent Node

[0040] S17, the remaining candidate nodes The parent node is changed to x new , calculate x init to x new The cost and x new arrive The cost and;

[0041] S18. If the sum of the costs is less than the sum of the costs of the parent node that has not been changed before, then The parent of the node is changed to x new ;

[0042] S19, repeat S12-S18 process until reaching the target node x goal .

[0043] Steps S12-S16 are the process of reselecting the parent node. The specific schematic diagram of the process is as follows: Figure 3 As shown; Steps S17-S18 are the process of rewiring the random tree, and the specific schematic diagram of the process is as follows Figure 4 shown.

[0044] S2. Design of dynamic model of multi-redundant robotic arm system under complex actuator failure, specifically:

[0045] S21. Define the fault model of the mth actuator of robot arm i as:

[0046]

[0047] Among them, μ i,m represents the non-zero bounded proportionality factor caused by actuator failure, τ i,m (t) represents the control input of the m-th actuator of robot arm i, represents the bounded fault signal in the actuator. The actuator faults covered by the above fault model are: i,m =1 and When 0<μ i,m <1 and When the mth actuator of the robot arm i in the system fails partially; when μ i,m <0 and When , the control direction of the mth actuator of the robot arm i in the system suddenly changes;

[0048] S22. The Lagrange equation is used to model the dynamics of the multi-redundant robotic arm system under fault conditions. The specific model is as follows:

[0049]

[0050] Among them, q i , They represent the joint position, joint velocity and joint acceleration of robot i respectively. The multi-redundant robot system in this design is composed of i 7-DOF redundant robot arms, that is, m=1,…,7 in the actuator fault model, M i (q i )∈R 7×7 is a symmetric positive definite inertia matrix, is the Coriolis force and centripetal force matrix, G i (q i )∈R 7 is the gravity matrix, is the output torque of each joint actuator of robot arm i after failure, J i (q i )∈R 7×7 F is the Jacobian matrix that reflects the transformation relationship between the robot joint velocity and the end effector velocity. ei ∈R 7 is the output force at the end of the robot;

[0051] make The dynamic model of the above multi-redundant robotic arm system is expressed as:

[0052]

[0053]

[0054] in The transformed model will be used in the design of adaptive compensation control algorithm.

[0055] S3. Design of a distributed event-triggered state observer, which includes a communication topology, an event triggering mechanism, and a distributed observer. Specifically:

[0056] S31. Design a communication topology structure of a multi-redundant robotic arm system. The communication topology structure is represented by a weighted directed graph, denoted as G≡(V,E,A), where V={v1,v2,...,v N} represents a set of nodes, node v i represents the i-th robotic arm; represents the edge set. When node i sends information to node j, the edge (v j ,v i )∈E;A=[a ij ] N×N represents an adjacency matrix, where a ij Represents the edge (v i ,v j ), that is, node i receives information from node j, when a ij = 0, then the edge (v i ,v j ) does not exist, the reference signal is generated by a virtual linear system, marked as node v0, and its dynamic model is as follows:

[0057]

[0058] in is the state of the leader node, indicating the reference signal of the robot joint space, q0 is the reference joint position, is the reference joint velocity. A∈R 14×14 is a known constant matrix in the form of a block matrix, i.e. A=block{07,I7;A0,A1}, 07 represents a 7×7 all-zero matrix, I7 represents a 7×7 identity matrix, A0 and A1 represent a 7×7 constant matrix, and the leader node can be observed by some nodes in the directed graph G. If node i can observe the leader, there is an edge (vi,v0) with weighted gain gi>0 connecting them. We call node i a controlled node and define the controlled matrix as G=diag{g i}∈R N×N In this embodiment, N=5, that is, there are 5 7-DOF redundant robotic arms in the multi-redundant robotic arm system, and its topological structure is shown in the figure below: Figure 2 As shown, there is at least one spanning tree with node v0 as the root node in this directed graph.

[0059] S32. Assume that robot arms 1 to 5 need to track a reference signal. Due to the limitation of the communication topology, not every robot arm can directly obtain the relevant information of the reference signal. Therefore, it is necessary to design a distributed state observer so that each robot arm can use the neighboring robot arms directly connected to it to estimate the relevant information of the reference signal. The design of the distributed event-triggered state observer is as follows:

[0060]

[0061] where i = 1,...,5, β i >0, represents the estimation of the reference signal of the joint space by robot i, is the estimated value of the joint position, is the estimated joint velocity, represents the triggering moment of robot arm i, and

[0062] S33, introduce event trigger conditions, and define the following new variables:

[0063]

[0064]

[0065] in is the neighbor error of robot i, representing the comprehensive error of information that robot i can receive, is the neighbor error of robot i after the event is triggered. The triggering moment is generated by the event triggering mechanism. Based on the new variables defined above, an event triggering condition is designed to determine when the observer estimated state should be transmitted, and the state after the triggering is used as the state variable of the controller. The specific event triggering mechanism is as follows:

[0066]

[0067]

[0068] in θ i and δ i are given normal numbers, reflecting The magnitude and rate at which it approaches zero.

[0069] S4, adaptive compensation controller design, the adaptive compensation controller is implemented by backstepping method, the feedback controller is obtained by constructing the Lyapunov function of the closed-loop system, and the Nussbaum function and virtual control law are introduced. Specifically:

[0070] S41. The error vector of the controller is defined as follows:

[0071]

[0072]

[0073] where α i =-c1z i1 It is a virtual control law, and c1>0;

[0074] S42. Design the Nussbaum function as follows:

[0075]

[0076] S43. Design Lyapunov function:

[0077]

[0078] For signal Estimation Error d i,m for The supremum of is d i,m An estimated value of

[0079] S44. Design of adaptive compensation control algorithm:

[0080]

[0081]

[0082]

[0083]

[0084] in And ψ , c1 and c2 are both positive constants.

[0085] In this embodiment, in order to verify that the designed adaptive compensation controller enables the multi-redundant robot system to have all states of each robot follow the given reference signal changes in the case of complex actuator failure, the following dynamic model parameters are selected: M i (x i1 ) is the 7-dimensional identity matrix, Q i (x i1 ,x i2 )=-ones(7,1) is a 7-dimensional column vector whose elements are all -1, μ i,m =-1.5, The state matrix of the reference signal is selected as: A = block {07, I7; A0, A1}, where A0 = -I7, A1 = 07, and the initial value is represents a 7-dimensional column vector whose elements are all 1. In the distributed event-triggered observer, β i =150,θ i =0.3 and δ i =0.5. The relevant parameters of the adaptive compensation controller are: ψ =0.5, c1=5,c2=15,the initial values ​​of other parameters are all 0. The simulation results are as follows Figures 5 to 11 As shown, the total time is 15s, the step size is 0.001s, and the total number of steps is 15000.

[0086] Although the position and velocity of the reference signal are both 7-dimensional vectors, the only difference is the communication topology because the joint reference given curves and the parameter settings of different manipulators are the same. In order to intuitively display the effect, the figure only uses the position and velocity of one joint to represent the position and velocity vectors of all manipulators.

[0087] Figure 5 and Figure 6 It is the observer position and speed estimation curve. It can be seen from the figure that the designed distributed event-triggered state observer can make each manipulator track the reference signal after 5s, and the tracking error is extremely small. At 0-5s, the tracking curve is a step-by-step change, which is caused by the event trigger mechanism. A counter is added to the observer, and the event trigger times of each manipulator are measured to be 8908, 8944, 8860, 8860, 8860, saving about 40% of communication resources. Therefore, the reliability and practicality of the designed distributed event-triggered state observer can be explained.

[0088] Figure 7 , Figure 8 This is the position and speed curve of the system after the introduction of the adaptive compensation controller. It can be seen intuitively that the system position and speed can quickly track the reference signal. The speed and position errors are defined as:

[0089] e i1 =x i1 -q0

[0090]

[0091] Where i = 1,...,5. The system position error and speed error curves are as follows: Fig. 9 and Fig.10 As shown in the figure, it can be seen that the position error is finally within 10 -5 The speed error is also 10 -2The order of magnitude can therefore illustrate the effectiveness and reliability of the overall solution.

[0092] Fig.11 This is a demonstration diagram of the RRT* algorithm in three-dimensional space. The coordinates of the starting point are (150,150,150), the coordinates of the target point are (10,10,10), and five spherical obstacles are set in the space. As can be seen from the figure, after a finite number of iterations, the RRT* algorithm can achieve the spherical obstacle avoidance task in three-dimensional space.

Claims

1. A method for collaborative control of a multi-redundant robotic arm system under complex actuator failure, characterized in that: The following steps are involved: S1. Design a robot motion constraint algorithm, which adopts the asymptotically optimal RRT* algorithm and consists of collision detection, trajectory planning, and forward and inverse dynamics; S2. Design a dynamic model of a multi-redundant robotic arm system under complex actuator failures; S3. Design a distributed event-triggered state observer, wherein the distributed event-triggered state observer includes a communication topology, an event triggering mechanism, and a distributed observer; S4. Design an adaptive compensation controller, wherein the adaptive compensation controller is implemented by backstepping method, a feedback controller is obtained by constructing a Lyapunov function of a closed-loop system, and a Nussbaum function and a virtual control law are introduced; Step S1 is specifically as follows: S11, the initial point of the robot arm is used as the root node x init , from which branches begin to form; S12. Generate a random point in the robot's "configuration" space x rand ; S13, traverse the points in the tree and find the distance x rand The nearest point x near ; S14, from x near Towards x near The direction grows at a certain step length. If there is no obstacle, the grown branches and endpoints are added to the tree, recorded as x new , The collision conditions are: in, are the coordinates of the center of the spherical obstacle, r 0 is the ball diameter, l is the expanded size of the obstacle after expansion treatment; S15. In the newly generated node x new Define a radius around The nodes in the region are x new Parent node alternatives ; S16, calculate all x init arrive The cost and arrive x new The cost and the minimum cost are selected As x new Parent Node ; S17, the remaining candidate nodes The parent node of x new ,calculate x init arrive x new The cost and x new arrive The cost and; S18. If the sum of the costs is less than the sum of the costs of the parent node that has not been changed before, then The node's parent node is changed to x new ; S19, repeat S12-S18 process until reaching the target node x goal ; Step S2 is specifically as follows: S21, Robotic Arm i No. m The fault model of an actuator is: in, represents the non-zero bounded proportionality factor caused by actuator faults, Represents a robotic arm i No. m The control input of each actuator is represents the bounded fault signal in the actuator. The actuator faults covered by the above fault model are: and When No. m There is noise interference in the actuator; when and When No. m An actuator has a partial failure; when and When No. m The control direction of an actuator suddenly changes; S22. The Lagrange equation is used to model the dynamics of the multi-redundant robotic arm system under fault conditions. The specific model is as follows: in, , , Respectively represent the robotic arm The multi-redundant robotic arm system in this design consists of The actuator failure model consists of a 7-DOF redundant robot arm. , is a symmetric positive definite inertia matrix, is the Coriolis force and centripetal force matrix, is the gravity matrix, For robotic arm Output torque of each joint actuator after failure, is the Jacobian matrix that reflects the transformation relationship between the robot joint velocity and the end effector velocity. is the output force at the end of the robot; make , then the dynamic model of the above multi-redundant robotic arm system is expressed as: in ,The transformed model will be used in the design of adaptive compensation control algorithm; Step S3 is specifically as follows: S31. Design a communication topology structure of a multi-redundant robotic arm system. The communication topology structure is represented by a weighted directed graph, denoted as ,in Represents a set of nodes, nodes Representative A robotic arm; Represents an edge set, when the node To Node Send information, then ; represents an adjacency matrix, where Represents edge The weight of the node Received node information, when , then the edge does not exist, the reference signal is generated by a virtual linear system, marked as nodes , and its dynamic model is as follows: in is the state of the leader node, indicating the reference signal of the robot joint space, is the reference joint position, is the reference joint velocity, is a known constant matrix in the form of a block matrix, namely , Indicates a The all-zero matrix, Indicates a The identity matrix of and Indicates a The constant matrix of , and define the controlled matrix as ; S32, the design of the distributed event-triggered state observer is as follows: in , , Represents a robotic arm Estimation of the reference signal in the joint space, is the estimated value of the joint position, is the estimated joint velocity, Represents a robotic arm The triggering moment of ; S33, introduce event trigger conditions, and define the following new variables: in For robotic arm Neighbor error, representing the robotic arm The comprehensive error of the information that can be received, The robot arm after the event is triggered The specific event triggering mechanism is as follows: in , and are given positive constants, reflecting The magnitude and rate at which it approaches zero; Step S4 is specifically as follows: S41. The error vector of the controller is defined as follows: in is a virtual control law, and ; S42. Design the Nussbaum function as follows: S43. Design Lyapunov function: For signal Estimation Error , for supremum , for An estimated value of S44. Design of adaptive compensation control algorithm: in , ,and All are normal numbers.

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