PID (Proportion Integration Differentiation) control method for actual stability of robot based on evolution function

Abstract

The invention relates to a PID (Proportion Integration Differentiation) control method for the actual stability of a robot based on an evolution function, which belongs to the technical field of automatic robot control and comprises the steps of determining PID input parameters, generating a particle swarm, approximately calculating a reachable set, calculating stable time and carrying out PID control iteration. And finally, taking the PID control parameter which is actually stable as fast as possible as a control instruction of the robot. According to the invention, a specific obstacle certificate template is constructed based on PID control, so that a proper obstacle certificate can be quickly found to carry out actual stability verification, and the method has universality. According to the method, PID control parameters are iteratively solved by adopting the particle swarm optimization algorithm, and the problem of actual stability of a robot system starting from an initial set in infinite time is solved; according to the invention, PID control is iteratively solved by using the particle swarm optimization algorithm, so that the efficiency and advantages of PID control are improved.

Description

Technical Field

[0001] The present invention relates to the technical field of robot automatic control, and in particular to a PID control method for the actual stability of a robot based on an evolution function. Background Art

[0002] Practical stability is an important concept in robotic control theory, which generally considers the following two problems: designing a controller so that the system state oscillates sufficiently in a specific neighborhood of an equilibrium point; or designing a controller so that the trajectory starting from a specific initial set can reach a target set and remain in the target set (i.e., the reach-stay control problem).

[0003] In practical applications such as robotic systems, ensuring practical stability is of great significance for improving the reliability, adaptability, and safety of the system. Therefore, designing a control method to achieve the practical stability of the system has become a key issue in engineering design. PID control is widely used in system stability analysis due to its high reliability and simplicity. Designing the optimal PID control is challenging, especially for robotic systems with complex dynamics or nonlinear behavior. Therefore, to meet these challenges, scholars have developed methods such as adaptive PID control, particle swarm optimization algorithms, and machine learning to find the optimal PID control. Summary of the Invention

[0004] In view of the above problems, the present invention provides a PID control method for the actual stability of a robot based on an evolution function. The present invention includes the steps of determining PID input parameters, generating a particle swarm, approximate calculation of a reachable set, calculation of the stabilization time, and PID control iteration. Finally, the PID control parameters that achieve the fastest possible actual stability are used as the control instructions of the robot. The present invention constructs a specific obstacle certificate template based on PID control, which facilitates the rapid search for a suitable obstacle certificate for actual stability verification and has universality and applicability. The present invention uses a particle swarm optimization algorithm to iteratively solve the PID control parameters, solving the problem of the actual stability of a robot system starting from an initial set in infinite time.

[0005] The present invention provides a PID control method for actual stability of a robot based on an evolution function, comprising:

[0006] Step S1: construct an original robot power system and perform dimensionality upgrading to obtain a robot power system;

[0007] Step S2, let i=1, when i=1, it represents the first set of PID control parameters;

[0008] Step S3: input the i-th group of PID control parameters into the robot power system to obtain the i-th group of reachable sets;

[0009] Step S4: obtaining an over-approximation value of the i-th group of reachable sets based on the reachable set evolution function;

[0010] Step S5: Based on the over-approximation value of the i-th group of reachable sets, obtain the time when the i-th group of reachable sets reaches the obstacle certificate and stays in the target set;

[0011] Step S6: Based on the particle swarm genetic algorithm and the time when the i-th group of reachable sets reaches the obstacle certificate and stays in the target set, the final robot position of the i-th group and its corresponding PID control parameters are obtained as the final PID control parameters of the i-th group, and the process proceeds to the next step;

[0012] Step S7, determine whether i is greater than or equal to I, if so, obtain the optimal PID control parameters, if not, set i=i+1, and return to step S3;

[0013] Step S8: Control the robot power system based on the optimal PID control parameters.

[0014] Optionally, the expression of the robot power system is:

[0015]

[0016] Among them, z(t) represents the state after dimension upgrade at time t, h(.) represents the dynamic function, K represents the PID control parameter, represents the derivative of the state after dimension increase at time t, represents the total time, K0 represents the feasible set of PID control parameters.

[0017] Optionally, the expression of the reachable set evolution function is:

[0018]

[0019] in, represents the approximate value of the partial sum retained to the Nth term of the Taylor expansion based on the robot dynamic system h and the obstacle certificate constraint g, which is used to approximate the evolution trajectory of the reachable set, n = 1, 2, 3...N, N represents the total order of the Taylor expansion, z(t) represents the state after dimension upgrade at time t, h represents the robot dynamic system vector, g represents the obstacle certificate constraint, K represents the PID control parameter, represents the recursive function of the nth-order Taylor expansion based on the robot dynamics system h and the obstacle certificate constraint g, and n! represents the nth factorial term.

[0020] Optionally, the specific steps of obtaining the time for the i-th group of reachable sets to reach the barrier certificate and stay in the target set include:

[0021] Step S61: determine the initial position; determine the target set; determine the obstacle certificate corresponding to the reachable set based on the obstacle certificate template;

[0022] Step S62: simulating a trajectory point sequence 1 of a reachable set of the robot in the time period [0, T] based on the initial position;

[0023] Step S63: Find the first track point Z in the track point sequence 1 that enters the obstacle certificate. j ;

[0024] Step S64: Obtain trajectory point Z j Time to enter barrier certificate S j ;

[0025] Based on time S j , establish the corresponding symbolic function one;

[0026] Step S65: Determine whether the value of the corresponding symbol function 1 is greater than 0. If so, the time when the trajectory point sequence 1 reaches the obstacle certificate is time S. j If not, set j = j + 1 and return to step S64 until the value of the sign function 1 is greater than 0, and obtain the time t2 when the trajectory point sequence 1 reaches the obstacle certificate;

[0027] Step S66: Based on the initial position, simulate the second trajectory point sequence of the robot in the time period [0, t2];

[0028] Step S67: Find the last trajectory point Z′ in the second trajectory point sequence that does not belong to the target set. j ;

[0029] Step S68: Obtain trajectory point Z′ j The corresponding time S′ j , get the time period [S′ j+1 ,t2];

[0030] In the time period [S′ j+1 ,t1], establish the corresponding symbolic function 2;

[0031] Step S69: Determine whether the value of the corresponding symbol function 2 is greater than 0. If so, the last time in the trajectory point sequence 2 that does not belong to the target certificate is time S′ j+1 If not, let j=j+1 and return to step S68 until the value of the symbol function 2 is greater than 0, and the time t1 when the trajectory point sequence enters the obstacle certificate and stays in the target certificate is obtained, which is the time when the reachable set reaches the obstacle certificate and stays in the target set.

[0032] Optionally, the specific steps of obtaining the over-approximation value of the reachable set include:

[0033] Perform Taylor expansion on the i-th group of reachable sets and gradually increase the order of Taylor expansion;

[0034] Obtain the upper bound and lower bound of the remainder of the N-order Taylor expansion of the i-th group of reachable sets and the partial sum of the N terms of the Taylor expansion of the i-th group of reachable sets;

[0035] The global optimization algorithm is used to obtain the exact upper and lower bounds of the remainder of the N-order Taylor expansion of the i-th group of reachable sets.

[0036] According to the partial sum of N terms of Taylor expansion of the i-th group of reachable sets and the exact lower bound of the remainder of the N-order Taylor expansion of the i-th group of reachable sets, the over-approximation of the i-th group of reachable sets is obtained.

[0037] Optionally, the specific steps of obtaining the PID control parameters corresponding to the final robot positions of the i-th group as the final PID control parameters of the i-th group include:

[0038] Step S71, let d = 1, when d = 1, it indicates the first round of iteration;

[0039] Step S72: Based on the time when the reachable set of the i-th group reaches the obstacle certificate and stays in the target set, obtain the optimal position of the robot of the i-th group in the d-th iteration;

[0040] Based on the optimal position of the robot of the i-th group at the d-th iteration, the robot speed of the i-th group at the d-th iteration is updated to obtain the updated robot speed of the i-th group at the d-th iteration as the robot speed of the i-th group at the d+1-th iteration;

[0041] Step S73: Based on the robot update speed of the i-th group at the d-th iteration, obtain the robot update position of the i-th group at the d-th iteration as the robot position of the i-th group at the d+1-th iteration;

[0042] Step S74, determine whether d is greater than or equal to D. If so, obtain the final robot position of the i-th group, obtain the PID control parameters corresponding to the final robot position of the i-th group, and use them as the final PID control parameters of the i-th group, and go to the next step. If not, set d=d+1 and return to step S72.

[0043] Optionally, the expression for the updated position of the robot of the i-th group at the d-th iteration is:

[0044]

[0045] in, represents the robot update speed of the i-th group at the d-th iteration, w is the inertia coefficient, represents the robot speed of the i-th group at the d-th iteration, c1 represents a positive real number, rand represents a random number between [0,1], represents the optimal position of the robot of group i at iteration d, represents the robot position of the i-th group at the d-th iteration, c2 represents a positive real number two, and Rand represents a random number one between [0,1]. represents the optimal position of the robot at the dth iteration under the constraint of the obstacle certificate, represents the updated position of the robot of group i at the dth iteration.

[0046] Compared with the prior art, the present invention has at least the following beneficial effects:

[0047] (1) The present invention uses level sets to represent initial sets, such as the possible states of the robot at the start, including possible positions and velocities, and directly processes initial sets of non-convex or even non-connected sets to characterize more complex and universal initial sets, that is, to relax the restrictions on various initial states;

[0048] (2) The present invention uses zonotope set representation and global optimization algorithm to approximate the calculation of reachable sets, which significantly improves the efficiency of reachable set calculation;

[0049] (3) The present invention constructs a specific obstacle certificate template based on PID control, which is convenient for quickly finding a suitable obstacle certificate for actual stability verification and has universality and applicability;

[0050] (4) The present invention performs verification analysis on actual stability based on polar coordinate transformation of sets, which has the advantages of high speed and small computational complexity over the method based on quantifier elimination;

[0051] (5) The present invention improves the efficiency and advantages of PID control by using the particle swarm optimization algorithm to iteratively solve the PID control. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] The drawings are only for purposes of illustrating particular embodiments and are not to be considered limiting of the invention.

[0053] Figure 1 Schematic diagram of the process of obtaining optimal PID control parameters in an embodiment of the present invention;

[0054] Figure 2 A schematic diagram of a rectangular envelope formed by all elements of an initial set in an embodiment of the present invention;

[0055] FIG3( a ) is a schematic diagram of optimal PID control parameters in an embodiment of the present invention;

[0056] FIG3( b ) is a schematic diagram of the optimal PID control parameters in Comparative Example 1 of the present invention;

[0057] FIG3( c ) is a schematic diagram of the optimal PID control parameters in Comparative Example 2 of the present invention;

[0058] FIG3( d ) is a schematic diagram of the P control result in Comparative Example 1 of the present invention. DETAILED DESCRIPTION

[0059] In order to more clearly understand the above-mentioned objects, features and advantages of the present invention, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments can be combined with each other. In addition, the present invention can also be implemented in other ways different from those described herein. Therefore, the scope of protection of the present invention is not limited by the specific embodiments disclosed below.

[0060] A specific embodiment of the present invention, as Figure 1 -3, discloses a PID control method for the actual stability of a robot based on an evolution function. In order to illustrate the effectiveness of the method proposed by the present invention, the above technical solution of the present invention is described in detail below through a specific embodiment. The specific implementation steps are as follows:

[0061] Step S1, constructing an original robot power system;

[0062] Optionally, the expression of the original robot power system is:

[0063]

[0064] in, represents the acceleration of the robot at time t; u(t) is the PID control parameter at time t, x(t) is the state of the robot at time t, including position and speed; f(.) represents the force acting on the robot.

[0065] Furthermore, the expression of the PID control parameter at the time t is:

[0066]

[0067] Where e(t) represents the control error at time t, e(t)=x tar -x(t), x tar is the given target point, [P,I,D]∈K0, K0 represents the value range of PID controller parameters, P represents the proportional gain coefficient, I represents the integral gain coefficient, and D represents the differential gain coefficient.

[0068] Optionally, step S1 also includes the constraint conditions of the robot power system, which are expressed as:

[0069] x(0)∈{x(0)|g(x(0))≤0}

[0070] Wherein, x(0) represents the n-dimensional robot vector, including the robot's position, velocity, acceleration, angle and / or angular velocity; g is a scalar function of the n-dimensional robot vector.

[0071] Optionally, an initial level set is obtained according to the original robot power system and the constraint conditions; the initial set includes a plurality of starting states of the robot power system;

[0072] Step S2, performing dimensionality upgrading processing on the original robot power system described in step S1 to construct a robot power system;

[0073] Optionally, the expression of the robot power system is:

[0074]

[0075] Among them, z(t) represents the state after dimension upgrade at time t, h(.) represents the dynamic function, K represents the PID control parameter, K=[P,I,D], represents the derivative of the state after dimension increase at time t, represents the total time, K0 represents the feasible set of PID control parameters, a j Indicates the lower bound of the range of the j-th dimension of the PID controller parameter; b j Indicates the upper bound of the range of the j-th dimension of the PID controller;

[0076] Optionally, the projection of the reachable set of the robot power system on the first n-dimensional plane is the reachable set of the original robot power system;

[0077] It can be understood that the level set is used to describe the state set of the robot dynamic system;

[0078] It can be understood that the reachable set is a set of states that the robot can reach at time t starting from any initial state in the initial level set.

[0079] In this paper, the level set is used as the initial set for robot control. During the control process, the robot starts from the initial set and moves according to control instructions and constraints. Using the level set as the initial set can handle initial conditions of non-convex and even disconnected sets, and can characterize more complex and universal robot initial states.

[0080] Step S3, let i=1, when i=1, it represents the first set of PID control parameters;

[0081] Step S4: input the i-th group of PID control parameters into the robot power system to obtain the i-th group of reachable sets;

[0082] Step S5: Based on the reachable set evolution function, obtain the over-approximation value Over of the i-th group of reachable sets i ;

[0083] Optionally, the expression of the reachable set evolution function is:

[0084]

[0085] in, represents the approximate value of the partial sum retained to the Nth term of the Taylor expansion based on the robot dynamic system h and the obstacle certificate constraint g, which is used to approximate the evolution trajectory of the reachable set, n = 1, 2, 3...N, N represents the total order of the Taylor expansion, z(t) represents the state after dimension upgrade at time t, h represents the robot dynamic system vector, g represents the obstacle certificate constraint, K represents the PID control parameter, represents the recursive function of the nth-order Taylor expansion based on the robot dynamics system h and the obstacle certificate constraint g, and n! represents the nth factorial term;

[0086] Furthermore, the expression of the recursive function of the n-th order Taylor expansion of the Taylor expansion of the robot dynamic system h and the scalar constraint g is:

[0087]

[0088] in, represents the recursive function of the primary Taylor expansion based on the robot dynamic system h and the obstacle certificate constraint g, z(0) represents the state after dimensionality increase at the initial moment, represents the partial derivative.

[0089] It can be understood that the level set evolution function is represented as a process starting from the level set and evolving along the time axis, obtaining a set of possible states of the robot at different time points, that is, the evolution process of the level set.

[0090] In the present invention, the level set evolution function is used to describe how the state variables of the robot power system after dimensionality increase change over time; in the robot power system after dimensionality increase, the evolution function of the reachable set of the robot power system after dimensionality increase contains additional state variables, which may represent unmodeled dynamics, external interference or constraints.

[0091] Step S6: Overapproximation value based on the i-th group of reachable sets i , the time to obtain the barrier certificate of the i-th reachable set and stay in the target set;

[0092] Optionally, the specific steps of obtaining the reachable set barrier certificate and the time of staying in the target set include:

[0093] Step S61: determine the initial position; determine the target set; determine the obstacle certificate corresponding to the reachable set based on the obstacle certificate template;

[0094] Step S62: Based on the initial position, using the Runge-Kutta method to simulate the trajectory point sequence 1 of the reachable set of the robot in the time period [0, T];

[0095] Step S63: Find the first track point Z in the track point sequence 1 that enters the obstacle certificate. j ;

[0096] Step S64: Obtain trajectory point Z j Time to enter barrier certificate S j ;

[0097] Based on time S j , establish the corresponding symbolic function one;

[0098] Step S65: Determine whether the value of the corresponding symbol function 1 is greater than 0. If so, the time when the trajectory point sequence 1 reaches the obstacle certificate is time S. j If not, set j = j + 1 and return to step S64 until the value of the sign function 1 is greater than 0, and obtain the time t2 when the trajectory point sequence 1 reaches the obstacle certificate;

[0099] Step S66: Based on the initial position, use the Runge-Kutta method to simulate the second trajectory point sequence of the reachable set of the robot in the time period [0, t2];

[0100] Step S67: Find the last track point Z′ in the track point sequence 2 that does not belong to the target certificate. j ;

[0101] Step S68: Obtain trajectory point Z′ j The corresponding time S′ j , get the time period [S′ j+1 ,t2];

[0102] In the time period [S′ j+1 ,t1], establish the corresponding symbolic function 2;

[0103] Step S69: Determine whether the value of the corresponding symbol function 2 is greater than 0. If so, the last time in the trajectory point sequence 2 that does not belong to the target certificate is time S′ j+1 , if not, set j = j + 1 and return to step S68 until the value of the sign function 2 is greater than 0, and the time t1 at which the trajectory point sequence enters the obstacle certificate and remains in the target certificate;

[0104] Optionally, the expression of the symbolic function 1 is:

[0105] Sign1=maxl＝1 ,2,3{O(α1,…α 2q-1 ,s j ,K)},

[0106] Among them, α 2q-1 Represents the parameter of the polar coordinate transformation of the 2q-1th boundary point of the level set of the obstacle certificate, q represents the boundary point, which is an integer, and O(.) represents the reachable set evolution function.

[0107] The expression of the second symbolic function is:

[0108] Sign2=max l＝1,2,3 {O(α1,…α q-1 ,y,t,K)},

[0109] Among them, α q-1 is the parameter of the polar coordinate transformation of the q-1th boundary point of the target set, and y represents the robot state after the coordinate transformation.

[0110] Optionally, the obstacle certificate is elliptical; the target set is circular; and the boundaries of the obstacle certificate and the target set are represented by polar coordinate transformation.

[0111] It is understood that the obstacle certificate is a mathematical tool that proves that the robot dynamic system will not enter an unsafe area under set conditions;

[0112] Optionally, the expression of the obstacle certificate template is:

[0113]

[0114] Where B(z) represents the obstacle certificate template of the robot position, z represents the robot position, and z ta2 represents the target position of the robot, K1 is the positive parameter one, K2 is the positive parameter two, r is the safety radius, and y represents the robot state after coordinate conversion.

[0115] Furthermore, the target set G tar =R(z tar ,r).

[0116] Optionally, obtain the reachable set over-approximation Over i The specific steps include:

[0117] Based on the robot power system and obstacle certificate constraints, Taylor expansion is performed on the i-th group of reachable sets, and the order of Taylor expansion is gradually increased. Under the condition that the approximate accuracy of the reachable set epsilon1 is met, the approximate value of the partial sum of the corresponding Taylor expansion retained to the N-th term is obtained;

[0118] Get the n-th order Taylor expansion remainder of the i-th group of reachable sets

[0119] Continuously increase the N-th term of the Taylor expansion and estimate the upper bound U and lower bound L of the N-th order Taylor expansion remainder of the i-th group of reachable sets;

[0120] When the difference between the upper bound U and the lower bound L of the remainder of the N-order Taylor expansion of the i-th group of reachable sets is less than or equal to the approximate accuracy threshold, the partial sum of the N terms of the Taylor expansion of the i-th group of reachable sets is obtained, which is represented as the partial sum of the N terms of the Taylor expansion of the reachable set evolution function;

[0121] Using the global optimization algorithm, we can get the exact upper bound U of the N-order Taylor expansion remainder of the i-th group of reachable sets. i ′ and the exact lower bound L i ';

[0122] According to the partial sum of the N terms of the Taylor expansion of the i-th group of reachable sets and the exact lower bound L of the remainder of the N-order Taylor expansion of the i-th group of reachable sets i ′, get the over-approximation value of the i-th group of reachable sets Over i , the expression is:

[0123]

[0124] Among them, Over i Indicates that the i-th group of reachable sets is over-approximated, represents the approximation of the partial sum of the i-th group of reachable sets based on the Taylor expansion of the robot dynamics h and the obstacle certificate constraint g, which is retained up to the N-th term; z i (t) represents the robot state corresponding to the i-th reachable set at time t, K i represents the robot position corresponding to the i-th reachable set, L i ′ represents the exact lower bound L of the N-order Taylor expansion remainder of the i-th group of reachable sets i ′.

[0125] Step S7: Based on the particle swarm genetic algorithm, obtain the final robot position of the i-th group, obtain the PID control parameters corresponding to the final robot position of the i-th group, use them as the final PID control parameters of the i-th group, and proceed to the next step;

[0126] Optionally, the specific steps of obtaining the PID control parameters corresponding to the final robot positions of the i-th group as the final PID control parameters of the i-th group include:

[0127] Step S71, let d = 1, when d = 1, it indicates the first round of iteration;

[0128] Step S72: Based on the time when the reachable set of the i-th group reaches the obstacle certificate and stays in the target set, obtain the optimal position of the robot of the i-th group in the d-th iteration;

[0129] Based on the optimal position of the robot of the i-th group at the d-th iteration, the robot speed of the i-th group at the d-th iteration is updated to obtain the updated robot speed of the i-th group at the d-th iteration as the robot speed of the i-th group at the d+1-th iteration;

[0130] Step S73: Based on the robot update speed of the i-th group at the d-th iteration, obtain the robot update position of the i-th group at the d-th iteration as the robot position of the i-th group at the d+1-th iteration;

[0131] Optionally, the expression for the updated position of the robot of the i-th group at the d-th iteration is:

[0132]

[0133] in, represents the robot update speed of the i-th group at the d-th iteration, w is the inertia coefficient, represents the robot speed of the i-th group at the d-th iteration, c1 represents a positive real number, rand represents a random number between [0,1], represents the optimal position of the robot of group i at iteration d, represents the robot position of the i-th group at the d-th iteration, c2 represents a positive real number two, and Rand represents a random number one between [0,1]. represents the optimal position of the robot at the dth iteration under the constraint of the obstacle certificate, represents the updated position of the robot of group i at the dth iteration.

[0134] Step S74: Determine whether d is greater than or equal to D. If so, obtain the final robot position of the i-th group, obtain the PID control parameters corresponding to the final robot position of the i-th group, and use them as the final PID control parameters of the i-th group, and proceed to the next step. If not, set d = d + 1, and return to step S72.

[0135] Step S8, determine whether i is greater than or equal to I, if so, obtain the optimal PID control parameters, if not, set i=i+1, and return to step S4;

[0136] Step S9: Control the robot power system based on the optimal PID control parameters.

[0137] Comparative Example 1

[0138] The steps S7 to S11 in the embodiment are replaced by using a trial-and-error method to obtain the optimal PID control parameters.

[0139] Comparative Example 2

[0140] The steps S7 to S11 in the embodiment are replaced by using a simulated annealing algorithm to obtain the optimal PID control parameters.

[0141] At the same time, by comparing with P control, PI control and PD control, the advantages of PID control are reflected, as shown in Table 1;

[0142] Table 1

[0143] P I D <![CDATA[t1]]> Iterations PSO 1.4744 0.0000 0.9845 1.9926 180 SA 1.2738 0.0646 1.0000 2.1084 207 TE 1.2000 0.0050 0.7250 3.4800 189

[0144] The above description is only a preferred specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by any technician familiar with this technical field within the technical scope disclosed by the present invention should be covered by the scope of protection of the present invention.

Claims

1. A PID control method for practical stability of a robot based on evolution function, characterized in that: include: Step S1: construct an original robot power system and perform dimensionality upgrading to obtain a robot power system; Step S2, let i=1, when i=1, it represents the first set of PID control parameters; Step S3: input the i-th group of PID control parameters into the robot power system to obtain the i-th group of reachable sets; Step S4: obtaining an over-approximation value of the i-th group of reachable sets based on the reachable set evolution function; Step S5: Based on the over-approximation value of the i-th group of reachable sets, obtain the time when the i-th group of reachable sets reaches the obstacle certificate and stays in the target set; Step S6: Based on the particle swarm genetic algorithm and the time when the i-th group of reachable sets reaches the obstacle certificate and stays in the target set, the final robot position of the i-th group and its corresponding PID control parameters are obtained as the final PID control parameters of the i-th group, and the process proceeds to the next step; Step S7, determine whether i is greater than or equal to I, if so, obtain the optimal PID control parameters, if not, set i=i+1, and return to step S3; Step S8: Control the robot power system based on the optimal PID control parameters.

2. The PID control method for actual stability of a robot based on an evolution function according to claim 1, characterized in that: The expression of the robot power system is: Among them, z(t) represents the state after dimension upgrade at time t, h(.) represents the dynamic function, K represents the PID control parameter, represents the derivative of the state after dimension increase at time t, represents the total time, K0 represents the feasible set of PID control parameters.

3. The PID control method for actual stability of a robot based on an evolution function according to claim 2, characterized in that: The expression of the reachable set evolution function is: in, represents the approximate value of the partial sum retained to the Nth term of the Taylor expansion based on the robot dynamic system h and the obstacle certificate constraint g, n = 1, 2, 3...N, N represents the total order of the Taylor expansion, represents the recursive function of the nth-order Taylor expansion based on the robot dynamics system h and the obstacle certificate constraint g, and n! represents the nth factorial term.

4. The PID control method for actual stability of a robot based on an evolution function according to claim 1, characterized in that: The specific steps to obtain the reachable set barrier certificate and stay in the target set for a certain period of time include: Step S61: determine the initial position; determine the target set; determine the obstacle certificate corresponding to the reachable set based on the obstacle certificate template; Step S62: simulating a trajectory point sequence 1 of a reachable set of the robot in the time period [0, T] based on the initial position; Step S63: Find the first track point Z in the track point sequence 1 that enters the obstacle certificate. j ; Step S64: Obtain trajectory point Z j Time to enter barrier certificate S j ; Based on time S j , establish the corresponding symbolic function one; Step S65: Determine whether the value of the corresponding symbol function 1 is greater than 0. If so, the time when the trajectory point sequence 1 reaches the obstacle certificate is time S. j If not, set j = j + 1 and return to step S64 until the value of the sign function 1 is greater than 0, and obtain the time t2 when the trajectory point sequence 1 reaches the obstacle certificate; Step S66: Based on the initial position, simulate the second trajectory point sequence of the reachable set of the robot in the time period [0, t2]; Step S67: Find the last trajectory point Z′ in the second trajectory point sequence that does not belong to the target set. j ; Step S68: Obtain trajectory point Z′ j The corresponding time S′ j , get the time period [S′ j+1 ,t2]; In the time period [S′ j+1 ,t1], establish the corresponding symbolic function 2; Step S69: Determine whether the value of the corresponding symbol function 2 is greater than 0. If so, the last time in the trajectory point sequence 2 that does not belong to the target certificate is time S′ j+1 If not, let j=j+1 and return to step S68 until the value of the symbol function 2 is greater than 0, and the time t1 when the trajectory point sequence enters the obstacle certificate and stays in the target certificate is obtained, which is the time when the reachable set reaches the obstacle certificate and stays in the target set.

5. The PID control method for actual stability of a robot based on an evolution function according to claim 1, characterized in that: The specific steps to obtain the over-approximation of the reachable set include: Perform Taylor expansion on the i-th group of reachable sets and gradually increase the order of Taylor expansion; Obtain the upper bound and lower bound of the remainder of the N-order Taylor expansion of the i-th group of reachable sets and the partial sum of the N terms of the Taylor expansion of the i-th group of reachable sets; The global optimization algorithm is used to obtain the exact upper and lower bounds of the remainder of the N-order Taylor expansion of the i-th group of reachable sets. According to the partial sum of N terms of Taylor expansion of the i-th group of reachable sets and the exact lower bound of the remainder of the N-order Taylor expansion of the i-th group of reachable sets, the over-approximation of the i-th group of reachable sets is obtained.

6. The PID control method for actual stability of a robot based on an evolution function according to claim 1, characterized in that: The specific steps of obtaining the PID control parameters corresponding to the final robot positions of the i-th group as the final PID control parameters of the i-th group include: Step S71, let d = 1, when d = 1, it indicates the first round of iteration; Step S72: Based on the time when the reachable set of the i-th group reaches the obstacle certificate and stays in the target set, obtain the optimal position of the robot of the i-th group in the d-th iteration; Based on the optimal position of the robot of the i-th group at the d-th iteration, the robot speed of the i-th group at the d-th iteration is updated to obtain the updated robot speed of the i-th group at the d-th iteration as the robot speed of the i-th group at the d+1-th iteration; Step S73: Based on the robot update speed of the i-th group at the d-th iteration, obtain the robot update position of the i-th group at the d-th iteration as the robot position of the i-th group at the d+1-th iteration; Step S74, determine whether d is greater than or equal to D. If so, obtain the final robot position of the i-th group, obtain the PID control parameters corresponding to the final robot position of the i-th group, and use them as the final PID control parameters of the i-th group, and go to the next step. If not, set d=d+1 and return to step S72.

7. The PID control method for actual stability of a robot based on an evolution function according to claim 6, characterized in that: The expression for the updated position of the robot of the i-th group at the d-th iteration is: in, represents the robot update speed of the i-th group at the d-th iteration, w is the inertia coefficient, represents the robot speed of the i-th group at the d-th iteration, c1 represents a positive real number, rand represents a random number between [0,1], represents the optimal position of the robot of group i at iteration d, represents the robot position of the i-th group at the d-th iteration, c2 represents a positive real number two, and Rand represents a random number one between [0,1]. represents the optimal position of the robot at the dth iteration under the constraint of the obstacle certificate, represents the updated position of the robot of group i at the dth iteration.

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