Outdoor two-wheeled robot path planning method based on improved crown porcupine optimization algorithm

Abstract

The invention discloses an outdoor double-wheel-foot robot path planning method based on an improved crown porcupine optimization algorithm, and the method comprises the steps: S1, enabling a user to activate a double-wheel-foot robot through a terminal instruction, stabilizing a camera, adjusting the camera to a working state, and guaranteeing the stable operation of a sensor and an actuator, creating a grid map of the environment by taking a target needing to be detected as an end point and self coordinates as a starting point; s2, a crown porcupine optimization algorithm is improved; and S3, inputting the path grid map created in the S1 into an improved crown porcupine optimization algorithm, and outputting an optimal path. The method can be more effectively applied to path planning of the double-wheel-foot robot, and navigation efficiency and safety of the robot in a complex environment are improved.

Description

Technical Field

[0001] The invention relates to a path planning method for an outdoor two-wheeled foot robot based on an improved crested porcupine optimization algorithm. Background Art

[0002] Outdoor robots are unmanned ground wheeled robots that can sense autonomously, actively cruise, and complete predetermined tasks. High-quality mobile path planning is the key to ensuring that robots can move efficiently in complex environments. The technical requirements for mobile operations in related scenarios and the complexity of tasks are constantly increasing. Robots not only need to operate on preset routes and structured environments indoors, but also need to achieve stable, efficient and autonomous mobile behaviors in non-standard outdoor scenarios with random structures, unknown environments, and complex natural disturbances. However, due to factors such as the complex terrain structure, target distribution, and random disturbances in outdoor scenes, robots generally have many problems during mobile operations, such as uneven driving paths and low navigation efficiency, resulting in low overall mobile operation efficiency. Summary of the invention

[0003] The present invention aims to solve the problems existing in the above-mentioned prior art and provides a path planning method for an outdoor two-wheeled robot based on an improved crested porcupine optimization algorithm.

[0004] The technical solutions adopted in the present invention are:

[0005] The path planning method of an outdoor two-wheeled robot based on the improved crown porcupine optimization algorithm includes the following steps:

[0006] S1: The user activates the two-wheeled robot through terminal commands, stabilizes the camera and adjusts it to the working state, ensures the stable operation of sensors and actuators, and creates a grid map of the environment with the target to be detected as the end point and the robot's own coordinates as the starting point;

[0007] S2: Improve the crown porcupine optimization algorithm. The improvements are as follows:

[0008] (1) Introduce Kent mapping to initialize the population position of the crown porcupine optimization algorithm;

[0009] (2) In the development evolutionary iteration phase of the crested porcupine optimization algorithm, the NSGA-II algorithm is used to solve the multi-objective optimization problem, maintain population diversity through non-dominated sorting and crowding calculation, and generate the Pareto optimal solution set;

[0010] (3) When a predator approaches, the crested porcupine uses a mathematical function to simulate the crested porcupine's behavior of attacking the predator with its scent;

[0011] (4) By setting up mathematical functions, it is simulated that only the threatened crested porcupine activates its defense mechanism;

[0012] (5) Based on the global search, the Newton method is introduced to perform local search strategy, and the approximate solution found is locally optimized to improve the smoothness and optimization degree of the path;

[0013] S3: Input the path grid map created in S1 into the improved crested porcupine optimization algorithm and output the optimal path.

[0014] Furthermore, the initialization population sequence is randomly generated by the kent chaotic map, and the introduced kent chaotic map formula is defined as:

[0015]

[0016] Where a is the control parameter that determines the behavior of the chaotic map, and its value is in the open interval (0, 1). When the value of the control parameter a is different, the Kent map will show different dynamic behaviors; x n is the current iteration state, x n+1 is the state of the next iteration.

[0017] Furthermore, the formula of the crested porcupine optimization algorithm starting the search process from the initial individual set is:

[0018]

[0019] Among them, N represents the number of individuals, that is, the population size; X i is the i-th candidate solution in the search space, L and U are the lower and upper limits of the search range, respectively, and r is a random number between 0 and 1;

[0020] By considering multiple objectives in path planning, a multi-objective optimization model is established:

[0021] minf(X)=(f1(X), f2(X), f3(X))

[0022] Where f1(X) is the path length, f2(X) is the smoothness, and f3(X) is the energy consumption; X represents the decision variable of the path planning problem, that is, the coordinates of the path points;

[0023] The NSGA-II algorithm is used to solve the multi-objective optimization problem. The process is as follows:

[0024] For any two solutions x in the population i and x j ,if And there exists some l such that f l (x i )<f l (x j ), then x i dominatex j ;

[0025] For each solution x i The crowding degree d on the kth target k (x i ) is calculated as:

[0026]

[0027] Among them, f k (x i +1) and f k (x i -1) are x i The objective function value of the neighboring solutions on target k;

[0028] Using a selection strategy based on non-dominated sorting and crowding calculation, individuals are selected from the current population to enter the next generation with a selection probability P(x i ) is expressed as:

[0029]

[0030] Among them, F j is the number of solutions in the jth front;

[0031] Through the newly generated population, fast non-dominated sorting is performed to form new frontiers F1 and F2.

[0032] Furthermore, when a predator approaches, the crested porcupine uses a mathematical function to simulate the crested porcupine's behavior of attacking the predator by scent, and the mathematical function is:

[0033]

[0034] Among them, r3 is a random number between [1, N], and δ is a parameter used to control the search direction; is the position of the ith individual at iteration t, γ t is the defense factor defined by the user; τ3 is a random value in the interval [0,1], is the defined odor diffusion factor;

[0035] As shown below:

[0036]

[0037] in, represents the objective function value of the ith individual at iteration t, ε is a small value to avoid division by zero, rand is a vector of randomly generated numbers between 0 and 1, rand is a variable containing randomly generated numbers between 1 and 0, N is the population size, t is the number of the current iteration, and t maxis the maximum number of iterations; the U1 vector is used to simulate the possible situations that may occur during the odor attack on the predator.

[0038] Furthermore, a mathematical function is set to simulate that only the threatened crested porcupine activates the defense mechanism. The specific mathematical function is as follows:

[0039]

[0040] Where N represents the population size of the current iteration, N min represents the minimum population size set in the algorithm, N′ represents the initial population size or the maximum population size, T represents the current number of iterations, and T max Represents the maximum number of iterations set in the algorithm, Represents the remainder of the current number of iterations divided by the total number of iterations, that is: This remainder is used to determine the position of the current iteration in the total number of iterations, which is then used to calculate the reduction in population size;

[0041] As the number of iterations increases, the population size will gradually decrease from N′ to N min ,item Indicates the proportion by which the population size decreases.

[0042] Furthermore, after the global search of the crown porcupine optimization algorithm is completed, a number of points are selected as the initial points of the Newton method according to the results of the global search, and the Newton method is introduced for local search:

[0043] For each initial point, calculate the gradient vector and Hessian matrix of the objective function at that point:

[0044]

[0045] Iterative update formula: Using the information of gradient and Hessian matrix, the current solution is updated through the iterative formula of Newton's method:

[0046]

[0047] Among them, x new is the updated solution, x old is the current solution;

[0048] Introducing the downhill factor:

[0049]

[0050] in, λ is the downhill factor, which is used to ensure the decrease of the function value;

[0051] The step size for each search is determined by adaptively adjusting the step size:

[0052]

[0053] Among them, α k is the step size determined by the line search technique;

[0054] Termination condition check: The iteration process includes a termination condition check, which is: whether the norm of the gradient is less than the preset threshold or whether the number of iterations reaches the upper limit:

[0055]

[0056] When the norm of the gradient is less than the preset threshold ∈, the algorithm stops iterating and outputs the optimal solution.

[0057] The present invention has the following beneficial effects:

[0058] Introducing Kent mapping in the population initialization stage of the CPO algorithm can improve the diversity and uniformity of the initial population. Through multi-objective optimization, the optimal path that performs well in many aspects is found. The NSGA-II algorithm is used to solve the multi-objective optimization problem, and the population diversity is maintained through non-dominated sorting and crowding calculation, and the Pareto optimal solution set is generated. On the basis of global search, Newton's method is introduced to perform local search strategy, and the approximate solution found is locally optimized to improve the smoothness and optimization degree of the path. The present invention can be more effectively applied to the path planning of a two-wheeled foot robot, and improve the navigation efficiency and safety of the robot in a complex environment. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 It is a flow chart of the present invention.

[0060] Figure 2 Flowchart of the algorithm for improving crested porcupine optimization.

[0061] Figure 3 The robot path planning on the grid map based on the improved crested porcupine algorithm is demonstrated.

[0062] Figure 4 It is a performance comparison between the improved crested porcupine algorithm and the RIME algorithm. DETAILED DESCRIPTION

[0063] The present invention will be further described below in conjunction with the accompanying drawings.

[0064] like Figure 1 and Figure 2 The present invention provides a path planning method for an outdoor two-wheeled robot based on an improved crested porcupine optimization algorithm (CPO), comprising the following steps:

[0065] S1: The user activates the two-wheeled robot through terminal commands, stabilizes the camera and adjusts it to the working state, ensures the stable operation of sensors and actuators, and creates a grid map of the environment with the target to be detected as the end point and the robot's own coordinates as the starting point;

[0066] S2. Improve the CPO algorithm. The improvements are as follows:

[0067] (1) The Kent map is introduced to initialize the population position of the crowned porcupine optimization algorithm. By introducing this chaotic map, it has better uniform ergodicity, which can enhance the global search ability of the algorithm, avoid premature convergence, and increase the probability of finding the global optimal solution.

[0068] (2) In the development evolution and iteration phase of the CPO algorithm, multi-objective optimization is used to find the optimal solution set.

[0069] Multi-objective optimization: Considering multiple objectives in path planning, such as path length, smoothness, and energy consumption, multi-objective optimization is used to find the optimal path that performs well in multiple aspects. The NSGA-II algorithm is used to solve the multi-objective optimization problem. The algorithm maintains population diversity through non-dominated sorting and congestion calculation, and generates a Pareto optimal solution set.

[0070] (3) In the local optimization stage, based on the optimal solution set of multi-objective optimization in global search, this paper introduces Newton's method to perform local search strategy, and locally optimizes the approximate solution set found to improve the smoothness and optimization degree of the path.

[0071] S3. Input the path grid map created in S1 into the improved CPO optimization algorithm and output the optimal path.

[0072] Regarding improvement point 1:

[0073] The initial population sequence is randomly generated by the Kent chaotic map, and the introduced Kent chaotic map formula is defined as:

[0074]

[0075] Where a is the control parameter that determines the behavior of the chaotic map. The control parameter a usually takes a value in the open interval (0,1). When the value of a is different, the Kent map will exhibit different dynamic behaviors. The chaotic orbit state value range of the Kent map is (0,1), which makes it suitable for population initialization in path planning algorithms. n is the current iteration state, x n+1 is the state of the next iteration.

[0076] Regarding improvement point 2:

[0077] CPO starts the search process with an initial set of individuals (candidate solutions):

[0078]

[0079] Where N represents the number of individuals (population size N), X i is the i-th candidate solution in the search space, L and U are the lower and upper limits of the search range respectively, and r is a random number between 0 and 1.

[0080] Furthermore, by considering multiple objectives in path planning, such as path length f1(X), smoothness f2(X) and energy consumption f3(X), the following multi-objective optimization model is established:

[0081] minf(X)=(f1(X), f2(X), f3(X))

[0082] Among them, X represents the decision variable of the path planning problem, that is, the coordinates of the path points.

[0083] The NSGA-II algorithm is used to solve the multi-objective optimization problem as shown below:

[0084] For any two solutions x in the population i and x j :if And there exists some l such that f i (x i )<f l (x j ), then x i Dominate x j .

[0085] For each solution x i The crowding degree d on the kth target k (x i ) is calculated as:

[0086]

[0087] Among them, f k (x i +1) and f k (x i -1) are x i The objective function value of the neighboring solutions on the target k.

[0088] Using a selection strategy based on non-dominated sorting and crowding calculation, individuals are selected from the current population to enter the next generation. The selection probability P(x i ) is expressed as:

[0089] Among them, F jis the number of solutions in the jth front.

[0090] Furthermore, fast non-dominated sorting is performed through the newly generated population to form new frontiers F1 and F2.

[0091] The present invention maintains population diversity through non-dominated sorting and crowding calculation, and generates a Pareto optimal solution set. These solutions are non-dominated in multiple objectives, that is, the improvement in one objective will not lead to the performance degradation of another objective.

[0092] The Pareto optimal solution is the solution that is not dominated by other solutions, and other objective function values ​​are not better than the objective function value of this solution. Mathematically, the solution vector u = (u1, u2, ..., u m ) dominates another solution vector v = (υ1,υ2, ...,υ m ), if and only if for all i, there is u i ≤υ i , and there is at least one j such that u j <υ j .

[0093] Regarding improvement point 3:

[0094] The exploration behavior is dedicated to the global exploration of the search space by simulating the visual and acoustic defense strategies of crested porcupines:

[0095]

[0096]

[0097] in: represents the position of the i-th crested porcupine at time t+1;

[0098] represents the position of the i-th crested porcupine at time t;

[0099] τ_1: is a random factor used to control the step size of position update;

[0100] Indicates the best position from the current position to the crested porcupine group with the current position and another randomly selected crested porcupine position The distance of the midpoint, multiplied by a random factor τ_2;

[0101] Indicates the position of the best crested porcupine in the current group;

[0102] Indicates the midpoint between the current crested porcupine and another randomly selected crested porcupine;

[0103] represents the position of another randomly selected crested porcupine at time t;

[0104] When approached by predators, CP (crested porcupine) adopts scent attack strategy and physical attack strategy, which refers to the exploitation of potential areas.

[0105] In the odor attack strategy, the CP will secrete a foul odor and spread it in the surrounding area to prevent predators from approaching it. In order to mathematically simulate this behavior, the present invention proposes the following formula:

[0106]

[0107] Among them, r3 is a random number between [1,N], and δ is a parameter used to control the search direction. is the position of the ith individual at iteration t, γ t is the defense factor defined using τ3. τ3 is a random value in the interval [0,1], is the defined odor diffusion factor.

[0108] As shown below:

[0109]

[0110]

[0111] in, represents the objective function value of the ith individual at iteration t, ε is a small value to avoid division by zero, rand is a vector of randomly generated numbers between 0 and 1, rand is a variable containing randomly generated numbers between 1 and 0, N is the population size, t is the number of the current iteration, and t max is the maximum number of iterations.

[0112] The U1 vector is used to simulate three possible situations during the odor attack on the predator, corresponding to:

[0113] (1) When U1 is equal to 0, CP will stop odor diffusion because the predator will stop moving due to fear of CP, so the distance between the predator and CP remains unchanged;

[0114] (2) When U1 is equal to 1, the CP will emit a significant odor due to the presence of the predator nearby;

[0115] (3) When U1 is a combination of 0 and 1, the predator maintains a safe distance from the CP, and therefore, there is no need to release its scent extensively.

[0116] Regarding improvement point 4:

[0117] In order to maintain the diversity of the population and speed up the convergence, the improved CPO algorithm also proposes a new way to simulate that not all CPs activate the defense mechanism, but only those CPs that are threatened will activate the defense mechanism. The specific mathematical function is as follows:

[0118]

[0119] Where N represents the population size of the current iteration, N min represents the minimum population size set in the algorithm, N′ represents the initial population size or the maximum population size, T represents the current number of iterations, and T max Represents the maximum number of iterations set in the algorithm, Represents the remainder of the current number of iterations divided by the total number of iterations, that is: This remainder is used to determine the position of the current iteration in the total number of iterations. This position is then used to calculate the reduction in population size.

[0120] As the number of iterations increases, the population size will gradually decrease from N′ to N min .item Represents the ratio of population size reduction. As the number of iterations increases, this ratio gradually decreases, resulting in a decrease in population size. The purpose of the entire formula is to gradually reduce the population size during the iteration process, thereby encouraging exploration (larger population size) in the early stages of the algorithm and encouraging exploitation (smaller population size) in the later stages. This dynamic adjustment helps improve efficiency and solution quality.

[0121] Regarding improvement point 5:

[0122] After the global search of the CPO algorithm is completed, a number of points are selected as the initial points of the Newton method according to the results of the global search, and the Newton method is introduced for local search:

[0123] For each initial point, calculate the gradient vector and Hessian matrix of the objective function at that point:

[0124]

[0125] Iterative update formula: Using the information of gradient and Hessian matrix, the current solution is updated through the iterative formula of Newton's method:

[0126] Here, x new is the updated solution, x old is the current solution.

[0127] Introducing the downhill factor:

[0128]

[0129] Among them, λ is the downhill factor, which is used to ensure the decrease of the function value.

[0130] The step size for each search is determined by adaptively adjusting the step size:

[0131]

[0132] Here, α k is the step size determined by the line search technique.

[0133] Termination condition check: The iteration process should include a check of the termination condition, such as whether the norm of the gradient is less than a preset threshold or whether the number of iterations reaches an upper limit:

[0134]

[0135] When the norm of the gradient is less than the preset threshold ∈ When , the algorithm stops iterating and outputs the optimal solution.

[0136] The fast convergence characteristics of Newton's method and the global search capability of the CPO algorithm are combined to improve the efficiency and accuracy of path planning.

[0137] Figure 3 The robot path planning based on the improved crested porcupine algorithm on the grid map is shown. The red squares in the figure represent obstacles, the green squares represent the end point, and the pink circle represents the starting point. The blue path is the route that the robot takes under the guidance of the algorithm, starting from the starting point, avoiding obstacles, and finally reaching the end point. The improved crested porcupine algorithm enables the robot to successfully avoid obstacles and find a better path in the grid map.

[0138] Figure 4 The figure below is a performance comparison between the improved crested porcupine algorithm and the RIME algorithm. The three-dimensional graph on the left shows a typical optimization function, which is used to test the performance of the algorithm on different problems. The convergence curve graph on the right shows the trend of the fitness values ​​of the two algorithms as the number of iterations changes. As can be seen from the figure, the improved crested porcupine algorithm represented by the red curve is superior to the RIME algorithm (pink curve) in terms of convergence speed and final fitness value, indicating that the improved crested porcupine algorithm has better performance on this optimization problem.

[0139] The above description is only a preferred embodiment of the present invention. It should be pointed out that a person skilled in the art can make several improvements without departing from the principle of the present invention, and these improvements should also be regarded as within the protection scope of the present invention.

Claims

1. A path planning method for an outdoor two-wheeled robot based on an improved crown porcupine optimization algorithm, characterized in that: The steps include: S1: The user activates the two-wheeled robot through terminal commands, stabilizes the camera and adjusts it to the working state, ensures the stable operation of sensors and actuators, and creates a grid map of the environment with the target to be detected as the end point and the robot's own coordinates as the starting point; S2: Improve the crown porcupine optimization algorithm. The improvements are as follows: (1) Introduce Kent mapping to initialize the population position of the crown porcupine optimization algorithm; (2) In the development evolutionary iteration phase of the crested porcupine optimization algorithm, the NSGA-II algorithm is used to solve the multi-objective optimization problem, maintain population diversity through non-dominated sorting and crowding calculation, and generate the Pareto optimal solution set; (3) When a predator approaches, the crested porcupine uses a mathematical function to simulate the crested porcupine's behavior of attacking the predator with its scent; (4) By setting up mathematical functions, it is simulated that only the threatened crested porcupine activates its defense mechanism; (5) Based on the global search, the Newton method is introduced to perform local search strategy, and the approximate solution found is locally optimized to improve the smoothness and optimization degree of the path; S3: Input the path grid map created in S1 into the improved crested porcupine optimization algorithm and output the optimal path.

2. The path planning method for an outdoor two-wheeled robot based on an improved crown porcupine optimization algorithm as claimed in claim 1, characterized in that: The initial population sequence is randomly generated by the Kent chaotic map, and the introduced Kent chaotic map formula is defined as: Where a is the control parameter that determines the behavior of the chaotic map, and its value is in the open interval (0,1). When the value of the control parameter a is different, the Kent map will exhibit different dynamic behaviors; x n is the current iteration state, x n+1 is the state of the next iteration.

3. The path planning method for an outdoor two-wheeled robot based on an improved crown porcupine optimization algorithm as claimed in claim 1, characterized in that: The formula of the crown porcupine optimization algorithm starting the search process from the initial individual set is: Among them, N represents the number of individuals, that is, the population size; X i is the i-th candidate solution in the search space, L and U are the lower and upper limits of the search range, respectively, and r is a random number between 0 and 1; By considering multiple objectives in path planning, a multi-objective optimization model is established: minf(X)=(f1(X), f2(X), f3(X)) Where f1(X) is the path length, f2(X) is the smoothness, and f3(X) is the energy consumption; X represents the decision variable of the path planning problem, that is, the coordinates of the path points; The NSGA-II algorithm is used to solve the multi-objective optimization problem. The process is as follows: For any two solutions x in the population i and x j ,if And there exists some l such that f l (x i )<f l (x j ), then x i Dominate x j ; For each solution x i The crowding degree d on the kth target k (x i ) is calculated as: Among them, f k (x i +1) and f k (x i -1) are x i The objective function value of the neighboring solutions on target k; Using a selection strategy based on non-dominated sorting and crowding calculation, individuals are selected from the current population to enter the next generation with a selection probability P(x i ) is expressed as: Among them, F j is the number of solutions in the jth front; Through the newly generated population, fast non-dominated sorting is performed to form new frontiers F1 and F2.

4. The path planning method for an outdoor two-wheeled robot based on an improved crown porcupine optimization algorithm as claimed in claim 1, characterized in that: When a predator approaches, the crested porcupine uses a mathematical function to simulate the crested porcupine's behavior of taking the scent to attack the predator. The mathematical function is: Among them, r3 is a random number between [1, N], and δ is a parameter used to control the search direction; is the position of the ith individual at iteration t, γ t is the defense factor defined by the user; τ3 is a random value in the interval [0,1], is the defined odor diffusion factor; As shown below: in, represents the objective function value of the ith individual at iteration t, ε is a small value to avoid division by zero, rand is a vector of randomly generated numbers between 0 and 1, rand is a variable containing randomly generated numbers between 1 and 0, N is the population size, t is the number of the current iteration, and t max is the maximum number of iterations; the U1 vector is used to simulate the possible situations that may occur during the odor attack on the predator.

5. The path planning method for an outdoor two-wheeled robot based on an improved crown porcupine optimization algorithm as claimed in claim 4, characterized in that: By setting a mathematical function, it is simulated that only the threatened crested porcupine activates the defense mechanism. The specific mathematical function is as follows: Where N represents the population size of the current iteration, N min represents the minimum population size set in the algorithm, N′ represents the initial population size or the maximum population size, T represents the current number of iterations, and T max Represents the maximum number of iterations set in the algorithm, Represents the remainder of the current number of iterations divided by the total number of iterations, that is: This remainder is used to determine the position of the current iteration in the total number of iterations, which is then used to calculate the reduction in population size; As the number of iterations increases, the population size will gradually decrease from N′ to N min ,item Indicates the proportion by which the population size decreases.

6. The path planning method for an outdoor two-wheeled robot based on an improved crested porcupine optimization algorithm as claimed in claim 1, characterized in that: After the global search of the crown porcupine optimization algorithm is completed, a number of points are selected as the initial points of the Newton method according to the results of the global search, and the Newton method is introduced for local search: For each initial point, calculate the gradient vector and Hessian matrix of the objective function at that point: Iterative update formula: Using the information of gradient and Hessian matrix, the current solution is updated through the iterative formula of Newton's method: Among them, x new is the updated solution, x old is the current solution; Introducing the downhill factor: Among them, λ is the downhill factor, which is used to ensure the decrease of the function value; The step size for each search is determined by adaptively adjusting the step size: Among them, α k is the step size determined by the line search technique; Termination condition check: The iteration process includes a termination condition check, which is: whether the norm of the gradient is less than the preset threshold or whether the number of iterations reaches the upper limit: When the norm of the gradient is less than the preset threshold ∈, the algorithm stops iterating and outputs the optimal solution.

Images