CN115097814A - Mobile robot path planning method, system and application based on improved PSO algorithm - Google Patents
Mobile robot path planning method, system and application based on improved PSO algorithm Download PDFInfo
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Abstract
The invention belongs to the field of mobile robot path planning, and discloses a mobile robot path planning method, a mobile robot path planning system and application based on an improved PSO algorithm, wherein a fitness function is constructed to integrate two evaluation functions which respectively consider path length and obstacle risk; a bidirectional learning strategy is introduced into the improved PSO algorithm to enlarge the search range of particles and enrich the diversity of populations; in a bidirectional learning strategy, in order to overcome the problem that the optimization process cannot be well regulated when a complex function is optimized, a double self-adaptive strategy is provided, and the search behavior of particles in a group is well balanced. Then, through an attraction-repulsion strategy, the particles can be guided by the globally optimal particles and the globally worst particles respectively to evolve towards a better direction, and the local optimization performance and the convergence capability of the algorithm are improved. The invention completes the path planning method framework based on the improved PSO algorithm and realizes the optimal path planning of the robot in the static environment.
Description
Technical Field
The invention belongs to the field of mobile robot path planning, and particularly relates to a mobile robot path planning method based on an improved PSO algorithm.
Background
With the development of science and technology, mobile robots are widely used in different fields, such as robot rescue, robot patrol, robot monitoring and the like, wherein path planning is one of important skills of mobile robots. Rational path planning makes it possible to plan a smooth path from the starting point to the target point that is shortest and collision-free while the robot is performing the task. Due to the complex working environment of the robot, it is difficult to find the shortest and smooth path. Therefore, on the premise of meeting all constraint conditions, the method for planning the path under the optimal indexes (time, distance, energy consumption and the like) has important theoretical value and practical significance.
The current classical path planning methods can be divided into two broad categories.
One path planning method is a variation of some common methods such as artificial potential field methods and roadmap planning methods. In the manual potential field method, when the attraction force and the repulsion force at a certain point are equal and opposite in direction, the robot considers that the robot reaches a target point, stops moving or wanders in a certain area. Route map planning methods as the number of obstacles increases, the number of connections between vertices increases, resulting in increased planning complexity and planning time.
The other path planning method is a heuristic method, and the main heuristic methods adopted in the robot path planning include simulated annealing, genetic algorithm and particle swarm algorithm. Using heuristic algorithms, although there is no guarantee that a solution can be found, it will be much faster than a deterministic approach if a solution is found.
The PSO algorithm is used as an intelligent optimization algorithm, has the advantages of high searching speed, easiness in implementation and the like, and is widely applied to solving the problems of path planning, target searching and the like. In order to prevent the particle swarm optimization from falling into local optimum due to premature convergence in the searching process, scholars at home and abroad propose a plurality of improved particle swarm optimization. However, due to the existence of adjustable parameters such as the inertia weight w and the learning factor c of the algorithm, if the algorithm is improperly set, the problems of premature convergence and slow convergence speed exist in the optimization process of the algorithm, and the planned path is not optimal.
In order to overcome the above disadvantages, it is therefore desirable to develop a new PSO optimization method that achieves the shortest path planning and no collision for the mobile robot.
The difficulty of the problem that the above-mentioned prior art exists is solved: due to the adjustability of parameters such as PSO algorithm population size, inertia weight and learning factor, how to reasonably set the value set by such parameters and avoid the phenomena of premature convergence and even lack of population diversity of the PSO algorithm in the local optimal problem, the algorithm performance is improved, the mobile robot plans an optimal path, and the reduction of resource waste is a difficult point of the technology.
The significance of solving the problems existing in the prior art is as follows: the mobile robot path planning method based on the improved PSO algorithm can obviously improve the optimization effect of the basic PSO algorithm, effectively solves the problems of overlong path, unsmooth path and the like when the basic PSO algorithm is applied to path planning, and has the advantages of low energy consumption, small abrasion and the like.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a mobile robot path planning method based on an improved PSO algorithm.
The invention is realized by finding out a barrier-free path with low energy consumption aiming at the mobile robot working in a complex environment.
A mobile robot path planning method based on improved PSO algorithm, the fitness function constructed by the method integrates two evaluation functions which respectively consider path length and obstacle risk;
a bidirectional learning strategy is introduced into the improved PSO algorithm to enlarge the search range of particles and enrich the diversity of populations;
in the bidirectional learning strategy, the searching behaviors of particles in a group are balanced by using a dual self-adaptive strategy; through an attraction-repulsion strategy, the particles can be guided by the globally optimal particles and the globally worst particles respectively to evolve towards a better direction;
and realizing the optimal path planning of the robot in a static environment based on a path planning method framework of an improved PSO algorithm.
Further, the method comprises the following steps:
step 1: constructing a path planning optimization model f according to the path length cost L and the robot obstacle avoidance cost Ls;
step 2: initializing relevant parameters of a particle swarm algorithm;
and step 3: evaluating a path planning optimization model f;
and 4, step 4: sorting f from the best to the worst, randomly selecting a better individual from the group as a learning object xk by each individual, and updating the global optimal individual gbesti and the global worst individual gwesti;
and 5: adaptively updating a learning factor c, an inertia weight w and a choice factor F through the related parameters;
step 6: if R < F, adopting a bidirectional learning strategy, and updating the position xi and the speed vi of the particle; otherwise, updating the particle position xi by adopting an attraction and repulsion strategy;
and 7: updating the fitness function value f;
and 8: judging the iteration times, if the iteration times T reach the maximum times T, outputting an optimal result, and stopping operation; otherwise, t is t +1, and the step 4 is returned.
Further, the specific calculation formula of the path length L is:
wherein, (xi, yi) is a path node, n path nodes are total, and L is the sum of the lengths of the adjacent path nodes at the time t and represents the length of the path at the time t;
the barrier threat cost Ls for the mth path is defined as:
wherein, it is assumed that it is a circular obstacle, rk is the radius of the circular obstacle, and k is the k (k is 1,2, …, g) th obstacle; lk is the distance from the center of the circle to each section of path, then
Is the shortest distance from the path to the obstacle;
calculating a mobile robot path planning optimization model f according to the formula (1) and the formula (2):
f＝u 1 L+u 2 L s (3)
wherein u is 1 、u 2 Is [0,1 ]]Internal inertial weight factor.
Further, in step 2, the initialized relevant parameters include: population size M, particle dimension D, maximum iteration number T, adaptive learning factor c, and maximum learning factor c max Minimum value c min (ii) a Inertia weight w, maximum inertia weight w max Minimum value w min (ii) a The initial particle position xi and the velocity parameter vi; an adaptive choice factor F.
Further, the specific formula for updating the adaptive learning factor c through the relevant parameters is as follows:
wherein fit is the fitness value of the current particle individual, and fit is max Is the largest fitness value among the current generation of particles.
Further, the specific formula for updating the adaptive inertial weight w through the relevant parameters is as follows:
wherein A is a parameter for controlling the curvature of the curve, and t is the current iteration number; and T is the maximum iteration number.
Further, the specific formula of the adaptive decision factor F updated by the correlation parameter is as follows:
wherein d is 1 、d 2 Deciding an upper limit and a lower limit of a factor, wherein a is a parameter for controlling the curvature of a curve, and t is the current iteration number; and T is the maximum iteration number.
Further, the specific formula for calculating the particle velocity vi and the particle position xi is as follows:
1) if R < F adopts a bidirectional learning strategy, the calculation formula of the particle speed vi and the particle position xi is as follows:
xi(t+1)＝xi(t)+vi(t+1) (8)
wherein i is the ith particle, i is 1,2, … N; xk is a learning object, and r1 is a uniform random number.
2) If the attraction-repulsion strategy is adopted when R is larger than or equal to F, the calculation formula of the particle speed vi and the particle position xi is as follows:
x i (t+1)＝r 2 x i (t)+r 3 (gbest i (t)-x i (t))-r 3 (gworst i (t)-x i (t)) (9)
wherein r is 2 Is a uniform random number, r 3 ＝1/2(1-r 2 )，gbest i Global optimal individual, gworst i Global worst individual.
Another object of the present invention is to provide a mobile robot path planning system based on an improved PSO algorithm, which applies the mobile robot path planning method based on an improved PSO algorithm, including: the system comprises an environment modeling unit, an initialization parameter unit, a path searching unit and an optimal path output unit;
the environment modeling unit acquires working environment information by using a self-contained sensor group of the robot, and constructs a path planning optimization model f according to the path length cost L and the obstacle avoidance cost Ls of the robot;
the initialization parameter unit is used for initializing the related parameters of the particle swarm algorithm;
the path searching unit adaptively updates a learning factor c, an inertia weight w and a decision factor F through the relevant parameters;
if R < F, adopting a bidirectional learning strategy, and updating the position xi and the speed vi of the particle; otherwise, updating the particle position xi by adopting an attraction and repulsion strategy; updating the fitness function value f;
the optimal path output unit is used for evaluating a path planning optimization model f, sequencing the f from the best to the bad, randomly selecting a better individual from a group as a learning object xk by each individual, and updating the global optimal individual gbesti and the global worst individual gwesti.
It is another object of the present invention to provide a computer-readable storage medium storing a computer program which, when executed by a processor, causes the processor to perform the steps of:
collecting working environment information by using a self-contained sensor group of the robot, and constructing a path planning optimization model f according to the path length cost L and the obstacle avoidance cost Ls of the robot;
initializing relevant parameters of a particle swarm algorithm;
the path searching unit adaptively updates a learning factor c, an inertia weight w and a choice factor F through the relevant parameters;
if R < F, adopting a bidirectional learning strategy, and updating the position xi and the speed vi of the particle; otherwise, updating the particle position xi by adopting an attraction and repulsion strategy; updating the fitness function value f;
and evaluating a path planning optimization model f, sequencing f from good to bad, randomly selecting a better individual from a group as a learning object xk by each individual, and updating the global optimal individual gbesti and the global worst individual gwesti.
Another object of the present invention is to provide an information data processing terminal for implementing the above-mentioned mobile robot path planning system based on the improved PSO algorithm.
The invention has the advantages and positive effects that:
the mobile robot path planning method based on the improved PSO algorithm constructs a path planning objective function comprising path length and collision punishment between the mobile robot and the barrier. A method combining a two-way learning strategy and an attraction and repulsion strategy is provided, so that the improved PSO algorithm improves the global optimizing capability and the local searching capability at the same time. In addition, a double self-adaptive optimization strategy is adopted to perform self-adaptive adjustment on the inertia weight and the learning factor in the bidirectional learning strategy, so that the global optimizing capability and the local optimizing capability of the algorithm reach better balance capability. Finally, the invention completes the framework of path planning of the mobile robot by utilizing the improved PSO algorithm. The invention not only can realize the balance of global searching capability and local searching capability, but also can realize the path planning and solving of the mobile robot with low consumption and no collision.
Drawings
FIG. 1 is a schematic diagram of a mobile robot path planning method based on an improved PSO algorithm;
FIG. 2 is a block diagram of a mobile robot path planning system based on an improved PSO algorithm;
FIG. 3 is a particle fitness ranking graph;
FIG. 4 is a comparison graph of the movement locus of a two-dimensional path mobile robot of a traditional PSO algorithm and an improved PSO algorithm;
fig. 5 is a graph of the optimal fitness of a conventional PSO algorithm versus an improved PSO algorithm.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to the following embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
The application of the principles of the present invention will be further described with reference to the accompanying drawings and specific embodiments.
Example 1:
in order to solve the problems that due to the existence of adjustable parameters such as inertia weight w and learning factor c, if the parameters are not properly set, premature convergence and slow convergence speed exist in the optimization process of the algorithm, the planned path is not optimal, and further the operation efficiency and quality of the mobile robot in a two-dimensional environment are affected, as shown in fig. 1, the embodiment provides a flow diagram of a mobile robot path planning method based on an improved PSO algorithm, which comprises the following steps:
step 1: constructing a path planning optimization model f according to the path length cost L and the obstacle avoidance cost Ls of the robot;
and 2, step: initializing relevant parameters of a particle swarm algorithm;
and 3, step 3: evaluating a path planning optimization model f;
and 4, step 4: sorting f from the best to the poor, randomly selecting a better individual from the group as a learning object xk by each individual, and updating the global optimal individual gbesti and the global worst individual gwesti;
and 5: adaptively updating a learning factor c, an inertia weight w and a choice factor F through the related parameters;
step 6: if R < F, adopting a bidirectional learning strategy, and updating the position xi and the speed vi of the particle; otherwise, updating the particle position xi by adopting an attraction and repulsion strategy;
and 7: updating the fitness function value f;
and 8: judging the iteration times, if the iteration times T reach the maximum times T, outputting an optimal result, and stopping operation; otherwise, t is t +1, and the procedure returns to step 4.
Further, the specific calculation formula of the path length L is:
wherein, (xi, yi) is a path node, n path nodes are total, and L is the sum of the lengths of the adjacent path nodes at the time t and represents the length of the path at the time t;
the barrier threat cost Ls for the mth path is defined as:
it is assumed that it is a circular obstacle, rk is the radius of the circular obstacle, and k is the k-th (k is 1,2, …, g) obstacle(ii) a lk is the distance from the center of the circle to each section of path, then
Is the shortest distance from the path to the obstacle;
calculating a mobile robot path planning optimization model f according to the formula (1) and the formula (2):
f＝u 1 L+u 2 L s (3)
wherein u 1 、u 2 Is [0,1 ]]Internal inertial weight factor.
In step 2, the initialized relevant parameters include: population size M, particle dimension D, maximum iteration number T, adaptive learning factor c, and maximum learning factor c max Minimum value c min (ii) a Inertia weight w, maximum inertia weight w max Minimum value w min (ii) a The initial particle position xi and the velocity parameter vi; an adaptive choice factor F.
The specific formula for updating the adaptive learning factor c through the related parameters is as follows:
wherein fit is the fitness value of the current particle individual, and fit is max Is the largest fitness value among the current generation of particles.
The specific formula for updating the adaptive inertial weight w through the related parameters is as follows:
wherein A is a parameter for controlling the curvature of the curve, and t is the current iteration number; and T is the maximum iteration number.
The specific formula of the adaptive choice factor F updated by the related parameters is as follows:
wherein d is 1 、d 2 Deciding the upper and lower limits of a factor, wherein a is a parameter for controlling the curvature of the curve, and t is the current iteration number; and T is the maximum iteration number.
The specific formula for calculating the particle velocity vi and the particle position xi is as follows:
1) if R < F adopts a bidirectional learning strategy, the calculation formula of the particle speed vi and the particle position xi is as follows:
xi(t+1)＝xi(t)+vi(t+1) (8)
wherein i is the ith particle, i is 1,2, … N; xk is a learning object, and r1 is a uniform random number.
2) If R is larger than or equal to F and an attraction and repulsion strategy is adopted, the calculation formula of the particle speed vi and the particle position xi is as follows:
x i (t+1)＝r 2 x i (t)+r 3 (gbest i (t)-x i (t))-r 3 (gworst i (t)-x i (t)) (9)
wherein r is 2 Is a uniform random number, r 3 ＝1/2(1-r 2 )，gbest i Global optimal individual, gworst i Global worst individual.
As shown in fig. 2, an embodiment of the present invention provides a mobile robot path planning system based on an improved PSO algorithm, which applies the mobile robot path planning method based on the improved PSO algorithm, and includes: the system comprises an environment modeling unit, an initialization parameter unit, a path searching unit and an optimal path output unit;
the environment modeling unit acquires working environment information by using a sensor group of the robot and constructs a path planning optimization model f according to the path length cost L and the obstacle avoidance cost Ls of the robot;
the initialization parameter unit is used for initializing the related parameters of the particle swarm algorithm;
the path searching unit adaptively updates a learning factor c, an inertia weight w and a decision factor F through the relevant parameters;
if R < F, adopting a bidirectional learning strategy, and updating the position xi and the speed vi of the particle; otherwise, updating the particle position xi by adopting an attraction and repulsion strategy; updating the fitness function value f;
the optimal path output unit is used for evaluating a path planning optimization model f, sorting the f from good to bad, randomly selecting a better individual from a group as a learning object xk by each individual, and updating the global optimal individual gbesti and the global worst individual gwesti.
An embodiment of the present invention provides a computer-readable storage medium, in which a computer program is stored, and when the computer program is executed by a processor, the processor is caused to execute the following steps:
acquiring working environment information by using a self-contained sensor group of the robot, and constructing a path planning optimization model f according to the path length cost L and the obstacle avoidance cost Ls of the robot;
initializing relevant parameters of a particle swarm algorithm;
the path searching unit adaptively updates a learning factor c, an inertia weight w and a decision factor F through the relevant parameters;
if R < F, adopting a bidirectional learning strategy, and updating the position xi and the speed vi of the particle; otherwise, updating the particle position xi by adopting an attraction and repulsion strategy; updating the fitness function value f;
and evaluating a path planning optimization model f, sequencing f from good to bad, randomly selecting a better individual from a group as a learning object xk by each individual, and updating the global optimal individual gbesti and the global worst individual gwesti.
The embodiment of the invention provides an information data processing terminal, which is used for realizing the mobile robot path planning system based on the improved PSO algorithm.
Example 2:
in order to verify the feasibility and effectiveness of the mobile robot path planning method based on the improved PSO algorithm provided in embodiment 1, this embodiment is verified by a specific numerical simulation comparison experiment with the conventional PSO algorithm:
specifically, assume that the path planning model is established as follows: assuming that the robot avoids 5 static obstacles and moves from a starting point (0, 0) to a target point (6, 8), which are represented by circles with different radii, the position information of the static obstacles is shown in table 1:
TABLE 1 obstacle position information and radius size
According to the mobile robot path planning model f and the related data, an improved PSO algorithm is applied to optimize and select an optimal path motion track, wherein specific parameters are set as follows:
the population size M is 100, the maximum iteration number T is 400, c max ＝2、c min ＝0.5；w max ＝0.8、 w min ＝0.1A＝0.4；d 1 ＝0.4、d 2 ＝0.6，a＝10。
As can be seen from fig. 4, the improved PSO algorithm designed by the invention can realize the path planning task of the mobile robot. Compared with the traditional PSO algorithm, the improved PSO algorithm disclosed by the invention has the advantages that the planned paths when 1,2 and 5 obstacles are detected enable the robot to move along the edges of the obstacles, the movement track of the robot is smoother, and the shaft abrasion and the energy consumption of wheels of the robot under the real condition are reduced; in addition, as can be seen from fig. 5, the path of the method is shorter, and the purpose of reducing energy consumption can be achieved.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and should not be taken as limiting the scope of the present invention, which is intended to cover any modifications, equivalents, improvements, etc. within the spirit and scope of the present invention.
Claims (9)
1. A mobile robot path planning method based on an improved PSO algorithm is characterized by comprising the following steps:
step 1: constructing a path planning optimization model f according to the path length cost L and the obstacle avoidance cost Ls of the robot;
step 2: initializing relevant parameters of a particle swarm algorithm;
and step 3: evaluating a path planning optimization model f;
and 4, step 4: sorting f from the best to the worst, randomly selecting a better individual from the group as a learning object xk by each individual, and updating the global optimal individual gbesti and the global worst individual gwesti;
and 5: adaptively updating a learning factor c, an inertia weight w and a choice factor F through the related parameters;
step 6: if R is less than F, adopting a bidirectional learning strategy to update the position xi and the speed vi of the particle; otherwise, updating the particle position xi by adopting an attraction and repulsion strategy;
and 7: updating the fitness function value f;
and 8: judging the iteration times, if the iteration times T reach the maximum times T, outputting an optimal result, and stopping operation; otherwise, t is t +1, and the step 4 is returned.
2. The mobile robot path planning method based on the improved PSO algorithm according to claim 1, wherein the specific calculation formula of the path length L is:
wherein, (xi, yi) is a path node, n path nodes are total, and L is the sum of the lengths of the adjacent path nodes at the time t and represents the length of the path at the time t;
the barrier threat cost Ls for the mth path is defined as:
wherein, it is assumed that it is a circular obstacle, rk is the radius of the circular obstacle, and k is the k (k is 1,2, …, g) th obstacle; lk is the distance from the center of a circle to each path, then
The shortest distance from the path to the obstacle;
calculating a mobile robot path planning optimization model f according to the formula (1) and the formula (2):
f＝u 1 L+u 2 L s (3)
wherein u is 1 、u 2 Is [0,1 ]]An internal inertial weight factor;
in step 2, the initialized relevant parameters include: population size M, particle dimension D, maximum iteration number T, adaptive learning factor c and maximum learning factor c max Minimum value c min (ii) a Inertia weight w, maximum value of inertia weight w max Minimum value w min (ii) a The initial particle position xi and the velocity parameter vi; an adaptive choice factor F.
3. The PSO algorithm-based mobile robot path planning method according to claim 2, wherein the specific formula for updating the adaptive learning factor c through the relevant parameters is as follows:
wherein fit is the fitness value of the current particle individual, and fit is max Is the largest fitness value among the current generation of particles.
4. The improved PSO algorithm-based mobile robot path planning method according to claim 3, wherein the specific formula for updating the adaptive inertial weight w through the relevant parameters is as follows:
wherein A is a parameter for controlling the curvature of the curve, and t is the current iteration number; and T is the maximum iteration number.
5. The improved PSO algorithm based mobile robot path planning method according to claim 2, wherein the specific formula of the adaptive decision factor F updated by the related parameters is:
wherein, d 1 、d 2 Deciding the upper and lower limits of a factor, wherein a is a parameter for controlling the curvature of the curve, and t is the current iteration number; and T is the maximum iteration number.
6. The improved PSO algorithm-based mobile robot path planning method according to claim 2, characterized in that the particle velocity v is calculated i And the particle position x i The concrete formula of (1) is as follows:
1) if R < F adopts a bidirectional learning strategy, the calculation formula of the particle speed vi and the particle position xi is as follows:
xi(t+1)＝xi(t)+vi(t+1) (8)
wherein i is the ith particle, i is 1,2, … N; xk is a learning object, and r1 is a uniform random number.
2) If R is larger than or equal to F and an attraction and repulsion strategy is adopted, the calculation formula of the particle speed vi and the particle position xi is as follows:
x i (t+1)＝r 2 x i (t)+r 3 (gbest i (t)-x i (t))-r 3 (gworst i (t)-x i (t)) (9)
wherein r is 2 Is a uniform random number, r 3 ＝1/2(1-r 2 )，gbest i Global optimal individual, gworst i Global worst individual.
7. An improved PSO algorithm-based mobile robot path planning system applying the improved PSO algorithm-based mobile robot path planning method according to any one of claims 1-6, characterized in that the improved PSO algorithm-based mobile robot path planning system comprises: the system comprises an environment modeling unit, an initialization parameter unit, a path searching unit and an optimal path output unit;
the environment modeling unit acquires working environment information by using a sensor group of the robot and constructs a path planning optimization model f according to the path length cost L and the obstacle avoidance cost Ls of the robot;
the initialization parameter unit is used for initializing the related parameters of the particle swarm algorithm;
the path searching unit adaptively updates a learning factor c, an inertia weight w and a decision factor F through the relevant parameters;
if R is less than F, adopting a bidirectional learning strategy to update the position xi and the speed vi of the particle; otherwise, updating the particle position xi by adopting an attraction and repulsion strategy; updating the fitness function value f;
the optimal path output unit is used for evaluating a path planning optimization model f, sorting the f from good to bad, randomly selecting a better individual from a group as a learning object xk by each individual, and updating the global optimal individual gbesti and the global worst individual gwesti.
8. A computer-readable storage medium storing a computer program which, when executed by a processor, causes the processor to perform the steps of:
collecting working environment information by using a self-contained sensor group of the robot, and constructing a path planning optimization model f according to the path length cost L and the obstacle avoidance cost Ls of the robot;
initializing relevant parameters of a particle swarm algorithm;
the path searching unit adaptively updates a learning factor c, an inertia weight w and a choice factor F through the relevant parameters;
if R is less than F, adopting a bidirectional learning strategy to update the position xi and the speed vi of the particle; otherwise, updating the particle position xi by adopting an attraction and repulsion strategy; updating the fitness function value f;
and evaluating a path planning optimization model f, sequencing f from good to bad, randomly selecting a better individual from a group as a learning object xk by each individual, and updating the global optimal individual gbesti and the global worst individual gwesti.
9. An information data processing terminal, characterized in that the information data processing terminal is used for implementing the mobile robot path planning system based on the improved PSO algorithm according to claim 7.
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| CN115576332B (en) * | 2022-12-07 | 2023-03-24 | 广东省科学院智能制造研究所 | Task-level multi-robot collaborative motion planning system and method |
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