Multi-robot path planning using improved particle swarm optimization algorithm through novel evolutionary operators

https://doi.org/10.1016/j.asoc.2020.106312Get rights and content

Highlights

  • Kinematic analysis and design of objective function have been critically analyzed.

  • The concept of democracy has been incorporated in the inbuilt PSO equation.

  • Subsequently, PSO has been modified though Evolutionary operators.

  • It was employed to navigate the robots in shortest path and use of minimum energy.

  • The performance of the algorithm confirms the avoidance of deadlock situation.

  • The robustness of the algorithm verified through the comparison with state of arts.

Abstract

The highlight of this paper is to propose an innovative approach to compute an optimal collision free trajectory path for each robot in a known and complex environment. The problem under consideration has been solved by employing an improved version of particle swarm optimization (IPSO) with evolutionary operators (EOPs). In the present context, PSO is improved with the concept of governance in human society and two evolutionary operators such as multi-crossover inherited from the genetic algorithm, and bee colony operator to enhance the intensification capability of the IPSO algorithm. The algorithm proposed to compute the deadlock free subsequent coordinate of an individual robot from their present coordinate, in addition, to minimize the path length for each robot by maintaining a good balance between intensification and diversification. Results obtained from the proposed IPSO-EOPs have been compared with competitors such as DE and IPSO in a similar environment to substantiate the robustness and usefulness of the algorithm. It perceives from the result obtained from simulation and experimentation that IPSO-EOPs is succeeding IPSO, and DE in terms of arrival time, generating a safe optimal path, and energy utilization during the travel.

Introduction

A robot is a controlled manipulator, capable of taking a decision, performing complex tasks like human beings [1]. A robot can be extremely precious in various precarious situations where humans are not capable to reach certain targets because of terrain locations and dangerous environments. The multi-robot System (MRS) employs a group of the robot to perform a certain task through collective behavior. A various complex situation that is incomprehensible for a single robot would be achieved through the combined behavior of MRS. There are a few anticipated advantages of MRS contrasted with single robot frameworks such as to increase the ability for resolving the complexity of the task, enhancing the performance, including fast task completion time, increase in robustness, reliability, and simplicity in the scheme. These advantages have attracted many researchers to investigate and create strong adaptable MRS by solving numerous challenging problems such as object tracking, cooperative formation, exploration, industrial transportation, cooperative task handling, target tracking, human material handling, a military mission to name just a few. The main objective of autonomous mobile robotics is to develop a physical framework that can provide autonomy to robots for autonomous navigation tenaciously without the intervention of human operators in a cluttered known environment. Robot navigation is a process to find the goal location by keeping away from the obstacles in its pathway from the source position [2] by satisfying constraints like distance, energy and time [3], [4], [5], [6], [7]. This process consists of four separate modules: (1) perception, the robot extracts the necessary information through sensors; (2) localization, the robot determines to steer its position in the environment; (3) planning of the path, the robot decides its steering direction to achieve the goal position by avoiding obstacles; (4) motion control, adjust the motion to generate the required trajectory of the path [8], [9], [10]. The Robot Path planning has undergone a sequence of rotation and translation to reach the destination from their predefined initial position by keeping away from the obstacles on its pathway. The development of different meta-heuristic techniques to provide autonomy to mobile robots in path planning is one of the most challenging fields in the current exploration. This inclination is encouraged to overcome the current gap between the existing technologies and demands of the new application, e.g., the present industrial robots have low flexibility in autonomy. The main objective of the multiple mobile robots’ path planning is to compute an optimal collision free trajectory path from predefined source to target for each robot without colliding with any teammates or obstacles in the workspace [11]. Depending on the position of the robot in the environment and techniques, employed to resolve the path planning problem is presented in Fig. 1.

One of the most challenging problems in MRS is to compute an optimal collision free trajectory path for each robot to improve the system performance subjected to a set of constraints. One of the classical ways is to send the robot to discover its environment for localizing the landmark that can be used in path planning. In this situation, the robot trusts deeply on its sensors, map construction, and update its position. However, the environment consists of a large amount of uncertainty and mapping techniques take a large amount of memory, time and incapable to generate the optimality on the path.

In the last decades, several classical approaches have been developed for solving on MRS by the research community such as classical approaches are Road map method, potential field method, cell decomposition, Simulated Annealing [12], Voronoi-diagram [13], visibility graph-based, A* Algorithm [14], [15], [16], neural network and so on. Most of the classical approaches have been given attention to optimizing the path distance. But, the following weaknesses are associated with the traditional approaches [17] such as (1) larger problem space, involves more computational complexity and (2) there is a great chance that the solution of the problem space under consideration may fall at local minima. Therefore, these weaknesses cause the traditional approaches wasteful in the various problem spaces. A direction of current research in the robot system focuses on not only an accurate control of robot manipulators but also empowering them with intelligence.

Hence, an intelligent technique such as computational intelligence begins with the underlying principle of artificial intelligence. Artificial Intelligence emulates human intelligence on machines so that the machines think like human beings and act like them. Thus, artificial intelligence helps to raise knowledge about reasoning, machine learning, planning, intelligent search and also is essential to cope with all types of uncertainty present in the environment.

In recent years, many researchers are paying attention to the evolutionary based problem solving techniques. Evolutionary robotics based path planning are generalized for any dynamic environment situations because many natural evolution techniques are mimic into the programming like neural network [18], Tree structure Encoding [19], fuzzy logic [20], [21], gravitational search algorithm [22], [23], [24], particle swarm optimization [25], [26], differential evolution [27], reinforcement learning [28], Artificial immune system [29], Artificial bee colony [30], hybridization of evolutionary computing such as IPSO-GSA [31], IPSO-DV [17], multi-objective variable neighborhood search [32] and other evolutionary algorithms [30], [33].

Multi-objective Particle Swarm Optimization (MOPSO) is a variation of the PSO to solve multi-objective optimization problems [34]. Most of the multi-objective particle swarm optimization algorithms largely depend on the global or personal best particles stored in an external archive, the author has been used a competitive mechanism based multi-objective particle swarm optimizer, where the particles are updated based on the pairwise competitions performed in the current swarm at each generation. The performance of the proposed competitive multi-objective particle swarm optimizer is verified by benchmark comparisons with several state-of-the-art multi-objective optimizers. Infrared image segment and reconstruction of infrared image sequences have been carried out through fractional Darwin particle swarm optimization algorithm (FODPSO) [35]. Multi-level image thresholding method in which a Chaotic Darwinian Particle Swarm Optimization algorithm is applied to images compressed by using Fuzzy Transforms [36]. A dynamic group learning distributed particle swarm optimization (DGLDPSO) has been exercised for the large-scale cloud workflow scheduling [37]. In this algorithm, first, the entire population is divided into many groups, and these groups are coevolved by using the master–slave multi-group distributed model, forming a distributed PSO (DPSO) to enhance the algorithm diversity. Second, a dynamic group learning(DGL) has been adopted for DPSO to balance the convergence and diversity. These techniques are recently increasingly used by researchers and scientist community for various application domains of handling uncertainty and imprecision with a reasonable amount of computational complexity.

Hybridization of IPSO-EOPs has been projected to solve the multi-robot path planning problem, in the multi-robot problem, each robot computes its next position through the evaluation of objective function using IPSO to compute an optimal collision free path towards their corresponding goals. The velocity of IPSO is adjusted using the Evolutionary operators. The objective function is designed using two parts for IPSO. The first one is the generation of the subsequent point for each robot and the next one consists of a set of constraints that ensure colleagues, non-static and static obstacles do not collide with the robot.

The main emphasized of the work may be précised as : (i) The problem has expressed as multi-objective optimization with different constraints and resolve the problem through hybridization of IPSO-EOPs; (ii) the problem in the paper aims is to generate a collision free optimal trajectory path for each robot through the IPSO-EOPs by optimizing the energy utilization in the form of number turns essential to attain at the destination; (iii) the effectiveness and robustness of the our proposed algorithm has been validated through real khepera-II robot and simulation; (iv) the results obtained through the proposed algorithm is effectively validated by comparing the result obtained from its opponents such as IPSO and DE in simulation and real platform.

The main contribution of the paper highlights the implementation of the IPSO-EOPs to plane the path for multiple mobile robots in a complex environment. In this problem, the start position and the goal position are known to every robot. The task of each robot is to generate a collision free optimal trajectory path from a known source to their target by satisfying the environmental constraints and optimizing the different parameters which have been discussed in detail in the subsequent section. During the path generation, each robot computes its next local optimal coordinate in a stepwise manner. Here, the problem is considered as an optimization problem. The objective (fitness) function for the above problem has been constructed by considering three different criteria such as the Euclidean distance between the current position and a target position, avoiding of static obstacles, prediction of movable (dynamic) obstacles and path smoothness. The multi-objective function is formulated as a single objective function by the weighted sum of each objective function. The hybrid techniques have freshly established significant attention in the field of path planning in the multi-robot environment. In this work, we have used the projected IPSO-EOPs technique by modifying the basic PSO and hybridized with evolutionary operators to generate an optimal collision free path for each robot.

The flexibility and applicability of the proposed algorithm are validated through the real platform and simulation. The result demonstrates that the offered technique can enhance the quality of the solution in a rational quantity of time and the hybrid IPSO-EOPs technique is designed to generate an optimal path successfully by avoiding both static and dynamic obstacles on its path towards the goal. Finally, simulation and real platform results are demonstrated and compared with previously published results. The problem under current study can be further improved as follows (1) the robustness of the current method was assessed by considering important sets of parameters, (2) the selected parameters were restricted by the search method and it could be improved significantly using more complex search schemes.

The rest part of this work is structured as follows. The Basic Particle swarm optimization and its Improvement are presented briefly in Section 2. The proposed Evolutionary operators are presented in Section 3. Hybrid IPSO-EOPs for multiple mobile robot path planning is outlined in Section 4. The mathematical design of multiple mobile robots is explained in Section 5. Section 6 presents a detail description of the path planning algorithm. The outcomes of the simulation framework are outlined in Section 7. In Section 8, the experiment conducted through the real platform is presented. The comparative analysis of the proposed work with other related works has been explained in Section 9 and finally, Section 9 ends with conclusions and future direction of the proposed work.

Section snippets

Basic PSO (BPSO)

Basic PSO is an optimization algorithm inspired by the social behavior of fish and birds. The algorithm is simple, robust and efficient to find the optimal regions in the complex search spaces. PSO uses its members called a set of particles that represent the potential solutions that required to solve the optimization problem [38]. Each particle moves through its current velocity towards the optimal region and its position is updated at every iteration. PSO generates its global solution by

Proposed evolutionary operators

Two operators are introduced in this section, the first operator is based on multi-crossover [49] and the second one is similar to bee colony techniques [50]. These two operators help to improve the convergence and escape from local minima.

Operator 1: Operator 1 is based on multi-crossover in generating algorithm [49]. The multi-crossover used three chromosomes (α1,α2,α3) which has been selected randomly from mating pool, if the fitness value of the chromosome αi(where,i[1,2,3]) is smallest,

Hybrid of IPSO and evolutionary operators(EOPs)

The classical PSO algorithm suffers to generate an optimal solution and a slower convergence rate due to the dependency on external parameters like inertia weight and acceleration parameters. Therefore, the efficiency of the PSO algorithm is comparatively poor. Since the above problem encounters in the PSO algorithm, some measures have been taken care of to improve the performance of PSO as presented in the previous section. But experimentally, it has been observed that in most cases the

Formulation of problem for path planning of multi-robot

The main aim of the multi-robot path planning problem is to generate a collision free path for each robot from their current position to target position in a cluttered environment. Before formulating the problem, some assumption has been considered such as each robot in the environment knows their initial position and target position. During the movement of the robot, it selects any action from their existing action to reach the next subsequent position and the process will continue until the

Hybrid IPSO-EOPs algorithm for path planning of multi-robot

In this section, the path planning of multiple mobile robots has been resolved through the projected algorithm. The single objective function presented in Eq. (35) is used in the IPSO-EOPs for computing the successive optimal position of every robot from their existing position at the same time satisfying all the constraints and enhanced the convergence speed. The proposed algorithm also generates the optimal path for every robot from their initial position to the designation in a static and

Computer simulation

The simulated environment has been considered for realizing the mobile robots path planning problem. The simulation has been carried out through C programming language. Each robot in the simulation is designated as a circular shape of radius 6 pixels with different color codes. Before the beginning of the experiment; the specified initial position and goal position is assigned for nR number of robots. The obstacles have been placed randomly on the world map. While performing the experiments,

Experiment on Khepera II robots

The description of Khepera II and its numerical values of the parameter has been presented in Table 13. The sensors are equipped in the kephera-II mobile robot in an anticlockwise manner and it has been number as 0 to 7 with the leftmost sensors designated 0 and the rightmost by 7. These parameters are exercised for conducting the experiment and robot is controlled through the personal computer via com port. The experiment is carried out through two Khepera-II mobile robots. The motor of wheels

Comparison study with Ref. [8]

This section provides a comparative study of the proposed approach of IPSO-EOPs with the existing approach suggested by Ali et al. [8] for navigation of multi-robot through the shortest distance algorithm. The proposed algorithm evaluates the collision free shortest trajectory path using the existing position and orientation of other algorithms. The simulation result of the proposed algorithm has been compared with the existing algorithm to verify the robustness and effectiveness of the

Conclusion and future direction

A hybridization of IPSO-EOPs algorithm has been proposed to enhance the exploration and exploitation capability for better convergence. A case study on multiple mobile robot path planning has been undertaken using the proposed technique IPSO-IGSA to compute the optimal trajectory path from the predefine initial position to target position for each robot in the environment by avoiding the static and dynamic obstacles. The experiments, undertaken on simulation, through the Khepera-II robot reveal

CRediT authorship contribution statement

P.K. Das: Conceptualization, Methodology, Software, Writing - review & editing. P.K. Jena: Data curation, Writing - original draft, Visualization, Investigation, Validation.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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