Regular PaperUnknown environment exploration of multi-robot system with the FORDPSO
Introduction
Unknown environment exploration is one of the most important problems in mobile robot research field, and it is also a research hotspot in recent years. In many practical cases which are too dangerous or difficult for human to reach (e. g., military assignments, interstellar exploration, searching for victims after earthquake, and nuclear/biological accidents), whether the robot can complete the tasks successfully depends on whether the environment exploration can be carried out smoothly. Comparing with the single robot system, multi-robot system has been widely used in many complex and abominable scenarios, due to its strong adaptation, excellent flexibility, and high reliability. Multi-robot system is getting more and more emphasis and studies [3], [4], [5]. Unknown environment exploration of the multi-robot system is also achieving more and more researches [6], [7], [8].
Traditional exploration strategies of multi-robot system adopt concentrating or semi-distributing control modes which use a few leading nodes to undertake swarm decision task, and these strategies suit the multi-robot system with a small swarm population. When the swarm population grows, the calculation of the leading nodes and communication burden will increase exponentially which make it unsuitable in practical application. Furthermore, in many conventional multi-robot exploration methods, due to the node׳s heterogeneity, one node fault can result in complicated task re-allocation and dynamic equilibrium. Moreover, traditional multi-robot exploration methods also bring some new problems, such as data fusion. Recently, swarm robot systems based on swarm intelligence become a new research direction for its robustness, excellent expandability and good performance on communication data control [9].
Swarm intelligence is a kind of collective behavior of distributed, self-organized system. It is a representative method of behaviorism artificial intelligence. The intuitive notion of “Swarm Intelligence” is that of a “swarm” of agents (biological or artificial) which, without central control, collectively (and only collectively) carry out (unknowingly, and in a somewhat-random way) tasks normally requiring some form of “intelligence” [10]. It originates the collective behavior research of social insects (e. g., ants, bees and fish school). Swarm intelligent behavior is reflected by simple rules and collective cooperation among a swarm of simple low intelligence individuals. Swarm intelligence has the following characteristics: (1) each individual communicates with others among the swarm or their surrounding environment in local scope; (2) each individual is very simple but isomorphic; (3) through individual׳s simple local feedback, the swarm can complete complex tasks.
Swarm intelligence has produced two famous algorithms: ant colony optimization [11], [12] and particle swarm optimization (PSO) [13], [14]. The former simulates the ant colony searching the food and has been applied in many discrete optimization problems [15], [16], [17]. PSO is inspired by birds flocking or fish school in search of food. Now the PSO algorithm has become an excellent optimization tool. These two optimization algorithms have been widely used in multi-robot cooperation [18], [19], [20].
However, PSO and other optimization algorithms have a general drawback – they may be trapped in a local optimal solution, which may work well in some problems but fails in others [21]. In order to overcome these drawbacks, Darwinian PSO (DPSO) algorithm was proposed by Tillett et al. [1] who introduced the natural selection in PSO. In this algorithm, multiple swarms of test solutions, each of them performing just like an ordinary PSO, may exist at any time with some rules governing the collection of swarms which are designed to simulate natural selection [22]. Couceiro et al. [2], [22], [23] firstly applied the DPSO into multi-robot exploration field and proposed the Robotic DPSO (RDPSO), taking into accounting obstacle avoidance. It benefits from the dynamical partitioning of the whole population of robots, thus decreasing the amount of required information exchange among the robots. Further, in order to control the convergence rate of RDPSO, they introduced the fractional order RDPSO (FORDPSO) [24]. It uses the fractional calculus to control the convergence rate of robots toward the optimal solutions.
Performance of FORDPSO greatly depends on its coefficients. In conventional methods, these coefficients are set randomly and subjectively [24], so the algorithm performance cannot be guaranteed well. In order to control the swarm susceptibility to the main mission, obstacle avoidance, etc., FORDPSO should be improved to systematically adjust its parameters. Based on the above analysis, this paper adopts fuzzy inferring system to adjust the coefficients in FORDPSO and compares the algorithm performance of two kinds of FORDPSO: adaptive parameter adjustment with fuzzy inferring and fixed parameter, through two typical environment exploration experiments with the multi-robot system. Simulation results show that performance of FORDPSO with adaptive parameter adjustment is better than that of the algorithm with fixed parameters.
The remainder of the paper is organized as follows. Section 2 introduces the theory for PSO and DPSO. Section 3 describes the theory of RDPSO. Section 4 represents the fractional order RDPSO and discusses the coefficient ranges. Section 5 analyzes the coefficients influence of FORDPSO algorithm and designs the fuzzy inferring system to dynamically adjust the coefficients. In Section 6, we design the simulation procedure, compare and analyze the simulation results of two typical scenarios with fuzzy parameter adjustment FORDPSO and fixed parameter FORDPSO, while the conclusions and future study are given in the last section.
Section snippets
Particle swarm optimization
The PSO proposed by James Kennedy and R.C. Eberhart is a population-based stochastic optimization method based on the social behavior of groups of organisms like bird flocks or fish schools [25]. The method was inspired by the movement of flocking birds and their interactions with their neighbors in the group. Each individual in the group is regarded as a particle that flies in a given virtual search space, and each of them represents a potential solution. Movement of a particle is determined
Robotic Darwinian particle swarm optimization algorithm
Particles in PSO are regarded as without mass and volume, without considering the collision in real world. If DPSO algorithm is transplanted into mobile robot field, each robot is treated as a “particle” and it heritages particle׳s two characteristics: position and velocity. All robots interact with each other and share information in unknown environment. They explore together until they find the global optimal solution.
However, dislike the virtual particles, robots are designed to act in real
Fractional calculus
The traditional integral and derivative are, to say the least, a staple for the technology professional, essential as a means of understanding and working with natural and artificial systems. Fractional calculus is a field of mathematic study that grows out of the traditional definitions of the calculus integral and derivative operators in much the same way fractional exponents is an outgrowth of exponents with integer value [31]. Fractional calculus extends the common notion of integer order
FORDPSO coefficients influence analysis
Fractional order coefficients α can finely control algorithm convergence rate, different α has a different effect on the algorithm performance. If α is large, the algorithm has relatively strong global search ability. While it can find the new solution and keep the diversity of the solutions, thus it can find the swarm optimal solution with big probability. But large α will result in slow convergence, even unstable and un-convergence. If α is small, the algorithm has relatively strong local
Simulation experiments
This section, we choose two representative scenarios to test the environment exploration procedure with fixed parameter FORDPSO algorithm and fuzzy adaptive parameter FORDPSO algorithm. In order to compare the performance of the two methods, their initial parameters are set the same. Each robot equips a laser scanner with scan angle scope 180°, angle resolution 0.5°, and the maximal scan range 2 m. The maximal moving step of each robot is 0.1 m. Because the environment information are stored as
FORDPSO with different particle neighborhood topologies
In order to testify the performance of the FORDPSO further, in this section, we compare the performances of the FORDPSO with different particle neighborhood topologies.
Since particle neighborhood topology is a significant factor influencing the local PSO algorithm performance, different particle neighborhood topologies have different effects on the final solutions, in this section, we compare the performances of FORDPSO with different neighborhood topologies, such as ring topology, Von Neumann
Comparisons between FORDPSO and other PSO
In this section, the performance of FORDPSO is compared with other PSOs, such as basic PSO, adaptive particle swarm optimization (APSO), Quantum-based PSO (QPSO), dynamic neighborhood PSO (DNPSO), GA-PSO and DE-PSO.
In APSO, we adopt (0,1) uniform distribution inertial weight ω to substitute linearly decreasing method. This method can guarantee the particles to obtain a small ω in early time and a large one in later time. But when the global optimal Pg does not change, we hope a large ω achieved
Conclusions and future work
This paper realized an effective unknown environment exploration with FORDPSO algorithm which is based on basic DPSO algorithm. DPSO is an evolutionary algorithm that extends the PSO with natural selection, i. e., survival of the fittest, to improve the ability to escape from the local optima. It can dynamically partition the whole population of the swarm, therefore, decrease the amount of required information exchange among the robots. The concepts of social exclusion and social inclusion are
Acknowledgment
The authors want to thank Dr Couceiro for providing simulation software, useful discussions and many concrete suggestions in program design. Every talking with Dr Couceiro has brought us new viewpoints and ideas.
This work was supported by the Natural Sciences Foundation of China (Grant no. 61174085).
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