1. Introduction
As the interests in space and other planets increase, several space exploration missions including planetary missions are scheduled [
1]. Among several planets within our solar system, Mars is the most attractive planet for human exploration and missions because of the characteristics of Mars that provide moderate temperatures, atmosphere, and the nearly identical day length, etc. [
2]. Currently, robotic explorations for acquiring the geological and biological information of Mars and for preparing human missions are planned [
3]. In particular, human missions on Mars require construction of outposts and infrastructures and/or (re)locate such large structures or experimental devices to support a long-duration scientific expedition to extreme environments. This leads to the necessity of means to support those activities, and the use of exploration-assisting robots would be one of the good approaches.
Up until now, a single robot system such as a rover with high-power capacity and various functions has been used to conduct several space explorations missions [
4]. This required a complex mechanism that includes multiple sensors and experimental devices, and thus, it yielded high costs for building and management and provoked high risks of mission failures [
5]. Such disadvantages of operating the single robot system can possibly be resolved by utilizing a multi-robot system (MRS) that operates multiple and small robotic platforms cooperatively. The combination of multiple single-functioning robots, when compared to the multi-functioning single robot system, can bring huge advantages that include, but are not limited to lower cost, better system reliability, greater redundancy, and larger flexibility. In light of this, the operation of the MRS would be beneficial for planetary missions, especially supporting the transportation task.
By virtue of such advantages, the MRS-based object transportation problem has been studied in recent decades. Wang and Schwager [
6] proposed a multi-robot manipulation algorithm, which allows the MRS to move an object along the desired trajectory to a goal location. The robots coordinate their actions by sensing the motion of the object without an explicit communication network among themselves, and a force consensus technique using the sensing information is applied to achieve the mission. Chand et al. [
7] solved a deformable object transportation problem using a leader-follower formation control algorithm. A path planning algorithm was used to avoid static obstacles for the virtual leader, and a constrained optimization method for the multi-robot formation control was proposed. In addition, in the research investigated by Alonso-Mora et al. [
8], a local planner calculates a large obstacle-free convex region around robots, and the parameters of the formation were optimized by sequential convex programming. Then, global path planning is performed via the constrained optimization. Bujarbaruah et al. [
9] proposed a leader-follower hierarchical strategy for collaborative object transportation using two robots. Here, the leader solved a model predictive control problem at any given time with the known obstacles to planning a trajectory, and the follower assisted the leader while reacting to additional obstacles. Eoh et al. [
10] proposed a cooperative object transportation technique that creates a corridor around objects by lining up two rows using robots. By following a unified field that is composed of a virtual electric dipole field and potential fields, the robots generated an extended corridor to a goal.
Artificial intelligence (AI) is generally divided into (i) deterministic AI that uses the physics of the underlying problem or system and (ii) stochastic AI that has no knowledge of the problem or system [
11]. The use of deterministic AI allows an agent to respond to uncertainties or even damages, but re-parameterization of the underlying problem with complexity may be a challenge. For this reason, several studies based on stochastic AI have been actively investigated for an object transportation problem using multiple robots. Jhang et al. [
12] proposed an interval type-2 fuzzy neural controller based on a dynamic group differential evolution, which combines a group concept with improved differential evolution, to implement the carrying control and wall-following control for multiple mobile robots. In addition, the authors adopted a reinforcement learning technique to develop an adaptive wall-following control. Dai et al. [
13] utilized a fuzzy sliding mode control technique for tracking control of robots while transporting an object, and an artificial potential field approach is additionally applied to avoid obstacles. In addition to this, some scholars considered decentralized approaches to perform a collaborative task using an MRS. Sirineni et al. [
14] proposed a decentralized collision avoidance (CA) and motion planning approach for a multi-robot deformable payload transport system. This work solved a convex optimization problem by considering a multi-robot CA algorithm and multi-scale repulsive potential fields as constraints. Zhang et al. [
15] proposed a decentralized control scheme on an MRS. Each robot utilized a deep Q-network controller to perform an object transportation task. Since it used a deep reinforcement learning technique, the robots can learn appropriate control strategies through trial-error style interactions within the task environment without the knowledge of the dynamics for the environment.
Plenty of existing collaborative control strategies generally used a centralized controller. Some used a decentralized technique, but the environments considered were flat surfaces in general. Such control techniques were developed assuming the environment would only be flat, so they cannot be applicable for exploration missions on the surface of planets (e.g., the Moon and Mars) with rugged and rough terrain. Based on the authors’ preliminary work [
16], this work proposes a decentralized approach for an MRS using fuzzy inference systems (FISs) trained by a genetic algorithm (GA) in order to perform a collaborative task with a near-optimal navigation solution in an unstructured environment. By using only the information of the target and the nearest obstacle without knowledge of the states of the object and other robots, the robots are operated in a decentralized manner. In addition, the optimality of the trained FIS model is evaluated by comparing the results obtained by the trained FIS model with one obtained from solving a path optimization problem. Then, the trained model is validated through various testing scenarios in unstructured environments that mimic rough terrain.
The remainder of this paper contains the following contents.
Section 2 introduces preliminary knowledge related to the proposed system, and
Section 3 explains the environment model considered and problem formulations for the system.
Section 4 presents the proposed genetic fuzzy system model including the FISs to determine the inputs for the MRS. In
Section 5, a formulation for the path optimization problem that is used as a metric for the optimality evaluation of the proposed model is introduced.
Section 6 describes the training and testing processes and discusses the simulation results. Then, the last section summarizes this work.
2. Preliminary: Genetic Fuzzy System
The FIS can be utilized as an intelligent control technique that provides several benefits in the aspect of the design flexibility, its capability as a universal approximator, and the ability to combine with optimization techniques [
17]. It has three processes to make decisions, such as fuzzification, inference, and defuzzification, and the grey region in
Figure 1 represents the FIS. Through the fuzzification process, a crisp input is converted into a value of the input fuzzy set, and the value of the output fuzzy set is determined by the inference engine that contains the relationship between the input and output. Then, the obtained fuzzy output is transformed into a crisp value as an output through the defuzzification process. Here, the fuzzification and defuzzification steps are composed of the multiple numbers of membership functions that convert the crisp input into the value in the fuzzy set, and the rule-base in the inference engine consists of multiple rules. The main challenge to build FISs is to appropriately select the membership functions and rules of each FIS because the parameters of the membership functions and rules are generally determined by the expert’s knowledge. Therefore, it is difficult to anticipate that the FISs with the given expert’s knowledge provide the optimal solution.
When the FISs have many inputs and outputs whose relationships are not straightforward, the learning or tuning capability, which is surely useful to build FISs, can be given by using different optimization algorithms, such as an artificial neural network and the GA. While the adaptive network-based FIS (ANFIS) [
18] automatically creates sufficient rules considering input and output data and uses the benefit of the learning capability of neural networks, the genetic fuzzy system (GFS) [
19] automates the selection of all the parameters of the FISs by using the optimization algorithm, which is the GA, and provides a near-optimal set of FISs’ parameters (membership functions and rules) to minimize the pre-defined cost function.
Figure 1 illustrates the concept of the GFS. One of the main benefits of the GFS is to utilize the FIS that can provide explainability in terms of the determination of the output that is expressed linguistically. In addition, the GA does not destroy the characteristics of the FIS and ensures a near-optimal solution using its aggressive search capability. Therefore, this work takes advantage of the GFS for the collaborative task of the MRS.