Distributed Fuzzy Semi-Infinite Auction Based Optimization for Cooperative Robots Tasks Allocation

Abstract

Task allocation solutions for autonomous agents are widely defined by imprecision (fuzziness) rather than exactness. Hence, the robustness of potential agent task assignments is difficult to evaluate analytically. Therefore, sampling-based approximations are used. Despite probability theory claiming to deliver decision-making under uncertainty, there are different facets of indeterminacy which are not covered by such methods. Spurred by these deficiencies and to efficiently deal with practical constraints more than conventional consensus-based models, this paper addresses the problem of distributed task allocation for a coordinated and cooperative fleet of autonomous robots with unknown system parameters. To do so, we introduce fuzziness in the robot’s parameters to adapt with the Consensus-Based Bundle Algorithm (CBBA). Indeed, the entire multi-robotic task allocation problem is reformulated as an optimization of an objective function containing fuzzy parameters. We solve the proposed Fuzzy CBBA (FCBBA) linear programming problem by adopting an adequate equivalent non-fuzzy linear programming and semi-infinite optimization scheme. In this work, a comparative study between the typical CBBA and the proposed FCBBA demonstrates that for a real-world system with inaccurate parameters, our novel algorithm improves the distributed multi-robot task allocation results. Experimental results developed for a space exploration scenario illustrate the efficiency of the proposed technique.