An RRT-Based Algorithm for Testing and Validating Multi-Robot Controllers

Abstract : We address the problem of testing complex reactive control systems and validating the effectiveness of multi-agent controllers. Testing and validation involve searching for conditions that lead to system failure by exploring all adversarial inputs and disturbances for errant trajectories. This problem of testing is related to motion planning, with one main difference. Unlike motion planning problems, systems are typically not controllable with respect to disturbances or adversarial inputs and therefore, the reachable set of states is a small subset of the entire state space. In both cases however, there is a goal or specification set consisting of a set of points in state space that is of interest, either for demonstrating failure or for validation. In this paper we consider the application of the Rapidly exploring Random Tree algorithm to the testing and validation problem. Because of the differences between testing and motion planning, we propose three modifications to the original RRT algorithm. First, we introduce a new distance function which incorporates information about the system's dynamics to select nodes for extension. Second, we introduce a weighting to penalize nodes which are repeatedly selected but fail to extend. Third we propose a scheme for adaptively modifying the sampling probability distribution based on tree growth. We demonstrate the application of the algorithm via three simple and one large scale example and provide computational statistics. Our algorithms are applicable beyond the testing problem to motion planning for systems that are not small time locally controllable.