Departmental Papers (MEAM)

Document Type

Journal Article

Subject Area


Date of this Version

December 2006


Postprint version. Published in International Journal of Robotics Research, Volume 25, Issue 12, December 2006, pages 1257-1272.
Publisher URL:


The problem of testing complex reactive control systems and validating the effectiveness of multi-agent controllers is addressed. 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. In both cases, there is a goal or specification set consisting of a set of points in state space that is of interest, either for finding a plan, demonstrating failure or for validation. Unlike motion planning problems, the problem of testing generally involves systems that are 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 this work, sampling-based algorithms based on the Rapidly-exploring Random Trees (RRT) algorithm are applied to the testing and validation problem. First, some of the factors that govern the exploration rate of the RRT algorithm are analysed, this analysis serving to motivate some enhancements. Then, three modifications to the original RRT algorithm are proposed, suited for use on uncontrollable systems. First, a new distance function is introduced which incorporates information about the system's dynamics to select nodes for extension. Second, a weighting is introduced to penalize nodes which are repeatedly selected but fail to extend. Third, a scheme for adaptively modifying the sampling probability distribution is proposed, based on tree growth. Application of the algorithm is demonstrated using several examples, and computational statistics are provided to illustrate the effect of each modification. The final algorithm is demonstrated on a 25 state example and results in nearly an order of magnitude reduction in computation time when compared with the traditional RRT. The proposed algorithms are also applicable to motion planning for systems that are not small time locally controllable.


sampling-based algorithm, motion planning, testing, validation



Date Posted: 21 March 2007

This document has been peer reviewed.