No abstract

Most robot control and planning algorithms are complex, involving a combination of reactive controllers, behavior-based controllers, and deliberative controllers. The switching between different behaviors or controllers makes such systems hybrid, i.e. combining discrete and continuous dynamics. While proofs of convergence, robustness and stability are often available for simple controllers under a carefully crafted set of operating conditions, there is no systematic approach to experimenting with, testing, and validating the performance of complex hybrid control systems. In this paper we address the problem of generating sets of conditions (inputs, disturbances, and parameters) that might be used to "test" a given hybrid system. We use the method of Rapidly exploring Random Trees (RRTs) to obtain test inputs. We extend the traditional RRT, which only searches over continuous inputs, to a new algorithm, called the Rapidly exploring Random Forest of Trees (RRFT), which can also search over time invariant parameters by growing a set of trees for each parameter value choice. We introduce new measures for coverage and tree growth that allows us to dynamically allocate our resources among the set of trees and to plant new trees when the growth rate of existing ones slows to an unacceptable level. We demonstrate the application of RRFT to testing and validation of aerial robotic control systems.

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 Rapidlyexploring 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.

Abstract. It has been observed that there are a variety of situations in which the most popular hybrid simulation methods can fail to properly detect the occurrence of discrete events. In this paper, we present a method for detecting discrete which, using techniques borrowed from control theory, selects integration step sizes in such a way that the simulation slows down as the state approaches a set which triggers an event (a guard set). Our method guarantees that the state will approach the boundary of this set exponentially; and in the case of linear or polynomial guard descriptions, terminating on it, without entering it. Given that any system with a nonlinear guard description can be transformed to an equivalent system with a linear guard description, this technique is applicable to a broad class of systems. Even in situations where nonlinear guards have not been transformed to the canonical form, the method is still increases the chances of detecting and event in practice. We show how to extend the method to guard sets which are constructed from many simple sets using boolean operators (e.g. polyhedral or semi-algebraic sets) . The technique is easily used in combination with existing numerical integration methods and does not adversely affect the underlying accuracy or stability of the algorithms.

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. AbstractWe 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. 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. We choose to apply sampling-based algorithms to the testing and validation problem. Our work is based on the Rapidly-exploring Random Trees (RRT) algorithm. First we analyse some of the factors that govern the exploration rate of the RRT algorithm. The analysis serves to motiv...