Yinan Li

Ye Zhao, Yinan Li, Luis Sentis et al.

Contact-based decision and planning methods are becoming increasingly important to endow higher levels of autonomy for legged robots. Formal synthesis methods derived from symbolic systems have great potential for reasoning about high-level locomotion decisions and achieving complex maneuvering behaviors with correctness guarantees. This study takes a first step toward formally devising an architecture composed of task planning and control of whole-body dynamic locomotion behaviors in constrained and dynamically changing environments. At the high level, we formulate a two-player temporal logic game between the multi-limb locomotion planner and its dynamic environment to synthesize a winning strategy that delivers symbolic locomotion actions. These locomotion actions satisfy the desired high-level task specifications expressed in a fragment of temporal logic. Those actions are sent to a robust finite transition system that synthesizes a locomotion controller that fulfills state reachability constraints. This controller is further executed via a low-level motion planner that generates feasible locomotion trajectories. We construct a set of dynamic locomotion models for legged robots to serve as a template library for handling diverse environmental events. We devise a replanning strategy that takes into consideration sudden environmental changes or large state disturbances to increase the robustness of the resulting locomotion behaviors. We formally prove the correctness of the layered locomotion framework guaranteeing a robust implementation by the motion planning layer. Simulations of reactive locomotion behaviors in diverse environments indicate that our framework has the potential to serve as a theoretical foundation for intelligent locomotion behaviors.

Yinan Li, Jun Liu

This paper focuses on the invariance control problem for discrete-time switched nonlinear systems. The proposed approach computes controlled invariant sets in a finite number of iterations and directly yields a partition-based invariance controller using the information recorded during the computation. In contrast with Lyapunov-based control methods, this method does not require the subsystems to have common equilibrium points. Algorithms are developed for computing both outer and inner approximations of the maximal controlled invariant sets, which are represented as finite unions of intervals. The general convergence results of interval methods allow us to obtain arbitrarily precise approximations without any stability assumptions. In addition, invariant inner approximations can be computed provided that the switched system satisfies a robustly controlled invariance condition. Under the same condition, we also prove the existence of an invariance controller based on partitions of the state space. Our method is illustrated with three examples drawn from different applications and compared with existing work in the literature.

Yinan Li, Jun Liu, Necmiye Ozay

This paper proposes a method to compute finite abstractions that can be used for synthesizing robust hybrid control strategies for nonlinear systems. Most existing methods for computing finite abstractions utilize some global, analytical function to provide bounds on the reachable sets of nonlinear systems, which can be conservative and lead to spurious transitions in the abstract systems. This problem is even more pronounced in the presence of imperfect measurements and modelling uncertainties, where control synthesis can easily become infeasible due to added spurious transitions. To mitigate this problem, we propose to compute finite abstractions with robustness margins by over-approximating the local reachable sets of nonlinear systems. We do so by linearizing the nonlinear dynamics into linear affine systems and keeping track of the linearization error. It is shown that this approach provides tighter approximations and several numerical examples are used to illustrate of effectiveness of the proposed methods.