Noise-Induced Navigation in Non-convex Domains and Compact Manifolds

This paper addresses the autonomous robot navigation problem in a priori unknown n-dimensional environments containing disjoint convex obstacles of arbitrary shapes and sizes, with pairwise distances strictly greater than the robot's diameter. We propose a hybrid feedback control scheme that guarantees safe and global asymptotic convergence of the robot to a predefined target location. The proposed control strategy relies on a switching mechanism allowing the robot to operate either in the move-to-target mode or the obstacle-avoidance mode, based on its proximity to the obstacles and the availability of a clear straight path between the robot and the target. In the obstacle-avoidance mode, the robot is constrained to move within a two-dimensional plane that intersects the obstacle being avoided and the target, preventing it from retracing its path. The effectiveness of the proposed hybrid feedback controller is demonstrated through simulations in two-dimensional and three-dimensional environments.

We study feedback motion planning for continuous-time stochastic nonlinear systems under signal temporal logic (STL) specifications. We propose a framework that synthesizes control policies for chance-constrained STL trajectory optimization problems, with the goal of ensuring that the closed-loop stochastic system satisfies a given STL formula with high probability (e.g., 99.99%). Our approach is based on a predicate erosion strategy that transforms the intractable stochastic problem into a deterministic STL trajectory optimization problem with tightened STL formula constraints. The amount of erosion is determined by a probabilistic reachable tube (PRT) that bounds the deviation between the stochastic trajectory and an associated nominal trajectory. To compute such bounds, we leverage contraction theory and feedback design, and develop several tracking controllers. This yields a complete feedback motion planning pipeline which can be implemented by numerical optimizations. We demonstrate the efficacy and versatility of the proposed framework through simulations on several robotic systems and through experiments on a real-world quadrupedal robot, and show that it is less conservative and achieves higher specification satisfaction probability than representative baselines.

This paper presents a framework for safe navigation of a unicycle point robot to a goal position in an environment populated with obstacles from almost any admissible state, considering input limits. We introduce a novel QP formulation to create a Cinfinity-smooth vector field with reduced total bending and total turning. Then we design an analytic, non-linear feedback controller that inherently satisfies the conditions of Nagumo's theorem, ensuring forward invariance of the safe set without requiring any online optimization. We have demonstrated that our controller, even under hard input limits, safely converges to the goal position. Simulations confirm the effectiveness of the proposed framework, resulting in a twice faster arrival time with over 50% lower angular control effort compared to the baseline.