Noise helps steer systems safely around obstacles and on curved surfaces
Noise-Induced Navigation in Non-convex Domains and Compact Manifolds
Robotics
Summary
Steering a system safely to a target position can be tricky when the environment has obstacles or curved shapes. Continuous control methods often fail due to underlying topological issues. The authors show that intentionally adding randomness (noise) into the controls can help the system find and stay at the target reliably, even in complex, non-convex spaces. They provide a way to design simple control rules that use noise to guarantee success, demonstrated on shapes like circles and spheres. Their work also connects to solving optimization problems with difficult constraints.
What this means in practice
- •For robot motion planners: Design control strategies that reliably guide robots around obstacles using noise to overcome topological difficulties in the environment.
- •For autonomous vehicle engineers: Improve path following algorithms by incorporating controlled noise to stabilize trajectories on complex, curved surfaces.
Authors
Karthik Elamvazhuthi
Abstract
In this note, we study the problem of designing a feedback law that globally steers a system to a prescribed target configuration. Even if the system is fully actuated, topological obstructions generally prevent the existence of globally asymptotically stabilizing continuous feedback laws. We revisit this problem in a stochastic setting by allowing noise to enter through the control channels. Using a criterion for asymptotic stability in the large that combines local Lyapunov stability with positive recurrence, we constructively show that one can construct elementary feedback laws that achieve global asymptotic stability in the large, of the target equilibrium point in connected Euclidean domains with obstacles and manifolds without boundary. For Euclidean domains with obstacles, we also show that the method extends naturally to the problem of finding the minimizer of a strongly convex function with non-convex constraints. Numerical experiments illustrate the effectiveness of the approach for Euclidean domains with circular obstacles and the two dimensional sphere. Additionally, we study the role noise strength when there is a non-convex obstacle, in which case the system might show metastability.