A Stabilizing Gyroscopic Obstacle Avoidance Controller for Underactuated Systems

This work addresses the problem of controlling an underactuated system to a goal state in a cluttered environment. To this end, a gyroscopic obstacle avoidance controller is proposed for a class of underactuated systems, which take as inputs body torques and a thrust force along some known body-fixed axis. The Lyapunov stability of the controller in the presence of obstacles is shown in theory and verified through simulations. Care is taken to ensure stability even when the system has only a finite obstacle detection radius, and a novel gyroscopic obstacle avoidance gain selection is designed which smoothly attenuates the steering force as the robot heads away from an obstacle. Furthermore, a gyroscopic steering force tailored to two primitive obstacles, namely cylinders and spheres, is proposed. Simulations of a quadrotor system and a nanosatellite system validate that the controller is stable under a large number of obstacles and smoothly converges to the goal state.