Navigation functions with moving destinations and obstacles

Dynamic environments challenge existing robot navigation methods, and motivate either stringent assumptions on workspace variation or relinquishing of collision avoidance and convergence guarantees. This paper shows that the latter can be preserved even in the absence of knowledge of how the environment evolves, through a navigation function methodology applicable to sphere-worlds with moving obstacles and robot destinations. Assuming bounds on speeds of robot destination and obstacles, and sufficiently higher maximum robot speed, the navigation function gradient can be used produce robot feedback laws that guarantee obstacle avoidance, and theoretical guarantees of bounded tracking errors and asymptotic convergence to the target when the latter eventually stops moving. The efficacy of the gradient-based feedback controller derived from the new navigation function construction is demonstrated both in numerical simulations as well as experimentally.