Navigation Functions with non-Point Destinations and Moving Obstacles
Chuchu Chen, Caili Li, Herbert G. Tanner · 2020
This paper formally expands the application domain of robot motion planning methods that are based on navigation functions to the case of moving obstacles. It generalizes the navigation function methodology from static sphere world environments, to dynamic ones. Specifically, it allows the obstacles' locations to be time-varying, albeit unknown, and accommodates the case where the navigation goal is not a single isolated point, but rather a spherical manifold. For such cases, the paper presents analytical bounds on the tuning parameters that guarantee the navigation function properties of the time-varying potential function, uniformly in time. Thus using the same choice of tuning parameters, the agent is ensured that at every instance in time, the artificial potential field that directs it to its destination is free of local minima. The parameter bounds naturally depend on the geometry of the agent workspace, and include conditions on how close the obstacles can approach each other, the fixed workspace boundary, and the destination sphere. The bounds presented here are conservative; their analytic determination serves mainly the purpose of theoretically guaranteeing completeness properties for the methodology in the time-varying obstacle case.