Gyroscopic Forces and Collision Avoidance with Convex Obstacles

Abstract

Summary. This paper introduces gyroscopic forces as an tool that can be used in addition to the use of potential forces in the study of collision and convex obstacle avoidance. It makes use of the concepts of a detection shell and a safety shell and shows, in an appropriate context, that collisions are avoided, while at the same time guaranteeing that control objectives determined by a potential function are met. In related publications, we refine and extend the method to include flocking and swarming behavior.

Reciprocal collision avoidance for quadrotors using on-board visual detection

“…NF algorithms use an analytic function of which the gradient is the direction to follow. The NF can be adapted to fixed-wing aircraft [11], [12] or quadrotors [13]. Sensing limitations can also be incorporated.…”

Vehicle Motion Planning Using Stream Functions

“…Further extensions and applications of the theory presented here can be found in [3,19]. An alternative approach to collision avoidance that may have complementary applications to this work is the use of gyroscopic forces, introduced in [4] and discussed with particular application to multiple vehicle systems in [5]. This paper outlines a method for synthesizing stream functions which avoid obstacles while producing paths suitable for an aircraft-like vehicle.…”

“…A detailed examination of a new method proposed for modifying the existing theory to incorporate multiple obstacles exactly is presented in Section 6. Section 7 describes a few additional applications of stream function-based navigation currently being explored and discusses possible ties between this work and the gyroscopic force methods presented in [4,5]. Finally, Section 8 provides a summary and discusses the ongoing theoretical and experimental work related to this method.…”

“…Obstacle avoidance is not implemented using a vector field in this case, so the topological difficulties described by Koditshek and Rimon in [14] can be circumvented. The use of such forces for obstacle avoidance is introduced in [4] and examined in the context of multiple vehicle systems in [5]. In both of these papers a potential function is used to induce goal-seeking behavior while the gyroscopic forces are used for obstacle avoidance.…”

Cooperative hybrid control of robotic sensors for perimeter detection and tracking

“…Gyroscopic forces denote forces that do not do any work and create coupling between different degrees of freedom [13]. Gyroscopic forces act like steering forces and do not affect the total energy of the system.…”