This paper presents a novel method for reformulating non-differentiable collision avoidance constraints into smooth nonlinear constraints using strong duality of convex optimization. We focus on a controlled object whose goal is to avoid obstacles while moving in an n-dimensional space. The proposed reformulation does not introduce approximations, and applies to general obstacles and controlled...

Reciprocal collision avoidance has become a popular area of research over recent years. Approaches have been developed for a variety of dynamic systems ranging from single integrators to car-like, differential-drive, and arbitrary, linear equations of motion. In this paper, we present two contributions. First, we provide a unification of these previous approaches under a single, generalized rep...

We describe grant-to-send, a novel collision avoidance algorithm for wireless mesh networks. Rather than announce packets it intends to send, a node using grant-to-send announces packets it expects to hear others send. We present evidence that inverting collision avoidance in this way greatly improves wireless mesh performance. Evaluating four protocols from 802.11 meshes and 802.15.4 sensor ne...