This paper presents a new approach to the online planning of collision-free robot motions and evasive actions for redundant multi-robot/multi-obstacle environments. The approach, based on the collision avoidance methodology CARE (collision avoidance in real-time environments) presented by Rossmann (1993), is a local planning approach which considers the shortest distance and relative velocity between objects. This results in an intuitively comprehensible model to determine the potential collision and provides the basis of a new way of treating collision free path-planning as an optimization problem. This optimization problem is solved in real-time and provides a mathematically exact solution of the path-planning problem by considering all the static and dynamic obstacles in the environment.
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