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This paper is concerned with the difficult and interesting problem of real-time planning and efficient motion control of rigid multi-robot systems to dynamically avoid moving obstacles and/or robots as these move. Most techniques described so far in the literature deal with the simpler problem of generating (generally off-line) a path among stationary obstacles. For practical purposes, however, obstacles are not always static and most interesting environments are in general not known precisely and/or time varying. Motivated by the fact that robots capable of maneuvering among moving obstalces will be capable of accomplishing a much larger and more versatile class of tasks, and as a result of our current and past research investigations over the years, we present an innovative approach and tackle the problem from a different angle. The proposed method follows upon our previous work which employs a notion of complex potential fields representation, and involves the use of state variables which preserve the Newman Boundary condition of such complex potential fields while allowing mobile robots to autonomously and dynamically avoid each other as well as other moving obstacles. In the heart of the technique is the exploitation of the powerful and fundamental tool of conformal mapping to derive the path solution for obstacles of arbitrary shapes. The advantage this novel approach offers over traditional formulations is its handling of both static and arbitrary moving obstacles/multi-robots. To the author's best knowledge, the proposed technique is the only proposed approach in the literature for real-time mobile robots motion control and obstacles avoidance which not only guarantees the reaching of the robot's goal under some conditions but also focuses on the means by which both the obstacles positions and orientations can elegantly and efficiently be dealt with when these latter continuously change with time.
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