Due to the increasing demand for higher performance (throughput and efficiency) of robotic packaging systems, and the need to keep the system's footprint as small as possible, robots must operate closer to each other. This gives rise to progressively more difficult variants of the problems of collision detection and collision avoidance. In this work we focus on designing algorithms for collision detection between multiple parallel (Delta) robots, which are widely used in the packaging industry. The algorithms must operate in a real-time controller, which puts additional constraints on the processing power and memory requirements. We identify certain monotonicity properties in the composite configuration space of the underlying robots, which help us to devise highly effective collision detection algorithms for them. We lay out the theoretical basis of our development, describe the new algorithms, and report on simulation results. The results show that two of the new algorithms can reduce the memory requirements by 45% and 90%, respectively, without any loss of information as opposed to an approach based on solely existing techniques. Furthermore, our solution easily satisfies the real-time constraint with a typical query time of 3 microseconds. Finally, we demonstrate the real-time capabilities of our algorithms in an industrial setup.
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