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In this paper, we evaluate the performance of two candidate formulations for distributed motion planning of robot collectives within an Artificial Potential Field (APF) framework. We exploit the parallel between the formulation of motion planning for group of robots coupled by constraints and the forward dynamics simulation of constrained multibody systems to develop the candidate approaches. We compare and contrast these approaches on the basis of ease of formulation, distribution of computation and overall computational accuracy. Traditionally penalty formulations have enjoyed a prominent position in motion planning of robot collectives due to their ease of formulation, decentralization and scalability. However, the instabilities introduced in the form of “formulation stiffness” at the algorithm development stage have the potential to hinder the subsequent control. Representative results from the distributed motion planning for a group of 3 point-mass robots moving in formation to a desired target location are used to highlight the differences.