Abstract
Modeling and trustworthy simulation of impact play an important role in research on robotic contact tasks. Impact dynamic equations, based on Newton impact law, and their solution for planar multi-link robotic collisions have been well developed in literature in the context of determined contact problems. Rank-deficient Jacobian matrices cause the impact equations to be indeterminate. However this issue has not been investigated in previous research. In this paper, the solution for the velocity changes due to impact is proved to be unique in spite of rank-deficient Jacobian matrices and it is solved in a closed form that can be easily employed for simulating robotic system contact states. Furthermore, a set of linear equations with unknown impulses is obtained whereas the impulses can only be solved if extra contact constraints are provided. Two robot collision problems with rank-deficient Jacobian matrices are presented to exemplify the method.
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