Optimal motion planning of peg-in-hole task based on mixed logical dynamical system theory

The assembly skill can be regarded as one of the hybrid dynamical systems since the interactive dynamics between an end-effector and an environment varies according to the contact configurations (physical constraints). This paper, firstly, tries to make a model of the assembly skill based on the theory of a mixed logical dynamical system (MLDS), which includes both physical (continuous) dynamics and logical switching. The optimal control problem for standard MLDS can usually be formulated as a mixed integer quadratic programming (MIQP) problem, therefore an optimal sequence of both continuous and logical variables can be found simultaneously by solving MIQP. In case of assembly skill, however, the resulting MLDS includes nonlinear constraints unlike the standard MLDS. This implies that the MLDS based optimal control problem for assembly skill leads to mixed integer nonlinear programming (MINLP). It is also well-known that finding the solution for MINLP is much harder than that for MIQP. Therefore, secondly, this paper presents some ideas to find the optimal solution for assembly skill with less computation. Finally, some simulation results on peg-in-hole task are shown to verify the usefulness of our idea.