Increasing efficiency of optimization-based path planning for robotic manipulators

Path planning for robotic manipulators interacting with obstacles is considered, where an end-effector is to be driven to a goal region in minimum time, collisions are to be avoided, and kinematic and dynamic constraints are to be obeyed. The obstacles can be time-varying in their positions, but the positions should be known or estimated over the prediction horizon for planning the path. This non-convex optimization problem can be approximated by Mixed Integer Programs (MIPs), which usually leads to a large number of binary variables, and hence, to inacceptable computational time for the planning. In this paper, we present a geometric result whose application drastically reduces the number of binary decision variables in the aforementioned MIPs for 3D motion planning problems. This leads to a reduction in computational time, which is demonstrated for different scenarios.