Planning for kinematically smooth manipulator trajectories

This paper presents a general methodology and accompanying formulation for planning kinematically smooth path trajectories for serial robot manipulators. Starting from an initial point on the path, it is required to traverse a path trajectory without halting the motion (typically due to switch from one inverse solution to another). The problem focuses on determining a starting configuration at the initial point on the path. The problem is formulated in terms of a constraint function and characterized by a system of differential-algebraic equations (DAEs) of index 2. These DAEs are solved numerically by Runge-Kutta (RK) methods while a best starting configuration is chosen using a cost-function driven optimization method. The formulation is demonstrated through a planar 3 degree of freedom robot manipulator.