Inverse kinematics with closed form solutions for highly redundant robotic systems

This paper presents inverse position kinematics algorithms with real time capability for Justin, a robotic system with high redundancy and many degrees of freedom. The combination of closed form solutions for parts of the kinematic chain embedded in a nonlinear equation solver is shown to be advantageous. The algorithms are evaluated with DLR´s robot Justin both in simulation and reality. Calculation times of 1 ms are achieved, including various optimization criteria for redundancy resolution. In case only a single arm with 7 DoF is considered, a fast calculation time of 250 µs is reached. With inclusion of an iterative step, reachability can be shown in more than 99% of the calculations regardless of the initial guess. The problem of weighting in multi-criteria optimization problems remains, though in the chosen approach the tool tip position is never compromised by other criteria due to the partially closed form solution. The presented algorithm can be applied to inverse position kinematics for all manipulators with serial or tree structure and redundant joints in case closed form solutions are available for parts of the kinematic chain.