The minimum-time path for a robot arm has been a long-standing and unsolved problem of considerable interest. We present a general solution to this problem that involves joint-space tesselation, a dynamic time-scaling algorithm, and graph search. The solution incorporates full dynamics of movement and actuator constraints, and can be easily extended for joint limits and workspace obstacles, but is subject to the particular tesselation scheme used. The results presented show that, in general, the optimal paths are not straight lines, but rather curves in joint-space that utilize the dynamics of the arm and gravity to help in moving the arm faster to its destination. Implementation difficulties due to the tesselation and to combinatorial proliferation of paths are discussed.

An efficient algorithm is presented for the calculation of the inverse kinematic accelerations for a 6 degree-of-freedom manipulator with a spherical wrist. The inverse kinematic calculation is shown to work synergistically with the inverse dynamic calculation, producing kinematic parameters needed in the recursive Newton-Euler dynamics formulation. Additional savings in the dynamics computation are noted for a class of kinematically well-structured manipulators such as spherical-wrist arms and for manipulators with simply-structured inertial parameters.