A minimum-time trajectory planning method for two robots

A trajectory planning method that ensures collision-free and time-optimal motions for two robotic manipulators with limited actuator torques and velocities is proposed. In terms of parameters defining the positions along the paths of two robots, a two-dimensional coordination space and a maximum velocity curve are constructed to detect collision regions and to plan a time-optimal velocity curve, respectively. An algorithm is then provided for the case of zero initial velocities and a single collision region. A numerical example is included.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>