Minimum-time trajectory planning for two robots

The problem of time-optimum path planning for two robots working in the same workspace is discussed. The problem of planning minimum-time paths for robot manipulators becomes complicated when two manipulators are traveling in the same workspace, especially in intersecting paths. This problem is solved using a variational technique called the method of local variations (MLV), which allows constraints to be placed on both state and phase variables. To solve the problem, a collision-free path and a parameter are chosen for each manipulator. Each of these paths is then parameterized with respect to the parameter chosen for the manipulator. Geometric collision checking is then used with the MLV to ensure that the manipulator traveling at its maximum possible speed does not collide with the other. The proposed algorithm is tested through digital simulations