Path-constrained trajectory planning of robot arm passing through singularities

Path-constrained robot trajectory planning in the vicinity of ordinary singularities is studied in this paper. First, the desired end-effector path, is parameterized with an untimed variable q₀, by which the robot kinematics can be formulated as a nonlinear equation. The solution to this equation forms a spatial curve in the augmented joint space. Then the path-tracking problem can be fulfilled by computing the curve solution numerically. This produces a pseudo trajectory respected to an artificial independent parameter s, which represents the arc-length of the solution curve. The trajectory respected to time is can be obtained naturally by arbitrary assigning s(t). Numerical simulations are carried out to verify the algorithm.