A methodology for implementing the curvature theory approach to path tracking with planar robots

Planar motion can be synthesized with two-degree-of-freedom curvature theory by using the second-order Taylor series to coordinate planar path-tracking systems. Second-order control-variable coordination generates tracking error away from the reference point, and tracking becomes erratic when the driving variable experiences a dwell in its trajectory. This paper extends the technique through an algorithm that addresses both tracking errors and control variable dwells. The algorithm corrects the coefficients in the coordinating Taylor series when an error parameter is exceeded and switches the control variable when the current driving variable approaches a dwell. The algorithm is applied to a revolute–revolute mechanism to track a polynomial path. The approach utilizes local path information and executes tracking using an incremental approach. This is an advantage over the traditional method which requires knowledge of the entire path to compute exact joint variable motions before the motion of the system begins.