convex optimization approach for the path-following problem of two collaborative robots

This paper investigates the time-optimal path-tracking problem for a collaborative robotic system, considering some limitations and dynamic characteristics. this problem is formulated for a robotic system consisting of two-link planar manipulators with and without bar cases along a predetermined geometric path in minimum time. the main challenges are to satisfy both the co-position and co-time conditions of the end-effector movement, as well as the physical limitations of the applied torque to the joints. through discretization and convexification, we convert the problem into a convex cone optimization problem. the numerical example confirms the effectiveness of the method.