Convex time-optimal robot path following with Cartesian acceleration and inertial force and torque constraints

In time-optimal robot path following, a predetermined geometric trajectory is followed exactly in a time-optimal way considering system constraints, for example, actuator constraints. For a simplified robotic manipulator, this optimization problem can be reformulated into a convex optimization problem when only considering some system constraints. In this article, the convex approach is extended to account for Cartesian acceleration constraints and in turn account for inertial forces and torques acting on a load held by the robot. The focus of this article is on the reformulation of these Cartesian acceleration and inertial forces and torques to preserve the convexity of the optimization problem. We present a series of applications that result in solving a convex optimization problem, illustrating the practicality of the proposed reformulations.