Minimum-time control of robotic manipulators

This dissertation addresses the problem of minimum-time control (MTC) for rigid multi-link robotic manipulators subject to "hard" constraints on the control torques. The problem is classified into three categories. The emphasis of the thesis is placed on the study of the structure of the MTC law for robot systems with constrained path motion and point-to-point motion configurations in the task space.; First, a Hamiltonian canonical formulation of the robot dynamic equations is used to investigate the structure of the MTC law of the robotic manipulator for the point-to-point motion in the absence of obstacles. It is shown that the structure of the MTC law requires that on any finite time interval at least one of the actuators be always in saturation along the optimal trajectory while the rest of them may be saturated or singular. As a result, a partially singular MTC structure is defined and characterized in terms of singular optimal control theory for the purpose of examining the non-bang-bang MTC solution of the robot system. A perturbation-based transformation algorithm is applied to solve this category of the MTC problem. In this algorithm, the original MTC problem, possibly a partially singular one, is converted into a totally non-singular optimal control problem by introducing a perturbed energy term into the original objective functional. It is shown that in the limiting case the solution to the transformed problem is convergent to that of the original MTC problem. The numerical solutions to several example manipulators are presented to verify the theoretical result on the structure of the MTC law. Some of the characteristics of the resulting optimal trajectories are analyzed by using a dynamic scaling approach.; Second, by using the so-called "Extended Pontryagin's Minimum Principle" and a parameterization approach, the structure of the MTC law for robot motion along a prespecified geometric path is explicitly addressed. It is shown that on every finite subinterval of time one and only one actuator is always saturated along the time-optimal trajectory while the others adjust their values of the torques between the upper and lower bounds so that the prespecified path constraints are not violated. Numerous existing results from computer simulations demonstrate this structure.; The results on the structure of the MTC solution for robotic manipulators provide new insight into the dynamic characteristics of robot arms, pertaining to both path planning and design specifications.