Redundancy in a manipulator structure yields increased dexterity and versatility for performing a task due to infinite number of joint motions called ``self-motion,' which result in no end-effector motion. The redundancy of manipulators have been used to achieve some subgoals such as singularity avoidance, obstacle avoidance, joint limit avoidance, minimization of instantaneous kinetic energy, or optimization of joint torque, while also satisfying the primary specification of end-effector trajectory tracking.
For obstacle avoidance control, proposed many algorithms require potential function of distances between manipulator links and obstacles. Obstacle avoidance control only with distance information is acted even when manipulator links move away from obstacles. Hence, a new measure is necessary for economic obstacle avoidance control. Next, because joint velocities or joint torques are bounded in practice, efficient kinematic/dynamic control method is necessary considering actuator saturation. For dual-manipulator systems, efficient on-line collision avoidance control law is necessary to do each works without collision between them. In this dissertation, by introducing new measures for economic obstacle avoidance, we present an efficient obstacle avoidance control algorithm for redundant manipulators. The main contents are organized as follows.
First, we present an efficient obstacle avoidance control algorithm for redundant manipulators using new measures called {\emph} directional-collidability measure} and {\emph} temporal-collidability measure}. Considering relative movements between manipulator links and obstacles, the directional-collidability/temporal-collidability measure is defined as the sum of inverse of predicted collision distances/times between manipulator links and obstacles. Using these proposed measures which contains distance information and relative movements between manipulator links and obstacles, we can reduce the magnitude of obstacle avoidance action considerably, especially when manipulator links move away from obstacles. When manipulator links move to obstacles slowly, the directional-collidability measure makes stronger avoidance action than the temporal-collidability measure. In the other case, the temporal-collidability is superior to the directional collidability measure.
Next, we propose a velocity-bounded kinematic control law and a simple dynamic control law with bounded joint torques. For kinematic or dynamic redundancy resolution, null space control is utilized to avoid obstacles by optimizing a cost function. By considering joint velocity bounds, joint velocity saturation function is used to scale null-space joint velocities. Also, torque-bounded dynamic control law is presented which allows reasonably large gain to improve the system performance. By clarifying decomposition in the joint acceleration level, a simple dynamic control law with kinematic performance measure is presented which guarantees trajectory tracking while performing a subtask such as obstacle avoidance.
Finally, on-line collision avoidance control law for dual-manipulator systems using collidability measure is presented. Using linear link model for manipulator links, collidability measure is derived for dual-manipulator systems. Several examples show that the proposed control law is efficient and economic for collision avoidance.
