Redundancy Control of Robot Manipulators using Task Priority Ashish Singla * , Prasad Kulkarni † , Sandeep Kumar † , Bhaskar Dasgupta † * Department of Aerospace Engineering † Department of Mechanical Engineering Indian Institute of Technology Kanpur – 208016, INDIA Email: asingla@iitk.ac.in Abstract— In this paper, the concept of task priority is discussed and implemented in relation to the inverse kinematic problem of redundant manipulators. A required task is divided into a number of subtasks depending on the order of priority. Several cases are discussed for utilizing the redundancy to fulfil the subtasks like achieving the required orientation, obstacle avoidance etc. The entire procedure is formulated using the pseudoinverse of the Jacobian matrix. The numerical simulations show the efficacy of the redundancy control scheme. I. INTRODUCTION Redundant manipulators are the class of manipulators in which the number of degrees-of-freedom (DOF) are more than what is required to perform a given task. For example six DOF are enough for complete position and orientation control of an end-effector and a manipulator with seven DOF is said to be redundant for the task. Even manipulators with six or less DOF are often regarded as redundant because the particular task to be performed may require fewer DOF than the manipulator actually has. A kinematically redundant manipulator has more number of joints (DOF) than required to completely specify the position and orientation of the end-effector. The linear equa- tions relating unknown joint velocities to given end-effector velocity components in world coordinates have infinite so- lutions and we need to choose a solution which can give optimum performance of the manipulator while tracking a desired trajectory. Performance of the manipulator depends upon the various criteria like torque requirements at joint motors, extent of obstacle avoidance, singularity avoidance etc. The idea for active utilization of redundancy was first proposed in [1] in which the author used the generalized inverse of the Jacobian matrix for the general solution of the joint velocity. He proposed to determine the arbitrary vector as a gradient vector of a scalar function for keeping the joint angles under limits. Then the pseudoinverse control [2] of redundant manipulators in terms of SVD representation was reviewed. The authors supplemented the pseudoinverse con- trol with the homogeneous solution for joint angle distribu- tion. Further the homogeneous solution is utilized to include criteria that is better described in Cartesian co-ordinates such as obstacle avoidance [3]. Here a computationally efficient algorithm is developed to meet the demands of obstacle avoidance in real-time applications. Then the manipulating ability of the robotic arm in positioning and orienting the end-effector is proposed as the manipulability measure and used for singularity avoidance [4]. The same concept is further utilized in manipulability measure for determining the best postures [5] of various manipulators. Thereafter a variety of local versus global optimization methods were investigated for minimizing the torque loading [6] at the joints. The same concept of redundancy resolution is also utilized for various measures of dexterity in [7], [8]. Finally, a systematic framework to the problem of redundancy uti- lization using task priority was given in [9]. Different control schemes used so far can be classified as (1) locally optimal control and (2) globally optimal control. Although the local approach that resolves redundancy based on present information is computationally inexpensive, it lacks a guarantee of global optimality. On the other hand, the second approach guarantees global optimality, but is computationally very expensive. The former one is suitable for real time applications, such as sensor-based obstacle avoidance; the later is better for off-line trajectory planning for tasks requiring the strict optimality, such as obstacle avoidance in a complex workspace and energy minimization. This paper describes and simulates a control scheme based on local optimal control approach for redundant manipulators using the task priority based redundancy control [10]. The concept of task priority is that a task is divided into subtasks with different levels of significance according to their priority and call them tasks with the order of priority. For example, when a redundant manipulator is required to follow a trajec- tory of the end-effector while avoiding obstacles, trajectory tracking may be given as the first priority and obstacle avoidance as the second priority. Each subtask is performed using the DOF that remain after all the subtasks with higher priority have been implemented. This paper highlights the idea with different simulation runs by varying the parameters and DOF of the manipulators. The organization of the paper is as follows. In section 2, the problem is formulated in the framework of resolved motion rate control. Numerical simulations are carried out in section 3 to show the effectiveness of the formulation where it is further extended to the framework of resolved acceleration rate control to include the dynamics of the manipulator. Finally, we summarize the results in section 4. Proceedings of the International Conference on Advances in Control and Optimization of Dynamical Systems (ACODS2007) © ACODS2007 72