Constraint-based resolution and control of redundant manipulators via pseudovariables
Abstract
The primary motion objective for the controller of the robotic manipulator is to make the end-effector follow the desired trajectory. Redundant manipulators have extra degrees of freedom and are often proposed for applications where avoiding obstacles, increasing dexterity, or improving the dynamic response are needed. Achieving such motion goals may be regarded as secondary objective. Redundant manipulators are usually capable of achieving both motion goals. A unified approach to resolve the redundancy and to control the redundant manipulators is proposed. While the dynamical model of the arm accounts for the motion constraints, the redundancy is solved by imposing additional constraints on the motion of the arm. A systematic procedure to eliminate superfluous variables in the model is presented to obtain the model of the minimal order. A new set of variables, termed pseudovariables, is introduced. The procedure leads to the model of the redundant arms in the pseudovariable space, the dimension of which is lower than that of the joint space. The controller is designed in the pseudovariable space. It controls both motion and constraint forces. The non-adaptive version of the proposed control law guarantees asymptotic stability of the closed loop system. The non-adaptive controller can decouple the motion from constraint force. An adaptive version of the proposed controller compensates for the structural uncertainties in the dynamical model. The asymptotic stability of the system with the adaptive controller is also investigated. It is shown that many secondary goals specified to achieve certain objectives related to subtasks can be expressed in the constraint form. Furthermore, it has been demonstrated that most secondary goals, proposed in the literature to resolve the redundancy, may be converted into our constraint form. The redundancy resolution and the control of the redundant manipulators have also been formulated as an optimal control problem. The chosen performance measure specified in conjunction with the pseudovariables, includes terms representing secondary goals.
Degree
Ph.D.
Advisors
Koivo, Purdue University.
Subject Area
Electrical engineering|Systems design
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