Simplified Dynamic Control of Redundant Manipulators NASA 's Jet Propulsion Laboratory Pasadena, California
A simplified scheme has been proposed for the dynamic control of a robotic manipulator that has redundant joints; that is, extra degrees of freedom beyond those needed to perform the task, which is to position and orient the end effecto r at a specified position and/or move it along a specified trajectory. The extra degrees of freedom can be used to perform a simultaneous subtask (for example, to avoid obstacles or to keep joint angles within ranges that maximize manipulability). The new control scheme is adaptive and is based on the observed performance of the manipulator. It involves neither a complicated mathematical model of the dynamics of the manipulator nor a time-consuming inverse kinematic transformation In a system of n-degrees-of-freedom, the position and orientation of the end effector are represented by an m- dimensional coordinate vector , while the kinematic functions are represented by the r-dimensional vector , where r + m = n. The redundancy can be utilized by placing kinematic equality constraints on to specify the subtask. Then the task and subtask vectors can be combined to obtain , the augmented n-dimensional vector, which increases the apparent dimension of the task space from m to n. In this formulation, the configuration of the manipulator is fully specified and is not redundant. The velocities of the manipulator are related via where t = time, represents the joint angles, and is the n x n augmented Jacobian matrix. The m x n submatrix is associated with the end effector, while the r x n submatrix is related to the kinematic functi ons. The two submatrices and combine to form the square augmented Jacobian matrix . The problem is to devise a scheme that makes track the desired trajectory as closely as possible. In the control scheme shown in Figure 1, the actual end effector coordinates and the current values of the kinematic functions are computed and fed back to the controller. The controller uses this feedback information together with the commanded end-effector motion and the desired kinematic functions to compute the driving torques that are applied at the manipulator joints so as to meet the task and subtask requirements simultaneously. The scheme involves feedforward and feedback paths with adjustable gains, which implement a control law based on the theory of model-reference adaptive control, and is illustrated in Figure 2. The control signal is produced on the ba sis of the performance of the manipulator, with minimal information on the manipulator and payload. Thus, the scheme can cope with unpredictable gross variations of the payload.
More details can be found in:
Seraji, H.: RTask-based configuration control of redundant robots,S Journal of Robotic Systems, 1992, 9(3), pp. 411-451.
Seraji, H., and Colbaugh, R.: RImproved configuration control for redundant robots,S Journal of Robotic Systems, 1990, 7(6), pp. 897-928.
Point of Contact:
Homayoun Seraji,
Mail Stop 198-219
Jet Propulsion Laboratory
4800 Oak Grove Drive
Pasadena, CA 91109
seraji@telerobotics.jpl.nasa.gov
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Last updated: May 10, 1996