NASA 's Jet Propulsion Laboratory, Pasadena, California
A robotic control system causes a remote manipulator to follow closely a reference trajectory in a Cartesian reference frame in the work space, without resort to a computationally intensive mathematical model of robot dynamics and without knowledge of the robot and load parameters. The system, derived from linear multivariable theory, uses relatively simple feedforward and feedback controllers with model-reference adaptive control . The system requires measurements of the position and velocity of the end effector of the manipulator. These can be obtained directly from optical sensors or by calculation using the known kinematic relationships between the measured manipulator-joint angles and the end-effector position. In deriving the control equations, the coupled nonlinear differential equations o f the robot dynamics and kinematics are first expressed in general form, then linearized by the calculation of perturbations about a specified operating point in the Cartesian coordinates of the end effector. The resulting mathematical model is a linear multivariable system of order 2n (where n = the number of independent spatial coordinates of the manipulator) that expresses the relationship between the increments of the n actuator control voltages (inputs) and the increments of the n coordinates of end-effector trajectory (outputs). The problem then becomes one of making the end-effector trajectory increments track the reference-trajectory increments: this requires independent feedback and feedforward controllers. The feedback controller provides a stable closed-loop system with poles at desired locations in the Laplace-transform complex- frequency domain and ensures that initial tracking errors decrease asymptotically to zero with time. For this purpose, it suffices to apply position and velocity feedback through n x n position- and velocity-feedback gain matrices. The feedforward controller causes the actual position to track the reference position. The incremental feedforward controller is chosen to be the minimal- order inverse of the end-effector transfer function. The total control law combin es the trajectory and actuator-voltage increments with the values of the actuator voltages and positions at the nominal operating point. The gains of the controllers and the operating-point term in the total control la w are varied continuously to adapt to variations in the coefficients of the robot model due to changes in the operating point. The adaptation laws, derived by the
Lyapunov method, do not require the knowledge of any robot parameters or of the payload and are based entirely on the reference trajectory and the tracking error, both of which are available. Thus, the adaptive controller treats the robo t as a "black box.''
Point of Contact:
Homayoun Seraji,
Mail Stop 198-219
Jet Propulsion Laboratory
4800 Oak Grove Drive
Pasadena, CA 91109
seraji@telerobotics.jpl.nasa.gov
Telerobotics Program
page
Please email the site webmaster
with any comments, criticisms or corrections
for this page.
Maintained by: Dave Lavery
Last updated: May 10, 1996