NASA's Jet Propulsion Laboratory, Pasadena, California
In an improved method for generating the trajectory of a robotic manipulator, each straight-line segment of the trajectory is composed of a constant- velocity main portion sandwiched between smooth acceleration at the start and smooth deceleration at the finish. The algorithm that implements this method computes the velocity in each accelerating portion as a sinusoidal function of position along the line. This kind of motion was chosen for two reasons: It closely approximates the motion of a human hand along a straightline trajectory, and it provides very smooth transitions between the constant- velocity portion and the accelerational and decelerational end portions.
Heretofore, typical trajectory generating alogorithms have been based on polynomials in position-vs.-time state space The new algorithm yields smoother motions. The algorithm perfoms its computations in the Cartesian coordinates of the workspace. The operator or a higher-level planning computer program sets three parameters: the total distance to be traveled along the specifled straight-line segment, the velocity in the constant-velocity main portion, and the length of the accelerational and decelerational end portions. The algorithm then computes those incremental changes of position along the Cartesian axes that, when implemented at the measurement- sampling-and-command rate of the robotic system (typically, 1 kHz), result in the desired velocity-vs.-position profile.
The figure illustrates a position- servocontrol loop that is closed in the Cartesian workspace. This subsystem can be used in conjunction with a force- reflecting hand controller to implement manual control, or with a computer running the improved trajectory- generating algorithm. Cartesian position commands are supplied by the algorithm or by the hard controller. The actual Cartesian coordinates of the robotic manipulator are computed via a forward kinematic transformation from the manipulator joint angles. The errors (the differences between the commanded and actual Cartesian coordinates) are converted via an inverse kinematic transformation into manipulator-joint- angle set-point commands. The improved trajectory generating algorithm can also be combined with an active-compliance algorithm by use of this servocontrol loop. Two kinds of active compliance have been tested thus far: spring compliance, in which the deviation in the position of the end effector of the robot is proportional to the sensed force; and integrating compliance, in which the velocity of the end effector is proportional to the force sensed in the corresponding direction.
Point of Contact:
Antal K. Bejczy
Mail Stop 198-219
Jet Propulsion Laboratory
4800 Oak Grove Drive
Pasadena CA 91109
818-354-4568
bejczy@telerobotics.jpl.nasa.gov
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Maintained by: Dave Lavery
Last updated: May 10, 1996