Kinematic predictor for articulated mechanisms

摘要

A predictor usable for rapid and accurate calculation of joint commands of an articulated mechanism describes relationship between the joints in the form of a differential equation. The predictor solves this differential equation by direct substitution of a power series for each of its variables and the combining of selected sets of coefficients of these power series into linear systems of equations which may be solved to determine power series coefficients to arbitrary order.

主权项

1. A predictor system comprising:
an articulated linkage providing a system of links connected by joints including at least one ground link referenced to a global ground reference; an electronic computer executing a. stored program held in non-transitory media to: (1) store at least two systems of differential equations, a first system describing a rate of change in joint states as a function of other joint states, and a second system accounting for continuous changes in that function as the linkage articulates, wherein the joints are held as joint state variables, and wherein the joints include at least one work joint; (2) expand the joint state variables with power series representations of the joint state variables; (3) receive an input describing a trajectory of at least one joint state variable of the at least one work joint; (4) determine values of multiple orders of coefficients of the power series representations of the state variables for joints other than the at least one work joint satisfying a linear relationship among power series coefficients for the state variables; and (5) output data describing displacement of the joints other than the at least one work joint necessary to produce the input trajectory of the joint state variable of the at least one work joint; wherein each joint includes an actuator controllably changing a joint position providing and wherein the outputs are adapted to drive the actuators.