Abstract

A combined trajectory planning problem and adaptive control problem for a two-link rigid manipulator is presented in this paper. The problem is divided into two parts: path planning for off-line processing, followed by on-line path tracking using an adaptive controller. The path planning is done at the joint level. The motion of the robot is specified by a sequence of knots (positions of the robot’s tip) in space Cartesian coordinates. These knots are then transformed into two sets of joint displacements, and piecewise cubic polynomials are used to fit these two sequences of joint displacements. The cubic spline function is used to construct a trajectory with the velocity and the acceleration as constraints. Linear scaling of the time variable is used to accommodate the velocity and acceleration constraints. A nonlinear scaling of the time variable is performed to fit the velocity to a pre-specified velocity profile. The adaptive scheme used takes full advantage of the known parameters of the manipulator while estimating the unknown parameters. In deriving the dynamic equations of motion, all of the physical parameters of the manipulator, including the distributed masses of the links, are taken into account. Some simulation results for the manipulator with unknown payload masses following a planned trajectory are presented.

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