This paper utilizes the modified pattern search method to solve the nonlinear optimization problem of design of minimum-time robot trajectories between given end states in a workspace containing obstacles. This method is applied to a collision-free path of a two-degree-of-freedom elbow manipulator. Bezier curves, B-spline curves, and parabolic blend curves are used to simplify end-effector path planning.

Motion of the manipulator, represented by a sequence of Cartesian knots along the end-effector path, is first transformed into sets of joints displacements. Piecewise cubic spline functions are then fit to the sequence of joint displacements. The minimum-time trajectory planning problem is formulated as the problem of minimizing the total traveling time, taken as objective function, subject to constraints on joint positions, velocities, accelerations, jerks, motor torques, and end-effector acceleration.

The computer program, ROBOPATH, has been developed to implement this algorithm for generating end-effector paths and joint trajectories for a manipulator with two links. The results show the modified pattern search method to be a very effective nonlinear optimization technique in design of minimum-time robot trajectories. Also, ROBOPATH can be a useful tool in the design of manipulators, robot tasks and workcells.

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