Abstract
ABSTRACTDirect collocation is a method that converts a two-point boundary-value problem into a nonlinear programming problem by approximating the state variables and controls into parameters. It has been broadly used in studies of space and orbital mechanics yet has been rarely applied in the fields of robotics. This study builds up a mathematical model of a five-linked manipulator arm. Gradually reducing the upper and lower bounds of the five joint actuator outputs, this paper explores the variations in the least-energy cost function and the final time. Special attention has been focused on whether restrictions would ever arouse any un-anticipated oscillation in the joints. The numerical results show some irony. Excessively restricting the upper and lower output bounds of actuators does not actually gain traction in minimizing the cost index. On the contrary, the value of the cost index is increased by 41.77% from 924.87 to 1310.44 for a tunnel case whose radius is 1.5 m. The simulation cautions that unwanted frequency of oscillation begins to surface due to this wishful restricting. This paper demonstrates how Direct Collocation with Nonlinear Programming can be successfully applied to solve robotic path planning problems. It also cautions the users and designers of the manipulator about the unwanted frequency drift so that the users and designers can amend it before the oscillation builds up.
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