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Application of direct methods in optimal path planning of redundant cooperative robots

This paper introduces a numerical technique for solving the optimal path planning problem of redundant cooperative manipulators. The technique is based on converting abstract optimization problems to parametric optimization problems using direct methods. In this approach, the state and control variables are expanded in finite numbers of Legendre polynomials and the kinematics of cooperative system as well as performance index of optimization problem are approximated. Application of this method results in the transformation of nonlinear differential and integral expressions into nonlinear algebraic expressions. The optimal states are then determined by solving a set of nonlinear equations in Legendre coefficients. The approach is applied to a cooperative manipulator system consisting of two 3-DOF serial manipulators jointly carrying an object. The results are compared with those obtained from solving a two point boundary value problem, as an abstract optimization approach.