Abstract: To resolve multi-objective programming problem of the continuous trajectory for redundant robots, the principle of the multi-objective arbitration is analyzed. A product arbitration method is designed and its feasibility is shown. The quotient exterior point penalty function method is proposed to deal with the constraints in the product arbitration model. The product arbitration based optimization model has complex local extremum point structure, and requires the solver to possess very strong ability to search the global extremum. Therefore, a Gaussian rovering particle swarm optimization (GR-PSO) method is proposed. The GR-PSO and the standard PSO algorithm are used to search the global extremum of five constrained and unconstrained optimization testing functions for a hundred times respectively. The results show that the success ratio of the GR-PSO is superior to the standard PSO obviously. In resolving a 7-dimensional optimization testing function with complex local extremum point structure, the success ratio of GR-PSO is 80%, and that of the standard PSO is zero, which shows the GR-PSO has stronger ability to search the global extremum point in resolving high-dimensional optimization problem. The GR-PSO can resolve the path planning problem for robots with multiple degrees of freedom.