A method for solving trajectory optimization problems with multiple no-fly zone constraints using direct collocation

When solving trajectory optimization problems with no-fly zone constraints using direct collocation, both the number of constraints and the number of non-zero elements in the Jacobian matrix escalate rapidly as the number of no-fly zones increases. To address this issue, this paper presents a method for solving trajectory optimization problems with multiple no-fly zone constraints. This method consolidates multiple no-fly zone constraints into a single path constraint, thereby maintaining a consistently low level of constraints and non-zero elements in the corresponding Jacobian matrix, even as the number of no-fly zones increases. It is also proved theoretically that the Karush-Kuhn-Tucker (KKT) solution of the nonlinear programming (NLP) problems before and after the handling are equivalent. The effectiveness of the proposed method is validated through three numerical examples involving multiple no-fly zone constraints. A comparison with the ordinary method for handling no-fly zone constraints is implemented, which confirms the superiority of the proposed method in improving the solving efficiency.