Subspace Optimal Control and Motion Camouflage

Abstract

Some insects can move towards female ones or their preys while minimizing the chance of being aware from their natural background using a technique called motion camouflage. In this paper, first as a prelude, an optimal steering law for the minimum time motion camouflage under a speed constraint is proposed. The result of the optimal steering law is then compared with the ones achieved numerically using the pseudospectral collocation and nonlinear programming. The findings from this comparison thereafter leads to a much deeper discussion of the proposed virtual motion camouflage subspace optimization method, which is expected to benefit widely experienced nonlinear constrained optimal control problems. Since the optimization is progressed in the subspace, the solution optimality is justified accordingly. Through this method, the dimension of the nonlinear constrained optimal control problem can be reduced and the rapidly achieved trajectory could be used as a good and feasible initial guess for further optimization.