Modulation of Aerodynamic Angles for Optimal Mars Descent Trajectory using Indirect Approach

A formulation, based on indirect approach, that uses both the aerodynamic angles: angle of attack and bank angle as control variables and maximizes the parachute deployment altitude of a Mars entry vehicle is presented. The complexity of handling the control variable ‘angle of attack’ in the indirect approach is overcome by expressing the aerodynamics coefficients as a quadratic polynomial of angle of attack. The problem is formulated as a two point boundary value problem using the Pontryagin’s principle of the optimal control theory. The solution is obtained using differential evolution technique, a heuristic optimization technique. This is an alternative formulation to the commonly used direct approach using non-linear programming. The solution procedure based on indirect approach reduces the number of unknowns drastically compared to the direct approach. The benefit of using angle of attack modulation in addition to bank angle modulation is quantified. The implication of constraints on minimum allowable altitude and maximum deceleration on the optimized trajectory is analyzed using the new formulation and the solution approach.