Mars Entry Trajectory Planning with Range Discretization and Successive Convexification

Abstract: This paper develops a sequential convex programming approach for Mars entry trajectory planning by range discretization. To improve the accuracy of numerical integration, the range of entry trajectory is selected as the independent variable rather than time or energy. A dilation factor is employed to normalize the entry dynamics and integration interval of the performance index so that the difficult free-final-time programming problem can be converted to a fixed-final-range optimization problem. The bank angle rate with respect to the range is introduced as the new control input in order to decouple the control from the state and facilitate convexification of constraints on the bank angle and its rate. The nonlinear bank angle rate constraint is further relaxed into a linear one via inequality relaxation. Moreover, the nonconvex minimum-time performance index is convexified by regarding flight time as a state variable. Then, the Mars entry trajectory planning problem can be formulated into the framework of convex programming after linearization. By range discretization and successive convexification, the reformulated Mars entry trajectory planning problem is transcribed into a series of convex optimization sub-problems that can be sequentially solved using the convex programming algorithm. The virtual control and adaptive trust-region techniques are employed to improve the accuracy, robustness, and computation efficiency of the algorithm. Numerical simulations with comparative studies are presented to demonstrate the convergence performance and efficiency of the proposed algorithm.