Characterizing the Controllable Entry States and Reachable Sites for Planetary Landing
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Future Mars missions requiring increased landing accuracy, higher landed mass, and higher elevation landing are driving the development of entry, descent and landing (EDL) technology. Understanding the envelope of trajectories of which a lander is capable of flying is important for mission analysis and design. In this paper trajectory optimization is used to characterize the envelope of entry trajectories and in particular to evaluate the impact of the vehicle aerodynamic performance (low or mid lift-over-drag ratio (LoD)) and the parachute deployment velocity (Mach 2 or Mach 5) on the envelope. Two characteristic are the focus of our attention: (1) the landing footprint (LFP), or more generally, the reachable set of parachute deployment states from a given entry state, and (2) the set of controllable entry states (CES), set of entry states from which there exists a feasible trajectory to a given parachute deployment state. We are especially interested in using this information in entry guidance development. The first part of the paper addresses the computation and interpretation of the LFP. A trajectory optimization program is used to compute trajectories from the entry state to the different deployment points that form the LFP. Trajectories are optimized to have maximum deployment altitude and are constrained to have high control authority to compensate for the dispersions due to modeling errors for the atmosphere and the vehicle aerodynamic performance. For a given nominal EDL mission, the study of the LFP qualitatively indicates the difficulty of the nominal mission. The second part of the paper addresses the computation and interpretation of the CES. The CES directly shows the allowed dispersions on the entry state. As with the LFP, the trajectories used to find the boundaries of the CES are constrained to have high control authority. It is shown how the CES can be used to provide the target for the skip phase guidance algorithm in a skip-entry guidance system. The target (for the end of the skip phase and beginning of the entry phase) is chosen from the CES so that the margins for errors both in the skip phase and the entry phase are large, ensuring high parachute deployment accuracy in the presence of large uncertainties. In both parts, a Viking- type capsule (low LoD) and an ellipsled-type vehicle (mid LoD) are considered, with deployment speeds of Mach 2 and Mach 5. Entry capability is studied from a guidance point of view, evaluating the performance of the guidance algorithms provided the LFP and CES. Lateral as well as longitudinal motion is considered.