# Terminal State Constrained Proportional Navigation Law for Lunar Soft Landing Mission

01 Mar 2018-

TL;DR: Simulation results indicate that the developed methodology can be successfully utilized in lunar landing scenarios, especially in the terminal phases where the Lander orientation has to be vertical at the end.

Abstract: With regards to a typical lunar soft landing guidance formulation, it is required to reach the desired position with terminal velocity and orientation constraints. For the terminal phase of lunar powered descent, an existing proportional navigation law developed for missile guidance is modified. Presently in the algorithm, at the beginning of each guidance cycle, a normal acceleration perpendicular to the instantaneous missile-target line-of-sight is computed. The design augmentation proposed in this paper for lunar landing, introduces a polynomial acceleration term along the line-of-sight direction in addition to the existing normal acceleration which would then ensure terminal velocity requirements. It also has the capability to meet zero line-of-sight angles at the end of trajectory maneuver. Simulation results indicate that the developed methodology can be successfully utilized in lunar landing scenarios, especially in the terminal phases where the Lander orientation has to be vertical at the end.

Citations

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TL;DR: In this article , a convex programming approach was used for planetary landing guidance originally developed for Mars landings and adapted to lunar soft landings, including the addition of state and control constraints that were previously not part of the lossless convexification framework.

Abstract: This paper builds upon a convex programming approach to propellant-optimal planetary landing guidance originally developed for Mars landings and adapts it to lunar soft landings. These novel adaptations include the addition of state and control constraints that were previously not part of the lossless convexification framework: maximum tilt rate, maximum tilt acceleration, maximum thrust ramp rate, and a terminal vertical descent phase. Additionally, we have included an inverse square central gravity model and a minimum altitude constraint in the Moon-centered, Moon-fixed (MCMF) frame. These constraints are convexified and the resulting second-order cone program is solved for an Apollo-like sample case.

References

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TL;DR: In this paper, interactive terminal-descent guidance enables the crew to control the essentially vertical descent rate in order to land in minimum time with safe contact speed, using concepts that make gimbal lock inherently impossible.

Abstract: Apollo Lunar-descent Guidance transfers the Lunar Module from a near-circular orbit to touchdown, traversing 17^o central angle and 15 km altitude in 11 min. A group of interactive programs in an onboard computer guide the descent, controlling altitude and the descent propulsion system throttle. A ground-based program precomputes guidance targets. This paper describes the concepts involved. Explicit and implicit guidance are discussed, guidance equations are derived, and the earlier Apollo explicit equation is shown to be an inferior special case of the later implicit equation. The paper describes interactive guidance by which the two-man crew selects a landing site in favorable terrain and directs the trajectory there. Interactive terminal-descent guidance enables the crew to control the essentially vertical descent rate in order to land in minimum time with safe contact speed. The attitude maneuver routine uses concepts that make gimbal lock inherently impossible. The throttle routine yields zero steady-state thrust-acceleration error or avoids operation within a thrust region forbidden because of hardware limitations. The ground-based program precomputes guidance targets which shape the trajectory to produce an efficient descent with adequate visibility and no transients at the final phasic interface.

185 citations

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Bradley A. Steinfeldt

^{1}, Michael J. Grant^{1}, Daniel A. Matz^{1}, Robert D. Braun^{1}, Gregg H. Barton^{2}•TL;DR: This assessment has shown that negligible propellant mass fraction benefits are seen for reducing the three-sigma position dispersion at the end of the hypersonic guidance phase (parachute deployment) below approximately 3 km.

Abstract: Landing site selection is a compromise between safety concerns associated with the site’s terrain and scientific interest. Therefore, technologies enabling pinpoint landing performance (sub-100-m accuracies) on the surface of Mars are of interest to increase the number of accessible sites for in situ research, as well as allow placement of vehicles nearby prepositioned assets. A survey of the performance of guidance, navigation, and control technologies that could allow pinpoint landing to occur at Mars was performed. This assessment has shown that negligible propellant mass fraction benefits are seen for reducing the three-sigma position dispersion at the end of the hypersonic guidance phase (parachute deployment) below approximately 3 km. Four different propulsive terminal descent guidancealgorithms were examined. Of these four, a near propellant-optimal analytic guidance law showed promisefortheconceptualdesignofpinpointlandingvehicles.Theexistenceofapropellantoptimumwithregardto theinitiationtimeofthepropulsiveterminaldescentwasshowntoexistforvarious flightconditions.Subsonicguided parachutes were shown to provide marginal performance benefits, due to the timeline associated with descent through the thin Mars atmosphere. This investigation also demonstrates that navigation is a limiting technology for Mars pinpoint landing, with landed performance being largely driven by navigation sensor and map tie accuracy.

79 citations

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21 Aug 2006

TL;DR: In this article, a number of powered terminal descent guidance algorithms for Mars pinpoint landing (PPL) are compared and a class of sub-optimal guidance laws based on simple polynomial basis functions are discussed.

Abstract: I. Abstract In this paper, we formulate and compare a number of powered terminal descent guidance algorithms for Mars pinpoint landing (PPL). The PPL guidance problem involves finding a trajectory that transfers the spacecraft from any g iven state at engine ignition to a desired terminal state (usually within 100m of a desired target) without violating fuel limits or any state constraints and control constraints. Sp ecifically, we first formulate the fuel-optimal guidance problem and show that a direct method can be used to reduce it to a finite-dimensional convex program. Modern interior point methods can then be used to find the global solution to any desired level of accuracy. Nex t, we discuss a class of suboptimal guidance laws based on simple polynomial basis functions. The performance of the sub-optimal guidance laws under a variety of realistic mission constraints are compared to the global fuel-optimal solution.

64 citations

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TL;DR: In this paper, two circular guidance laws have been developed based on a 3D vector approach: one circular guidance law without terminal velocity direction constraint and the other one with terminal velocity directional constraint.

Abstract: Two circular guidance laws have been developed based on a 3-D vector approach: one circular guidance law without terminal velocity direction constraint and the other circular guidance law with terminal velocity direction constraint. Both approaches can be implemented easily with predictable time to go and trajectory. They are effective for both stationary and moving targets.

11 citations

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B Ramkiran

^{1}, R Preethi^{1}, M.P. Rijesh^{1}, G. V. P. Bharat Kumar^{1}, N. K. Philip^{1}, P Natarajan^{1}•TL;DR: In this paper, the authors proposed to augment an existing optimal analytical guidance algorithm for the purpose of achieving terminal angle constraint during the terminal powered descent phase of a lunar soft landing mission.

Abstract: In this paper it is proposed to augment an existing optimal analytical guidance algorithm for the purpose of achieving terminal angle constraint during the terminal powered descent phase of a lunar soft landing mission. Basic algorithm formulation caters to minimizing the acceleration due to onboard engines to minimize the fuel spend and reach the desired position with desired velocity. However, in order to cope up with terminal angle constraint, an augmentation is proposed in the objective function wherein the aim is not only to minimize the energy but also to minimize the terminal error in acceleration achieved and the desired acceleration specified by the designer. This inadvertently leads to the desired terminal angle. Simulations done for the fine braking phase of lunar soft landing mission prove that terminal attitude constraints are met with the modification in objective function.

4 citations

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