Analytical optimal guidance algorithm for lunar soft landing with terminal control constraints
01 Jan 2016-pp 481-486
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.
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TL;DR: The proposed optimal trajectory technique satisfies the mission constraints in each phase and provides an overall fuel-minimizing guidance command history.
Abstract: A Legendre pseudo spectral philosophy based multi-phase constrained fuel-optimal trajectory design approach is presented in this paper. The objective here is to find an optimal approach to successfully guide a lunar lander from perilune ( 18 km altitude) of a transfer orbit to a height of 100 m over a specific landing site. After attaining 100 m altitude, there is a mission critical re-targeting phase, which has very different objective (but is not critical for fuel optimization) and hence is not considered in this paper. The proposed approach takes into account various mission constraints in different phases from perilune to the landing site. These constraints include phase-1 (‘braking with rough navigation’) from 18 km altitude to 7 km altitude where navigation accuracy is poor, phase-2 (‘attitude hold’) to hold the lander attitude for 35 sec for vision camera processing for obtaining navigation error, and phase-3 (‘braking with precise navigation’) from end of phase-2 to 100 m altitude over the landing site, where navigation accuracy is good (due to vision camera navigation inputs). At the end of phase-1, there are constraints on position and attitude. In Phase-2, the attitude must be held throughout. At the end of phase-3, the constraints include accuracy in position, velocity as well as attitude orientation. The proposed optimal trajectory technique satisfies the mission constraints in each phase and provides an overall fuel-minimizing guidance command history.
12 citations
09 Jan 2017
3 citations
09 Jan 2017
TL;DR: In this paper, an explicit guidance algorithm for multi-constrained terminal descent phase of lunar soft landing is presented, where a minimum jerk guidance is designed and extended for this purpose to achieve the terminal control and state constraints.
Abstract: An explicit guidance algorithm for multi-constrained terminal descent phase of lunar soft landing is presented in this paper. A minimum jerk guidance is designed and extended for this purpose to achieve the terminal control and state constraints. The closed form jerk expression, obtained using the minimum jerk guidance is analyzed to obtain an explicit expression for acceleration command, which is the physical control variable for the guidance loop. The guidance formulation ensures the minimum rate of change of acceleration and vertical touchdown of the spacecraft towards a designated landing site with high terminal accuracy. The design features of the proposed guidance law are demonstrated using simulation results.
3 citations
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.
1 citations
Cites background from "Analytical optimal guidance algorit..."
...Guidance algorithms mentioned in [7] and [8] are optimal and analytical in nature....
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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.
229 citations
"Analytical optimal guidance algorit..." refers methods in this paper
...A polynomial guidance algorithm wherein acceleration on the Lander is assumed to be a polynomial function of time is introduced in [5]....
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11 Aug 1997
TL;DR: In this article, a guidance law which minimizes the commanded acceleration along with the (weighted) final time is developed, which is a linear function of the states relative to the landing point.
Abstract: A guidance law which minimizes the commanded acceleration along with the (weighted) final time is developed. This guidance law is a linear function of the states (relative to the landing point) and a nonlinear function of the time-to-go. The time-togo is obtained as a solution to a quartic equation which is solved analytically. The advantage of this guidance law is that it does not involve any iterations whatsoever. It is the exact solution to the two-point boundary-value problem associated with the first variation necessary conditions. It also satisfies the second variation necessary conditions for a minimum. An example of a lunar landing is given to demonstrate the optimality of this guidance law.
140 citations
"Analytical optimal guidance algorit..." refers background or methods in this paper
...[2] – [4] discusses about an analytical optimal guidance algorithm with the objective of minimizing the real time acceleration on the vehicle due to actuation of onboard engines....
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...In this paper it is proposed to augment analytical optimal guidance algorithm [2] – [4] for terminal angle constraint by modifying the objective function....
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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.
87 citations
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.
72 citations
"Analytical optimal guidance algorit..." refers background in this paper
...The same polynomial guidance was augmented [7] to have fuel optimality by transforming the original polynomial guidance to a quadratic optimization problem with the objective of minimizing acceleration....
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TL;DR: The zero-effort-velocity (ZEV) error, analogous to the well-known zero- Effort-miss (ZEM) distance, is introduced, leading to a generalized ZEM/ZEV guidance law.
Abstract: This paper presents a comprehensive review of spacecraft guidance algorithms for asteroid intercept and rendezvous missions. Classical proportional navigation (PN) guidance is reviewed first, followed by pulsed PN guidance, augmented PN guidance, predictive feedback guidance, Lambert guidance, and other guidance laws based on orbit perturbation theory. Optimal feedback guidance laws satisfying various terminal constraints are also discussed. Finally, the zero-effort-velocity (ZEV) error, analogous to the well-known zero-effort-miss (ZEM) distance, is introduced, leading to a generalized ZEM/ZEV guidance law. These various feedback guidance laws can be easily applied to real asteroid intercept and rendezvous missions. However, differing mission requirements and spacecraft capabilities will require continued research on terminal-phase guidance laws.
41 citations
"Analytical optimal guidance algorit..." refers background or methods in this paper
...[2] – [4] discusses about an analytical optimal guidance algorithm with the objective of minimizing the real time acceleration on the vehicle due to actuation of onboard engines....
[...]
...In this paper it is proposed to augment analytical optimal guidance algorithm [2] – [4] for terminal angle constraint by modifying the objective function....
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...v(t0) = v0, v(tf) = vf Then the optimal feedback guidance law [2] is...
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