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Proceedings ArticleDOI

Inverse polynomial based explicit guidance for lunar soft landing during powered braking

05 Nov 2015-pp 768-773
TL;DR: An explicit guidance law for the powered descent phase of the soft lunar landing is presented and the proposed explicit method is extended to optimal guidance formulation to ensure the fuel minimum descent.
Abstract: In this paper an explicit guidance law for the powered descent phase of the soft lunar landing is presented. The descent trajectory, expressed in polynomial form is fixed based on the boundary conditions imposed by the precise soft landing mission. Adapting an inverse model based approach, the guidance command is computed from the known spacecraft trajectory. The guidance formulation ensures the vertical orientation of the spacecraft during touchdown. Also a closed form relation for the final flight time is proposed. The final time is expressed as a function of initial position and velocity of the spacecraft (at the start of descent) and also depends on the desired landing site. To ensure the fuel minimum descent the proposed explicit method is extended to optimal guidance formulation. The effectiveness of the proposed guidance laws are demonstrated with simulation results.
Citations
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Journal ArticleDOI
TL;DR: The proposed optimal trajectory technique satisfies the mission constraints in each phase and provides an overall fuel-minimizing guidance command history.

12 citations

Journal ArticleDOI
01 Mar 2020
TL;DR: An autonomous optimal guidance algorithm for multi-phase lunar soft landing is presented and an initial continuity of the guidance command is attempted in an approximate manner to facilitate a smooth transition between successive segments.
Abstract: In this paper, an autonomous optimal guidance algorithm for multi-phase lunar soft landing is presented. Various stringent requirements of a typical multi-phase soft landing are incorporated in guidance formulation. The proposed guidance law is formulated using the model predictive static programming (MPSP), which is an emerging computational guidance algorithm. High accuracy on the terminal position and velocity at the end of each phase is ensured, as the formulation of the MPSP inherently poses terminal output as a set of hard constraints. The spacecraft terminal orientation requirement is embedded in the guidance formulation in a soft constrained manner. Moreover, to facilitate a smooth transition between successive segments, an initial continuity of the guidance command is also attempted in an approximate manner. The effectiveness of the proposed method is demonstrated with simulation results. A processor-in-loop simulation study has been presented to demonstrate the feasibility of the proposed guidance law for possible on-board implementation.

12 citations

Journal ArticleDOI
19 Jul 2021
TL;DR: The last phases of autonomous lunar landing trajectories are addressed and the proposed guidance is based on the Particle Swarm Optimization, and the differential flatness approach, which is a subclass of the inverse dynamics technique.
Abstract: The problem of real-time optimal guidance is extremely important for successful autonomous missions. In this paper, the last phases of autonomous lunar landing trajectories are addressed. The proposed guidance is based on the Particle Swarm Optimization, and the differential flatness approach, which is a subclass of the inverse dynamics technique. The trajectory is approximated by polynomials and the control policy is obtained in an analytical closed form solution, where boundary and dynamical constraints are a priori satisfied. Although this procedure leads to sub-optimal solutions, it results in beng fast and thus potentially suitable to be used for real-time purposes. Moreover, the presence of craters on the lunar terrain is considered; therefore, hazard detection and avoidance are also carried out. The proposed guidance is tested by Monte Carlo simulations to evaluate its performances and a robust procedure, made up of safe additional maneuvers, is introduced to counteract optimization failures and achieve soft landing. Finally, the whole procedure is tested through an experimental facility, consisting of a robotic manipulator, equipped with a camera, and a simulated lunar terrain. The results show the efficiency and reliability of the proposed guidance and its possible use for real-time sub-optimal trajectory generation within laboratory applications.

7 citations

Proceedings ArticleDOI
08 Jan 2018

1 citations

Journal ArticleDOI
TL;DR: In this article , the vectorized high-order expansions (VHOE) method was used to extract commands and near-optimal trajectory of the booster landing in the presence of initial deviations and uncertainties.
References
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Proceedings ArticleDOI
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


"Inverse polynomial based explicit g..." refers background in this paper

  • ...Considering the linear equation of motion of the spacecraft derived in the inertial frame of reference, the constrained terminal velocity guidance (CTVG) [1] provides an analytic fuel optimal solution for planetary landing....

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Proceedings ArticleDOI
05 Aug 2002
TL;DR: To ensure successful future Mars landing missions, the lander must be capable of detecting hazards in the landing zone and maneuvering to a new and safe site.
Abstract: To ensure successful future Mars landing missions, the lander must be capable of detecting hazards in the landing zone and maneuvering to a new and safe site.

53 citations


"Inverse polynomial based explicit g..." refers methods in this paper

  • ...Considering the quadratic acceleration profiles in all three directions (downrange,crossrange and altitude) a modified Apollo guidance for terminal descent phase has been presented in [5]....

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Proceedings ArticleDOI
01 Jul 2015
TL;DR: The realization of pinpoint soft landing with terminal velocity and position constraints is achieved using Model Predictive Static Programming (MPSP) using a neural network to learn the mapping between various initial conditions in the domain of interest and the corresponding optimal flight time.
Abstract: In this paper the soft lunar landing with minimum fuel expenditure is formulated as a nonlinear optimal guidance problem. The realization of pinpoint soft landing with terminal velocity and position constraints is achieved using Model Predictive Static Programming (MPSP). The high accuracy of the terminal conditions is ensured as the formulation of the MPSP inherently poses final conditions as a set of hard constraints. The computational efficiency and fast convergence make the MPSP preferable for fixed final time onboard optimal guidance algorithm. It has also been observed that the minimum fuel requirement strongly depends on the choice of the final time (a critical point that is not given due importance in many literature). Hence, to optimally select the final time, a neural network is used to learn the mapping between various initial conditions in the domain of interest and the corresponding optimal flight time. To generate the training data set, the optimal final time is computed offline using a gradient based optimization technique. The effectiveness of the proposed method is demonstrated with rigorous simulation results.

11 citations

Proceedings ArticleDOI
29 Jul 2010
TL;DR: In this article, an approach based on the flatness property of the descent equations is proposed for the design of guidance law for planetary landing, and numerical schemes based on polynomial and pseudo-spectral approximations for the problem are considered and compared in a simulation study.
Abstract: The problem of guidance law design for planetary landing is considered and an approach based on the flatness property of the descent equations is proposed. Analytical solutions and numerical schemes based on polynomial and pseudo-spectral approximations for the problem are considered and compared in a simulation study.

7 citations


"Inverse polynomial based explicit g..." refers background in this paper

  • ...A flatness based guidance design for planetary landing has been proposed in [7]....

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Proceedings ArticleDOI
10 Jun 2011
TL;DR: The application of the Chebyshev pseudospectral is described on the optimal control problems, which employs Nth Lagrange polynomial approximations for the state and control variables to transform the state differential equations to algebraic equations.
Abstract: The optimization of lunar soft landing trajectory is an optimization control problem with non-linear free terminal time and control constrained‥ The application of the Chebyshev pseudospectral is described on the optimal control problems. This method employs Nth Lagrange polynomial approximations for the state and control variables to transform the state differential equations to algebraic equations. Finally the optimal control problem is transformed to a nonlinear programming problem. In process of solving the optimal control problem using matlab, control variables and flying time are used as optimal variables. Simulation results demonstrare the methodology for the optimal trajectory designing has strong convergence.

3 citations


Additional excerpts

  • ...Various numerical optimal guidance algorithms like pseudospectral [2], control vector parameterization [3], MPSP [4] has been studied to address the soft landing problem....

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