Uncertainty Quantication and Control During Mars Powered Descent and Landing using Covariance Steering

Ridderhof, Jack; Tsiotras, Panagiotis

doi:10.2514/6.2018-0611

Cited by 25 publications

(19 citation statements)

References 15 publications

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“…Fortunately, there exist excellent monographs and survey papers on this topic; see [202,203,92,242,5,243,185]. The range of applications has also increased exponentially; we mention quality control, industrial manufacturing, vehicle path planning [205,206], image processing [23], computer graphics [226,227,229,230,231,150], machine learning [228,9,174], and econometrics [109], among others. We shall only briefly review some concepts and results that are relevant to the topics of this paper.…”

Section: Kantorovichmentioning

confidence: 99%

“…In a twin paper[61], we review the by now vast literature[125,126,222,115,254,50,52,55,56,57,60,118,13,14,15,16,17,114,205,206,181,182,208,183,3,67] on optimal steering of probability distributions for Gauss--Markov models in continuous and discrete time, over a finite or infinite time horizon, with or without state and/or control constraints and applications.Downloaded 11/09/21 to 147.162.213.111 Redistribution subject to SIAM license or copyright; see https://epubs.siam.org/page/terms…”

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confidence: 99%

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Stochastic Control Liaisons: Richard Sinkhorn Meets Gaspard Monge on a Schrödinger Bridge

Chen¹,

Georgiou²,

Pavon³

2021

SIAM Rev.

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Schr\" odinger studied a hot gas Gedankenexperiment (an instance of large deviations of the empirical distribution). Schr\" odinger's problem represents an early example of a fundamental inference method, the so-called maximum entropy method, having roots in Boltzmann's work and being developed in subsequent years by Jaynes, Burg, Dempster, and Csisz\' ar. The problem, known as the Schr\" odinger bridge problem (SBP) with ``uniform"" prior, was more recently recognized as a regularization of the Monge--Kantorovich optimal mass transport (OMT) problem, leading to effective computational schemes for the latter. Specifically, OMT with quadratic cost may be viewed as a zerotemperature limit of the problem posed by Schr\" odinger in the early 1930s. The latter amounts to minimization of Helmholtz's free energy over probability distributions that are constrained to possess two given marginals. The problem features a delicate compromise, mediated by a temperature parameter, between minimizing the internal energy and maximizing the entropy. These concepts are central to a rapidly expanding area of modern science dealing with the so-called Sinkhorn algorithm, which appears as a special case of an algorithm first studied in the more challenging continuous space setting by the French analyst Robert Fortet in 1938--1940 specifically for Schr\" odinger bridges. Due to the constraint on end-point distributions, dynamic programming is not a suitable tool to attack these problems. Instead, Fortet's iterative algorithm and its discrete counterpart, the Sinkhorn iteration, permit computation of the optimal solution by iteratively solving the so-called Schr\" odinger system. Convergence of the iteration is guaranteed by contraction along the steps in suitable metrics, such as Hilbert's projective metric.In both the continuous as well as the discrete time and space settings, stochastic control provides a reformulation of and a context for the dynamic versions of general Schr\" odinger bridge problems and of their zero-temperature limit, the OMT problem. These problems, in turn, naturally lead to steering problems for flows of one-time marginals which represent a new paradigm for controlling uncertainty. The zero-temperature problem in the continuous-time and space setting turns out to be the celebrated Benamou--Brenier characterization of the McCann displacement interpolation flow in OMT. The formalism and techniques behind these control problems on flows of probability distributions have attracted significant attention in recent years as they lead to a variety of new applications in spacecraft guidance, control of robot or biological swarms, sensing, active cooling, and network routing as well as in computer and data science. This multifaceted and versatile framework, intertwining SBP and OMT, provides the substrate for the historical and technical overview \ast

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Section: Kantorovichmentioning

confidence: 99%

mentioning

confidence: 99%

Stochastic Control Liaisons: Richard Sinkhorn Meets Gaspard Monge on a Schrödinger Bridge

Chen¹,

Georgiou²,

Pavon³

2021

SIAM Rev.

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“…Since then, many works have been devoted to this problem of infinitehorizon covariance assignment, both for continuous and discrete time systems [5,6,7,8,9]. Recently, the finite-horizon covariance control problem has been investigated by a number of researchers [10,11,12,13,14], relating to the problems of Shrödinger bridges [15] and the Optimal Mass Transfer [16]. Others, including our previous work, showed that the finite covariance control problem solution can be seen as a LQG with a particular weights [17,18], which can be also formulated (and solved) as a LMI problem [19,20,21].…”

Section: Covariance Steering Problemmentioning

confidence: 99%

Optimal Covariance Control for Stochastic Systems Under Chance Constraints

Okamoto

Gol'dshtein

Tsiotras

2018

IEEE Control Syst. Lett.

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103

108

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This work addresses the optimal covariance control problem for stochastic discrete-time linear timevarying systems subject to chance constraints. Covariance steering is a stochastic control problem to steer the system state Gaussian distribution to another Gaussian distribution while minimizing a cost function. To the best of our knowledge, covariance steering problems have never been discussed with probabilistic chance constraints although it is a natural extension. In this work, first we show that, unlike the case with no chance constraints, the covariance steering with chance constraints problem cannot decouple the mean and covariance steering sub-problems. Then we propose an approach to solve the covariance steering with chance constraints problem by converting it to a semidefinite programming problem. The proposed algorithm is verified using two simple numerical simulations.

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“…Therefore, a control that solves the mean and covariance steering problems cannot be found by simply solving each problem separately. One solution would be to perform a fixed point iteration until the mean and covariance steering solutions are in agreement, as was done in [14], but such an iteration would be time consuming and would require guarantees on convergence to be suitable for onboard use. In this section, we present an alternate approach: we modify the covariance steering problem so that it does not depend on the mass.…”

Section: Covariance Steering With Mass Feedbackmentioning

confidence: 99%

Minimum-fuel Powered Descent in the Presence of Random Disturbances

Ridderhof

Tsiotras

2019

AIAA Scitech 2019 Forum

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It has recently been shown that minimum-fuel powered descent guidance can be solved onboard the spacecraft as a convex optimization problem. It therefore presents itself as a promising technology to enable future planetary exploration missions. However, since this approach is formulated as a deterministic optimal control problem, the resulting guidance law is only designed for a single pair of initial and target states without external disturbances. This paper is an attempt to extend this approach to the more general case of steering the initial position and velocity distributions to some target position and velocity distributions, while considering Brownian motion process noise acting on the system. It is shown that when using a stochastic model for powered descent, the design of the reference trajectory is coupled with the closed-loop control law through probabilistic constraints on the control.

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Uncertainty Quantication and Control During Mars Powered Descent and Landing using Covariance Steering

Cited by 25 publications

References 15 publications

Stochastic Control Liaisons: Richard Sinkhorn Meets Gaspard Monge on a Schrödinger Bridge

Stochastic Control Liaisons: Richard Sinkhorn Meets Gaspard Monge on a Schrödinger Bridge

Optimal Covariance Control for Stochastic Systems Under Chance Constraints

Minimum-fuel Powered Descent in the Presence of Random Disturbances

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