A review of uncertainty propagation in orbital mechanics

Luo, Yuling; Yang, Zhen

doi:10.1016/j.paerosci.2016.12.002

Cited by 155 publications

(59 citation statements)

References 129 publications

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“…Thus, the robot state is defined as x t = [p t v t ψ tψt ] and the nominal discrete dynamics f (x t , u t ) are obtained through 4th order Runge-Kutta integration of (18). The nominal state predictionx t and its covariance matrix Σ x t are approximated with a first-order Taylor expansion [21]: where u t is obtained from the predicted inputs of the MPC algorithm. Even though there exists more precise uncertainty propagation methods [21], we use Taylor expansion for the sake of computational efficiency.…”

Section: A Robot Modelmentioning

confidence: 99%

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A Real-Time Approach for Chance-Constrained Motion Planning With Dynamic Obstacles

Castillo-Lopez

Ludivig

Sajadi-Alamdari

et al. 2020

IEEE Robot. Autom. Lett.

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Uncertain dynamic obstacles, such as pedestrians or vehicles, pose a major challenge for optimal robot navigation with safety guarantees. Previous work on motion planning has followed two main strategies to provide a safe bound on an obstacle's space: a polyhedron, such as a cuboid, or a nonlinear differentiable surface, such as an ellipsoid. The former approach relies on disjunctive programming, which has a relatively high computational cost that grows exponentially with the number of obstacles. The latter approach needs to be linearized locally to find a tractable evaluation of the chance constraints, which dramatically reduces the remaining free space and leads to over-conservative trajectories or even unfeasibility. In this work, we present a hybrid approach that eludes the pitfalls of both strategies while maintaining the original safety guarantees. The key idea consists in obtaining a safe differentiable approximation for the disjunctive chance constraints bounding the obstacles. The resulting nonlinear optimization problem is free of chance constraint linearization and disjunctive programming, and therefore, it can be efficiently solved to meet fast real-time requirements with multiple obstacles. We validate our approach through mathematical proof, simulation and real experiments with an aerial robot using nonlinear model predictive control to avoid pedestrians.

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Section: A Robot Modelmentioning

confidence: 99%

“…The nominal state predictionx t and its covariance matrix Σ x t are approximated with a first-order Taylor expansion [21]: where u t is obtained from the predicted inputs of the MPC algorithm. Even though there exists more precise uncertainty propagation methods [21], we use Taylor expansion for the sake of computational efficiency.…”

Section: A Robot Modelmentioning

confidence: 99%

A Real-Time Approach for Chance-Constrained Motion Planning With Dynamic Obstacles

Castillo-Lopez

Ludivig

Sajadi-Alamdari

et al. 2020

IEEE Robot. Autom. Lett.

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“…17,18 Other nonlinear UQ methods include unscented transformation, 19,20 polynomial chaos expansions, 21 and Gaussian mixture models. [22][23][24] A thorough survey of many other UQ methods was provided by Luo nd Yang, 25 though none of these were deemed appropriate for our use due to our models' large number of states, the presence of stochastic inputs, and the need for rapid computations. For that reason, the linear covariance (LC) propagation method is an attractive choice for our problem.…”

Section: Literature Reviewmentioning

confidence: 99%

Rapid uncertainty propagation and chance‐constrained path planning for small unmanned aerial vehicles

et al. 2020

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With the number of small unmanned aircraft systems in the national airspace projected to increase in the next few years, there is growing interest in a traffic management system capable of handling the demands of this aviation sector. It is expected that such a system will involve trajectory prediction, uncertainty propagation, and path planning algorithms. In this work, we use linear covariance propagation in combination with a quadratic programming‐based collision detection algorithm to rapidly validate declared flight plans. Additionally, these algorithms are combined with a dynamic informed RRT∗ algorithm, resulting in a computationally efficient algorithm for chance‐constrained path planning. Detailed numerical examples for both fixed‐wing and quadrotor small unmanned aircraft system models are presented.

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“…The covariance matrix, P ∈ S 6 , is a common measure to characterize the state uncertainty. The covariance matrix propagates in time under the influence of the process and measurement errors [18]. Initial covariance matrix, P 1 , represents the uncertainty in initial state that could have emanated out of navigation error.…”

Section: Uncertainty Propagationmentioning

confidence: 99%

Covariance-Based Multiple-Impulse Rendezvous Design

Shakouri¹,

Kiani²,

Pourtakdoust³

2019

IEEE Trans. Aerosp. Electron. Syst.

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A novel trajectory design methodology is proposed in the current work to minimize the state uncertainty in the crucial mission of spacecraft rendezvous. The trajectory is shaped under constraints utilizing a multiple-impulse approach. State uncertainty is characterized in terms of covariance, and the impulse time as the only affective parameter in uncertainty propagation is selected to minimize the trace of the covariance matrix. Further, the impulse location is also adopted as the other design parameter to satisfy various translational constraints of the space mission. Efficiency and viability of the proposed idea have been investigated through some scenarios that include constraints on final time, control effort, and maximum thruster limit addition to considering safe corridors. The obtained results show that proper selection of the impulse time and impulse position fulfils a successful feasible rendezvous mission with minimum uncertainty.

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A review of uncertainty propagation in orbital mechanics

Cited by 155 publications

References 129 publications

A Real-Time Approach for Chance-Constrained Motion Planning With Dynamic Obstacles

A Real-Time Approach for Chance-Constrained Motion Planning With Dynamic Obstacles

Rapid uncertainty propagation and chance‐constrained path planning for small unmanned aerial vehicles

Covariance-Based Multiple-Impulse Rendezvous Design

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