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A Group Theoretic Metric for Robot State Estimation Leveraging Chebyshev Interpolation

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A Group Theoretic Metric for Robot State Estimation Leveragi...

IEEE International Conference on robotics and Automation (ICRA)

作者： Varun Agrawal Frank Dellaert Institute for Robotics and Intelligent Machines and School of Interactive Computing Georgia Institute of Technology Atlanta GA USA

ISBN: (数字)9798350384574

ISBN: (纸本)9798350384581

We propose a new metric for robot state estimation based on the recently introduced SE 2 (3) Lie group definition. Our metric is related to prior metrics for SLAM but explicitly takes into account the linear velocity of the state estimate, improving over current pose-based trajectory analysis. This has the benefit of providing a single, quantitative metric to evaluate state estimation algorithms against, while being compatible with existing tools and libraries. Since ground truth data generally consists of pose data from motion capture systems, we also propose an approach to compute the ground truth linear velocity based on polynomial interpolation. Using Chebyshev interpolation and a pseudospectral parameterization, we can accurately estimate the ground truth linear velocity of the trajectory in an optimal fashion with best approximation error. We demonstrate how this approach performs on multiple robotic platforms where accurate state estimation is vital, and compare it to alternative approaches such as finite differences. The pseudospectral parameterization also provides a means of trajectory data compression as an additional benefit. Experimental results show our method provides a valid and accurate means of comparing state estimation systems, which is also easy to interpret and report.

关键词： Measurement Interpolation Accuracy Lie groups Chebyshev approximation Polynomials Motion capture

Adaptive Dual Covariance Steering with Active Parameter Estimation

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Adaptive Dual Covariance Steering with Active Parameter Esti...

IEEE Conference on Decision and Control

作者： Jacob W. Knaup Panagiotis Tsiotras School of Interactive Computing College of Computing and the Institute for Robotics and Intelligent Machines Georgia Institute of Technology Atlanta GA USA School of Aerospace Engineering and the Institute for Robotics and Intelligent Machines Georgia Institute of Technology Atlanta GA USA

ISBN: (数字)9798350316339

ISBN: (纸本)9798350316346

关键词： Adaptation models Parameter estimation Uncertainty Additives Artificial neural networks Encoding Random variables Adaptive control

A Group Theoretic Metric for Robot State Estimation Leveraging Chebyshev Interpolation

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arXiv 2024年

作者： Agrawal, Varun Dellaert, Frank Institute for Robotics and Intelligent Machines School of Interactive Computing Georgia Institute of Technology AtlantaGA30332 United States

We propose a new metric for robot state estimation based on the recently introduced SE2(3) Lie group definition. Our metric is related to prior metrics for SLAM but explicitly takes into account the linear velocity of the state estimate, improving over current pose-based trajectory analysis. This has the benefit of providing a single, quantitative metric to evaluate state estimation algorithms against, while being compatible with existing tools and libraries. Since ground truth data generally consists of pose data from motion capture systems, we also propose an approach to compute the ground truth linear velocity based on polynomial interpolation. Using Chebyshev interpolation and a pseudospectral parameterization, we can accurately estimate the ground truth linear velocity of the trajectory in an optimal fashion with best approximation error. We demonstrate how this approach performs on multiple robotic platforms where accurate state estimation is vital, and compare it to alternative approaches such as finite differences. The pseudospectral parameterization also provides a means of trajectory data compression as an additional benefit. Experimental results show our method provides a valid and accurate means of comparing state estimation systems, which is also easy to interpret and report. © 2024, CC BY.

关键词： Trajectories

Recursively Feasible Stochastic Model Predictive Control for Time-Varying Linear Systems Subject to Unbounded Disturbances

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arXiv 2024年

作者： Knaup, Jacob W. Tsiotras, Panagiotis Georgia Institute of Technology School of Interactive Computing Institute for Robotics and Intelligent Machines AtlantaGA United States Georgia Institute of Technology School of Aerospace Engineering Institute for Robotics and Intelligent Machines AtlantaGA United States

Model predictive control solves a constrained optimization problem online in order to compute an implicit closed-loop control policy. Recursive feasibility—guaranteeing that the optimal control problem will have a solution at every time step—is an important property to guarantee the success of any model predictive control approach. However, recursive feasibility is difficult to establish in a stochastic setting and, in particular, in the presence of disturbances having unbounded support (e.g., Gaussian noise). The problem is further exacerbated for time-varying systems, in which case recursive feasibility must be established also in a robust sense, over all possible future time-varying parameter values, as well as in a stochastic sense, over all potential disturbance realizations. This work presents a method for ensuring the recursive feasibility of a convex, affine-feedback stochastic model predictive control problem formulation for systems with time-varying system matrices and unbounded disturbances using ideas from covariance steering stochastic model predictive control. It is additionally shown that the proposed approach ensures the closed-loop operation of the system will satisfy the desired chance constraints in practice, and that the stochastic model predictive control problem may be formulated as a convex program so that it may be efficiently solved in real-time. © 2024, CC BY.

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Adaptive Dual Covariance Steering with Active Parameter Estimation

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arXiv 2024年

作者： Knaup, Jacob W. Tsiotras, Panagiotis School of Interactive Computing College of Computing Institute for Robotics and Intelligent Machines Georgia Institute of Technology AtlantaGA30332-0250 United States School of Aerospace Engineering Institute for Robotics and Intelligent Machines Georgia Institute of Technology AtlantaGA30332-0150 United States

This work examines the optimal covariance steering problem for systems subject to unknown parameters that enter multiplicatively with the state and control, in addition to additive disturbances. In contrast to existing works, the unknown parameters are modeled as random variables and are estimated online. This work proposes the utilization of recursive least squares estimation for efficient parameter identification. A dual control problem is formulated in which the effect of the planned control policy on the parameter estimates is modeled and optimized for. The parameter estimates are then used to modify the pre-computed control policy online in an adaptive control fashion. Finally, the proposed approach is demonstrated in a vehicle control example with closed-loop parameter identification. © 2024, CC BY.

关键词： Parameter estimation

Computationally Efficient Covariance Steering for Systems Subject to Parametric Disturbances and Chance Constraints

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Computationally Efficient Covariance Steering for Systems Su...

IEEE Conference on Decision and Control

This work investigates the finite-horizon optimal covariance steering problem for discrete-time linear systems subject to both additive and multiplicative uncertainties as well as state and input chance constraints. In particular, a tractable convex approximation of the optimal covariance steering problem is developed by tightening the chance constraints and by introducing a suitable change of variables. The solution of the convex approximation is shown to be a valid (albeit potentially suboptimal) solution to the original chance-constrained covariance steering problem.

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Covariance Steering for Systems Subject to Unknown Parameters

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Covariance Steering for Systems Subject to Unknown Parameter...

IEEE Conference on Decision and Control

作者： Jacob W. Knaup Panagiotis Tsiotras School of Interactive Computing College of Computing Institute for Robotics and Intelligent Machines Georgia Institute of Technology Atlanta GA USA School of Aerospace Engineering Institute for Robotics and Intelligent Machines Georgia Institute of Technology Atlanta GA USA

This work considers the optimal covariance steering problem for stochastic systems subject to both additive noise and uncertain parameters which may enter multiplicatively with the state and the control. The unknown parameters are modeled as constant random variables sampled from distributions with known moments. The optimal covariance steering problem is formulated so as to include dependence between the unknown parameters and future states and is solved using sequential convex programming. The proposed approach is demonstrated numerically using a spacecraft control application.

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Covariance Steering for Systems Subject to Unknown Parameters

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arXiv 2023年

作者： Knaup, Jacob Tsiotras, Panagiotis School of Interactive Computing College of Computing Institute for Robotics and Intelligent Machines Georgia Institute of Technology AtlantaGA30332–0250 United States School of Aerospace Engineering Institute for Robotics and Intelligent Machines Georgia Institute of Technology AtlantaGA30332–0150 United States

This work considers the optimal covariance steering problem for systems subject to both additive noise and uncertain parameters which may enter multiplicatively with the state and the control. The unknown parameters are modeled as a constant random variable sampled from a distribution with known moments. The optimal covariance steering problem is formulated using a moment-based representation of the system dynamics, which includes dependence between the unknown parameters and future states, and is solved using sequential convex programming. The proposed approach is demonstrated numerically using a holonomic spacecraft system and an autonomous vehicle control application. © 2023, CC BY.

关键词： Additive noise

Computationally Efficient Covariance Steering for Systems Subject to Parametric Disturbances and Chance Constraints

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arXiv 2023年

作者： Knaup, Jacob W. Tsiotras, Panagiotis The School of Interactive Computing College of Computing the Institute for Robotics and Intelligent Machines Georgia Institute of Technology AtlantaGA30332–0250 United States The School of Aerospace Engineering the Institute for Robotics and Intelligent Machines Georgia Institute of Technology AtlantaGA30332–0150 United States

关键词： Stochastic systems