Consistent numerical methods for state and control constrained trajectory optimisation with parameter dependency

Walton, Claire; Kaminer, Isaac; Gong, Qi

doi:10.1080/00207179.2020.1717633

Cited by 5 publications

(16 citation statements)

References 27 publications

(33 reference statements)

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“…In [19], the consistency of P M is proved. This is the property that if optimal solutions to Problem P M converge as the number of nodes M Ñ 8, they converge to feasible, optimal solutions of Problem P. See [19] for detailed proof and assumptions.…”

Section: A Uncertain Parameter Optimal Controlmentioning

confidence: 97%

“…Proof: The convergence of tx M pt, θqu is given by [19], Lemmas 3.4, 3.5. The convergence of the sequence of solutions tλ M pt, θqu is guaranteed by the optimality of tu M u.…”

Section: B Main Theorem Proofmentioning

confidence: 99%

“…We we impose the assumptions of [19] Section 2. The definition of accumulation point used in the following proof can be found in [19] Definition 3.2.…”

Section: A Assumptions and Definitionsmentioning

confidence: 99%

“…We we impose the assumptions of [19] Section 2. The definition of accumulation point used in the following proof can be found in [19] Definition 3.2. The following assumption is placed on the choice of numerical integration scheme to be utilized in approximating Problem P:…”

Section: A Assumptions and Definitionsmentioning

confidence: 99%

“…The set Θ is compact and x 0 : Θ Þ Ñ R nx is continuous. Moreover, for the compact sets X and U defined in [19]'s Assumptions 2.3 and 2.4, and for each t P r0, T s, θ P Θ, the Jacobians r x and f x are Lipschitz on the set X ˆU , and the corresponding Lipschitz constants L r and L f are uniformly bounded in θ and t. The function F is C 1 on X for all θ P Θ; in addition, F and F x are continuous with respect to θ.…”

Section: A Assumptions and Definitionsmentioning

confidence: 99%

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Defense Against Adversarial Swarms with Parameter Uncertainty

Walton¹,

Kaminer²,

Gong³

et al. 2021

Preprint

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This paper addresses the problem of optimal defense of a High Value Unit against a large-scale swarm attack. We show that the problem can be cast in the framework of uncertain parameter optimal control and derive a consistency result for the dual problem of this framework. We show that the dual can be computed numerically and apply these numerical results to derive optimal defender strategies against a 100 agent swarm attack.

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Section: A Uncertain Parameter Optimal Controlmentioning

confidence: 97%

“…Proof: The convergence of tx M pt, θqu is given by [19], Lemmas 3.4, 3.5. The convergence of the sequence of solutions tλ M pt, θqu is guaranteed by the optimality of tu M u.…”

Section: B Main Theorem Proofmentioning

confidence: 99%

“…We we impose the assumptions of [19] Section 2. The definition of accumulation point used in the following proof can be found in [19] Definition 3.2.…”

Section: A Assumptions and Definitionsmentioning

confidence: 99%

Section: A Assumptions and Definitionsmentioning

confidence: 99%

Section: A Assumptions and Definitionsmentioning

confidence: 99%

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Defense Against Adversarial Swarms with Parameter Uncertainty

Walton¹,

Kaminer²,

Gong³

et al. 2021

Preprint

Self Cite

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Co-Contraction Embodies Uncertainty: An Optimal Feedforward Strategy for Robust Motor Control

Berret,

Verdel,

Burdet

et al. 2024

Preprint

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Despite our environment is often uncertain, we generally manage to generate stable motor behaviors. While reactive control plays a major role in this achievement, proactive control is critical to cope with the substantial noise and delays that affect neuromusculoskeletal systems. In particular, muscle co-contraction is exploited to robustify feedforward motor commands against internal sensorimotor noise as was revealed by stochastic optimal open-loop control modeling. Here, we extend this framework to neuromusculoskeletal systems subjected to random disturbances originating from the environment. The analytical derivation and numerical simulations predict a singular relationship between the degree of uncertainty in the task at hand and the optimal level of anticipatory co-contraction. This prediction is confirmed through a single-joint pointing task experiment where an external torque is applied to the wrist near the end of the reaching movement with varying probabilities across blocks of trials. We conclude that uncertainty calls for impedance control via proactive muscle co-contraction to stabilize behaviors when reactive control is insufficient for task success.Author summaryThis work presents a computational framework for predicting how humans modulate muscle co-contraction to cope with uncertainties of different origins. In our neuromusculoskeletal system, uncertainties have both internal (sensorimotor noise) and external (environmental randomness) origins. The present study focuses on the latter type of uncertainty, which had not been dealt with systematically previously despite its importance in everyday life. Therefore, we thoroughly investigated how random disturbances occurring with some probability in a motor task shape the feedforward control of mechanical impedance through muscle co-contraction. Here we provide theoretical, numerical and experimental evidence that the optimal level of co-contraction steeply increases with the uncertainty of our environment. These findings show that muscle co-contraction embodies uncertainty and optimally mitigates its consequences on task execution when feedback control is insufficient due to sensory noise and delays.

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