Finite Time Robust Control of the Sit-to-Stand Movement for Powered Lower Limb Orthoses

Narvaez-Arocho, Octavio; Packard, Andrew; Arcak, Murat

doi:10.23919/acc.2018.8431465

Cited by 4 publications

(5 citation statements)

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“…x (t) are directly estimated by minimizing/maximizing the i j entries of the solutions for S x (t; t 0 , x 0 , p) at time t for all p ∈ P b . The estimates for S y (t), S y (t) , and S u (t), S u (t) require first plugging the solutions sampled for the state sensitivity in (12), and then computing the extremal values for their respective entries.…”

Section: A Sensitivity-based Reachability Analysismentioning

confidence: 99%

“…t ∈T P vol r x (t), r x (t) , t ∈T P ν r x (t), r x (t) ,x(t) , t ∈T P vol r y (t), r y (t) , t ∈T P ν r y (t), r y (t) ,ŷ(t) , t ∈T P vol r u (t), r u (t) , t ∈T P ν r u (t), r u (t),û(t) , for the system in(9) under the action of the finite horizon LQR controller from[12]; which causes undesired variations of the loads at the shoulders[13]. Using the reciprocals of these values, we set the weights in (13) to w v := [6.98 × 10 7 ; 9.67 × 10 −7 ; 9.71 × 10 4 ],w o := [1.85 × 10 18 ; 7.24; 1.07 × 10 13 ],so that the performance metric for this baseline controller is J P = 6.…”

mentioning

confidence: 99%

“…PLLO This section describes the three-link robot model used for motion planning, control design, and reachability analysis. The contents of this section and Section III-A that follows were published in [12] and [13]. They are included here for self-containment of the paper.…”

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Robust Control of the Sit-to-Stand Movement for a Powered Lower Limb Orthosis

Narvaez-Aroche

Meyer

et al. 2020

IEEE Trans. Contr. Syst. Technol.

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The sit-to-stand movement is a key feature for wide adoption of powered lower limb orthoses for patients with complete paraplegia. In this paper we study the control of the ascending phase of the sit-to-stand movement for a minimally actuated powered lower limb orthosis at the hips. First, we generate a pool of finite horizon Linear Quadratic Regulator feedback gains, designed under the assumption that we can control not only the torque at the hips but also the loads at the shoulders that in reality are applied by the user. Next we conduct reachability analysis to define a performance metric measuring the robustness of each controller against parameter uncertainty, and choose the best controller from the pool with respect to this metric. Then, we replace the presumed shoulder control with an Iterative Learning Control algorithm as a substitute for human experiments. Indeed this algorithm obtains torque and forces at the shoulders that result in successful simulations of the sit-to-stand movement, regardless of parameter uncertainty and factors deliberately introduced to hinder learning. Thus it is reasonable to expect that the superior cognitive skills of real users will enable them to cooperate with the hip torque controller through training. I. IPowered Lower Limb Orthoses (PLLOs) are medical devices worn in parallel to the legs to assist standing and/or walking. State of the art PLLOs for people with paraplegia (≈ 114, 000 individuals in the USA [1]) are commercially known as medical exoskeletons. Their users must have healthy enough skeletal, cardiovascular, vestibular, and visual systems to tolerate standing, as well as mobility in hands, arms, and shoulders to interact with the ground by means of crutches. The majority of exoskeletons are equipped with actuation at the hips and knees [2]-[6], but the most affordable [7] uses a minimally actuated architecture where torque is exclusively applied at the hips [8]. In addition gait cycles on level ground with this design look more natural than those of its competitors. However, it is more difficult for users with complete paraplegia to perform the sit-to-stand (STS) movement, which is the sequence of actions for rising from a chair.The STS movement is executed in three distinctive phases: preparation, ascension, and stabilization, as illustrated in Figure 1. The ascension phase (Figure 1b) starts at seat-off and ends when the links of the shanks and thighs segments almost align with the vertical, and the torso has a slight forward tilt, with all angular velocities close to zero in order to facilitate stabilization about the standing position. It is the most challenging phase because of the greater ranges of joint motion, torques, and forces involved. It also requires precise coordination between the actuators of the PLLO and the loads applied by the upper limbs of the user to avoid sit-back or step failures [9]. This paper makes two main contributions. First, it provides a performance metric to quantify the robustness against parameter uncertainty of a controlle...

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Section: A Sensitivity-based Reachability Analysismentioning

confidence: 99%

mentioning

confidence: 99%

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Robust Control of the Sit-to-Stand Movement for a Powered Lower Limb Orthosis

Narvaez-Aroche

Meyer

et al. 2020

IEEE Trans. Contr. Syst. Technol.

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“…The over-approximations computed for the PLLO were finally provided in simulations to evaluate the worst-case performances of the system under the control design in [10]. The results highlighted its weaknesses to both track the reference trajectories for the kinematics of the CoM, and guarantee small variations of the inputs at the shoulders joints, by displaying large projections of the reachable sets on these variables.…”

Section: Conclusion and Further Workmentioning

confidence: 99%

“…The main objective of our study is to apply this reachability analysis approach to the PLLO, in order to evaluate the worst-case performances of the closed-loop behavior obtained from the finite horizon linear-quadratic regulator (LQR) designed in [10]. Since a proper evaluation of these performances should not be limited to the states, but also include the position and velocity of the Center of Mass (CoM), and the inputs; we extend the method in [8] to be able to apply the reachability analysis to static systems such as those defined by an output map of the system or the feedback controller.…”

Section: Introductionmentioning

confidence: 99%

Reachability Analysis for Robustness Evaluation of the Sit-to-Stand Movement for Powered Lower Limb Orthoses

Narvaez-Aroche

Packard

Meyer

et al. 2018

Volume 1: Advances in Control Design Methods; Advances in Nonlinear Control; Advances in Robotics; Assistive and Rehabilitation

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A sensitivity-based approach for computing over-approximations of reachable sets, in the presence of constant parameter uncertainties and a single initial state, is used to analyze a three-link planar robot modeling a Powered Lower Limb Orthosis and its user. Given the nature of the mappings relating the state and parameters of the system with the inputs, and outputs describing the trajectories of its Center of Mass, reachable sets for their respective spaces can be obtained relying on the sensitivities of the nonlinear closed-loop dynamics in the state space. These over-approximations are used to evaluate the worst-case performances of a finite time horizon linear-quadratic regulator (LQR) for controlling the ascending phase of the Sit-To-Stand movement.

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