Dissertation•
Inverse optimal control for redundant systems of biological motion
10 Dec 2015-
TL;DR: This thesis addresses inverse optimal control problems (IOCP) to find the cost functions for which the human motions are optimal, and proposed a new approach to solving the IOCP, in a bounded error framework.
Abstract: This thesis addresses inverse optimal control problems (IOCP) to find the cost functions for which the human motions are optimal. Assuming that the human motion observations are perfect, while the human motor control process is imperfect, we propose an approximately optimal control algorithm. By applying our algorithm to the human motion observations collected for: the human arm trajectories during an industrial screwing task, a postural coordination in a visual tracking task and a walking gait initialization task, we performed an open loop analysis. For the three cases, our algorithm returned the cost functions which better fit these data, while approximately satisfying the Karush-Kuhn-Tucker (KKT) optimality conditions. Our algorithm offers a nice computational time for all cases, providing an opportunity for its use in online applications. For the visual tracking task, we investigated a closed loop modeling with two PD feedback loops. With artificial data, we obtained consistent results in terms of feedback gains’ trends and criteria exhibited by our algorithm for the visual tracking task. In the second part of our work, we proposed a new approach to solving the IOCP, in a bounded error framework. In this approach, we assume that the human motor control process is perfect while the observations have errors and uncertainties acting on them, being imperfect. The errors are bounded with known bounds, otherwise unknown. Our approach finds the convex hull of the set of feasible cost function with a certainty that it includes the true solution. We numerically guaranteed this using interval analysis tools.
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Dissertation•
01 Jan 1988
551 citations
01 Nov 2016
TL;DR: A method to segment human movement by detecting changes to the optimization criterion being used via inverse optimal control is proposed, achieving a segmentation accuracy of 84%.
Abstract: A common hypothesis in human motor control is that human movement is generated by optimizing with respect to a certain criterion and is task dependent. In this paper, a method to segment human movement by detecting changes to the optimization criterion being used via inverse optimal control is proposed. The control strategy employed by the motor system is hypothesized to be a weighted sum of basis cost functions, with the basis weights changing with changes to the motion objective(s). Continuous time series data of movement is processed using a sliding fixed width window, estimating the basis weights of each cost function for each window by minimizing the Karush-Kuhn-Tucker optimality conditions. The quality of the cost function recovery is verified by evaluating the residual. The successfully estimated basis weights are averaged together to create a set of time varying basis weights that describe the changing control strategy of the motion and can be used to segment the movement with simple thresholds. The proposed algorithm is first demonstrated on simulation data and then demonstrated on a dataset of human subjects performing a series of squatting tasks. The proposed approach reliably identifies the squatting movements, achieving a segmentation accuracy of 84%.
36 citations
Cites background from "Inverse optimal control for redunda..."
...This term, denoted as the pivot, may be selected with some prior knowledge of the nature of the cost functions [31]....
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TL;DR: In this paper, an efficient and automatic tool to understand and analyze the human natural and fast gait tasks is proposed, in which the walking motions are the result of an optimization process, and the identification of plausible optimality criteria weight values is achieved with an inverse optimal control approach.
3 citations
Dissertation•
01 Jan 2004
TL;DR: In this paper, a modele de formation de la trajectoire capable of decrire le mode de fonctionnement du systeme and determiner the variable, which lui etait associee, garante du controle de l'equilibre.
Abstract: Le premier objectif de ce travail etait de developper un modele de formation de la trajectoire capable d'une part de decrire le mode de fonctionnement du systeme (definition d'une fonction objective) et d'autre part de determiner la variable, qui lui etait associee, garante du controle de l'equilibre. La theorie de l'optimisation dynamique a donc ete utilisee dans le but de favoriser la comprehension des principes d'organisation et de production de comportements moteurs diriges vers un but. Le second objectif a ete de tester les capacites de prediction de ce modele pour d'eventuels changements de strategie posturale en fonction des contraintes de la tâche a realiser. La validation de ce modele de formation de la trajectoire s'est concretisee par son application a l'analyse de la coordination pluri-articulaire pour un mouvement d'elevation des bras en station bipedique et pour une tâche de poursuite visuelle avec la tete. Le mode de fonctionnement du systeme serait alors relatif a la dynamique du systeme musculo-squelettique et le maintien de l'equilibre serait controler par una variable d'ordre dynamique. D'autre part, l'analyse des facteurs dynamiques d'une tâche de poursuite visuelle rend compte des causes sous-jacentes aux changements de strategies posturales.
3 citations
References
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TL;DR: A mathematical model is formulated which is shown to predict both the qualitative features and the quantitative details observed experimentally in planar, multijoint arm movements, and is successful only when formulated in terms of the motion of the hand in extracorporal space.
Abstract: This paper presents studies of the coordination of voluntary human arm movements. A mathematical model is formulated which is shown to predict both the qualitative features and the quantitative details observed experimentally in planar, multijoint arm movements. Coordination is modeled mathematically by defining an objective function, a measure of performance for any possible movement. The unique trajectory which yields the best performance is determined using dynamic optimization theory. In the work presented here, the objective function is the square of the magnitude of jerk (rate of change of acceleration) of the hand integrated over the entire movement. This is equivalent to assuming that a major goal of motor coordination is the production of the smoothest possible movement of the hand. Experimental observations of human subjects performing voluntary unconstrained movements in a horizontal plane are presented. They confirm the following predictions of the mathematical model: unconstrained point-to-point motions are approximately straight with bell-shaped tangential velocity profiles; curved motions (through an intermediate point or around an obstacle) have portions of low curvature joined by portions of high curvature; at points of high curvature, the tangential velocity is reduced; the durations of the low-curvature portions are approximately equal. The theoretical analysis is based solely on the kinematics of movement independent of the dynamics of the musculoskeletal system and is successful only when formulated in terms of the motion of the hand in extracorporal space. The implications with respect to movement organization are discussed.
4,226 citations
"Inverse optimal control for redunda..." refers methods in this paper
...The kinematics models help us to obtain maximum smoothness in Cartesian or joint spaces and includes the minimization of hand jerk [59], the minimization of the angle jerk [60] and the constraint minimization of the angle acceleration [61]....
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04 Jul 2004
TL;DR: This work thinks of the expert as trying to maximize a reward function that is expressible as a linear combination of known features, and gives an algorithm for learning the task demonstrated by the expert, based on using "inverse reinforcement learning" to try to recover the unknown reward function.
Abstract: We consider learning in a Markov decision process where we are not explicitly given a reward function, but where instead we can observe an expert demonstrating the task that we want to learn to perform. This setting is useful in applications (such as the task of driving) where it may be difficult to write down an explicit reward function specifying exactly how different desiderata should be traded off. We think of the expert as trying to maximize a reward function that is expressible as a linear combination of known features, and give an algorithm for learning the task demonstrated by the expert. Our algorithm is based on using "inverse reinforcement learning" to try to recover the unknown reward function. We show that our algorithm terminates in a small number of iterations, and that even though we may never recover the expert's reward function, the policy output by the algorithm will attain performance close to that of the expert, where here performance is measured with respect to the expert's unknown reward function.
3,110 citations
"Inverse optimal control for redunda..." refers methods in this paper
...[37] solves the inverse optimal control by using the max-margin inverse reinforcement learning method, where the cost function that produces realistic trajectories needs to be recovered....
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29 Jun 2000
TL;DR: Pharmacokinetics of ivermectin after IV administration were best described by a 2-compartment open model; values for main compartmental variables included volume of distribution at a steady state, area under the plasma concentration-time curve, and area underThe AUC curve.
Abstract: Objective—To evaluate the pharmacokinetics of a novel commercial formulation of ivermectin after administration to goats. Animals—6 healthy adult goats. Procedure—Ivermectin (200 μg/kg) was initially administered IV to each goat, and plasma samples were obtained for 36 days. After a washout period of 3 weeks, each goat received a novel commercial formulation of ivermectin (200 μg/kg) by SC injection. Plasma samples were then obtained for 42 days. Drug concentrations were quantified by use of high-performance liquid chromatography with fluorescence detection. Results—Pharmacokinetics of ivermectin after IV administration were best described by a 2-compartment open model; values for main compartmental variables included volume of distribution at a steady state (9.94 L/kg), clearance (1.54 L/kg/d), and area under the plasma concentration-time curve (AUC; 143 [ng•d]/mL). Values for the noncompartmental variables included mean residence time (7.37 days), AUC (153 [ng•d]/mL), and clearance (1.43 L/kg/d). After ...
2,794 citations
"Inverse optimal control for redunda..." refers methods in this paper
...[27], [28] and [29] used inverse reinforcement learning for Markov decision processes....
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TL;DR: This work shows that the optimal strategy in the face of uncertainty is to allow variability in redundant (task-irrelevant) dimensions, and proposes an alternative theory based on stochastic optimal feedback control, which emerges naturally from this framework.
Abstract: A central problem in motor control is understanding how the many biomechanical degrees of freedom are coordinated to achieve a common goal. An especially puzzling aspect of coordination is that behavioral goals are achieved reliably and repeatedly with movements rarely reproducible in their detail. Existing theoretical frameworks emphasize either goal achievement or the richness of motor variability, but fail to reconcile the two. Here we propose an alternative theory based on stochastic optimal feedback control. We show that the optimal strategy in the face of uncertainty is to allow variability in redundant (task-irrelevant) dimensions. This strategy does not enforce a desired trajectory, but uses feedback more intelligently, correcting only those deviations that interfere with task goals. From this framework, task-constrained variability, goal-directed corrections, motor synergies, controlled parameters, simplifying rules and discrete coordination modes emerge naturally. We present experimental results from a range of motor tasks to support this theory.
2,776 citations
"Inverse optimal control for redunda..." refers methods in this paper
...The neural models were often used to minimize the motor neural activity during a movement [71, 72]....
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10 Nov 2003
TL;DR: A new method of a biped walking pattern generation by using a preview control of the zero-moment point (ZMP) is introduced and a preview controller can be used to compensate the ZMP error caused by the difference between a simple model and the precise multibody model.
Abstract: We introduce a new method of a biped walking pattern generation by using a preview control of the zero-moment point (ZMP). First, the dynamics of a biped robot is modeled as a running cart on a table which gives a convenient representation to treat ZMP. After reviewing conventional methods of ZMP based pattern generation, we formalize the problem as the design of a ZMP tracking servo controller. It is shown that we can realize such controller by adopting the preview control theory that uses the future reference. It is also shown that a preview controller can be used to compensate the ZMP error caused by the difference between a simple model and the precise multibody model. The effectiveness of the proposed method is demonstrated by a simulation of walking on spiral stairs.
2,090 citations