Evidence for Composite Cost Functions in Arm Movement Planning: An Inverse Optimal Control Approach

An important issue in motor control is understanding the basic principles underlying the accomplishment of natural movements. According to optimal control theory, the problem can be stated in these terms: what cost function do we optimize to coordinate the many more degrees of freedom than necessary to fulfill a specific motor goal? This question has not received a final answer yet, since what is optimized partly depends on the requirements of the task. Many cost functions were proposed in the past, and most of them were found to be in agreement with experimental data. Therefore, the actual principles on which the brain relies to achieve a certain motor behavior are still unclear. Existing results might suggest that movements are not the results of the minimization of single but rather of composite cost functions. In order to better clarify this last point, we consider an innovative experimental paradigm characterized by arm reaching with target redundancy. Within this framework, we make use of an inverse optimal control technique to automatically infer the (combination of) optimality criteria that best fit the experimental data. Results show that the subjects exhibited a consistent behavior during each experimental condition, even though the target point was not prescribed in advance. Inverse and direct optimal control together reveal that the average arm trajectories were best replicated when optimizing the combination of two cost functions, nominally a mix between the absolute work of torques and the integrated squared joint acceleration. Our results thus support the cost combination hypothesis and demonstrate that the recorded movements were closely linked to the combination of two complementary functions related to mechanical energy expenditure and joint-level smoothness

Prediction of three-dimensional crutch walking patterns using a torque-driven model

Computational prediction of 3D crutch-assisted walking patterns is a challenging problem that could be applied to study different biomechanical aspects of crutch walking in virtual subjects, to assist physiotherapists to choose the optimal crutch walking pattern for a specific subject, and to help in the design and control of exoskeletons, when crutches are needed for balance. The aim of this work is to generate a method to predict three-dimensional crutch-assisted walking motions following different patterns without tracking any experimental data. To reach this goal, we collected gait data from a healthy subject performing a four-point non-alternating crutch walking pattern, and developed a 3D torque-driven full-body model of the subject including the crutches and foot- and crutch-ground contact models. First, we developed a predictive (i.e., no tracking of experimental data) optimal control problem formulation to predict crutch walking cycles following the same pattern as the experimental data collected, using different cost functions. To reduce errors with respect to reference data, a cost function combining minimization terms of angular momentum, mechanical power, joint jerk and torque change was chosen. Then, the problem formulation was adapted to handle different foot- and crutch-ground conditions to make it capable of predicting three new crutch walking patterns, one of them at different speeds. A key aspect of our algorithm is that having ground reactions as additional controls allows one to define phases inside the cycle without the need of formulating a multiple-phase problem, thus facilitating the definition of different crutch walking patterns.Postprint (author's final draft

An Inverse Optimal Control Approach to Explain Human Arm Reaching Control Based on Multiple Internal Models

Human motor control is highly efficient in generating accurate and appropriate motor behavior for a multitude of tasks. This paper examines how kinematic and dynamic properties of the musculoskeletal system are controlled to achieve such efficiency. Even though recent studies have shown that the human motor control relies on multiple models, how the central nervous system (CNS) controls this combination is not fully addressed. In this study, we utilize an Inverse Optimal Control (IOC) framework in order to find the combination of those internal models and how this combination changes for different reaching tasks. We conducted an experiment where participants executed a comprehensive set of free-space reaching motions. The results show that there is a trade-off between kinematics and dynamics based controllers depending on the reaching task. In addition, this trade-off depends on the initial and final arm configurations, which in turn affect the musculoskeletal load to be controlled. Given this insight, we further provide a discomfort metric to demonstrate its influence on the contribution of different inverse internal models. This formulation together with our analysis not only support the multiple internal models (MIMs) hypothesis but also suggest a hierarchical framework for the control of human reaching motions by the CNS

Movement curvature planning through force field internal models

Human motion studies have focused primarily on modeling straight point-to-point reaching movements. However, many goal-directed reaching movements, such as movements directed towards oneself, are not straight but rather follow highly curved trajectories. These movements are particularly interesting to study since they are essential in our everyday life, appear early in development and are routinely used to assess movement deficits following brain lesions. We argue that curved and straight-line reaching movements are generated by a unique neural controller and that the observed curvature of the movement is the result of an active control strategy that follows the geometry of one's body, for instance to avoid trajectories that would hit the body or yield postures close to the joint limits. We present a mathematical model that accounts for such an active control strategy and show that the model reproduces with high accuracy the kinematic features of human data during unconstrained reaching movements directed toward the head. The model consists of a nonlinear dynamical system with a single stable attractor at the target. Embodiment-related task constraints are expressed as a force field that acts on the dynamical system. Finally, we discuss the biological plausibility and neural correlates of the model's parameters and suggest that embodiment should be considered as a main cause for movement trajectory curvatur

From humans to humanoids: The optimal control framework

AbstractIn the last years of research in cognitive control, neuroscience and humanoid robotics have converged to different frameworks which aim, on one side, at modeling and analyzing human motion, and, on the other side, at enhancing motor abilities of humanoids. In this paper we try to cover the gap between the two areas, giving an overview of the literature in the two fields which concerns the production of movements. First, we survey computational motor control models based on optimality principles; then, we review available implementations and techniques to transfer these principles to humanoid robots, with a focus on the limitations and possible improvements of the current implementations. Moreover, we propose Stochastic Optimal Control as a framework to take into account delays and noise, thus catching the unpredictability aspects typical of both humans and humanoids systems. Optimal Control in general can also easily be integrated with Machine Learning frameworks, thus resulting in a computational implementation of human motor learning. This survey is mainly addressed to roboticists attempting to implement human-inspired controllers on robots, but can also be of interest for researchers in other fields, such as computational motor control

実験的・数理的アプローチに基づくヒト運動メカニズムに関する研究

国立大学法人長岡技術科学大

Humanoid Robots

For many years, the human being has been trying, in all ways, to recreate the complex mechanisms that form the human body. Such task is extremely complicated and the results are not totally satisfactory. However, with increasing technological advances based on theoretical and experimental researches, man gets, in a way, to copy or to imitate some systems of the human body. These researches not only intended to create humanoid robots, great part of them constituting autonomous systems, but also, in some way, to offer a higher knowledge of the systems that form the human body, objectifying possible applications in the technology of rehabilitation of human beings, gathering in a whole studies related not only to Robotics, but also to Biomechanics, Biomimmetics, Cybernetics, among other areas. This book presents a series of researches inspired by this ideal, carried through by various researchers worldwide, looking for to analyze and to discuss diverse subjects related to humanoid robots. The presented contributions explore aspects about robotic hands, learning, language, vision and locomotion

Fourth Annual Workshop on Space Operations Applications and Research (SOAR 90)

The proceedings of the SOAR workshop are presented. The technical areas included are as follows: Automation and Robotics; Environmental Interactions; Human Factors; Intelligent Systems; and Life Sciences. NASA and Air Force programmatic overviews and panel sessions were also held in each technical area

Movement Curvature Planning through Force Field Internal Models

Human motion studies have focused primarily on modeling straight point-to-point reaching movements. However, many goal-directed reaching movements, such as movements directed towards oneself, are not straight but rather follow highly curved trajectories. These movements are particularly interesting to study since they are essential in our everyday life, appear early in development and are routinely used to assess movement deficits following brain lesions. We argue that curved and straight-line reaching movements are generated by a unique neural controller and that the observed curvature of the movement is the result of an active control strategy that follows the geometry of one’s body, for instance to avoid trajectories that would hit the body or yield postures close to the joint limits. We present a mathematical model that accounts for such an active control strategy and show that the model reproduces with high accuracy the kinematic features of human data during unconstrained reaching movements directed toward the head. The model consists of a nonlinear dynamical system with a single stable attractor at the target. Embodiment-related task constraints are expressed as a force field that acts on the dynamical system. Finally, we discuss the biological plausibility and neural correlates of the model’s parameters and suggest that embodiment should be considered as a main cause for movement trajectory curvature

On the intrinsic control properties of muscle and relexes: exploring the interaction between neural and musculoskeletal dynamics in the framework of the equilbrium-point hypothesis

The aim of this thesis is to examine the relationship between the intrinsic dynamics of the body and its neural control. Specifically, it investigates the influence of musculoskeletal properties on the control signals needed for simple goal-directed movements in the framework of the equilibriumpoint (EP) hypothesis. To this end, muscle models of varying complexity are studied in isolation and when coupled to feedback laws derived from the EP hypothesis. It is demonstrated that the dynamical landscape formed by non-linear musculoskeletal models features a stable attractor in joint space whose properties, such as position, stiffness and viscosity, can be controlled through differential- and co-activation of antagonistic muscles. The emergence of this attractor creates a new level of control that reduces the system’s degrees of freedom and thus constitutes a low-level motor synergy. It is described how the properties of this stable equilibrium, as well as transient movement dynamics, depend on the various modelling assumptions underlying the muscle model. The EP hypothesis is then tested on a chosen musculoskeletal model by using an optimal feedback control approach: genetic algorithm optimisation is used to identify feedback gains that produce smooth single- and multijoint movements of varying amplitude and duration. The importance of different feedback components is studied for reproducing invariants observed in natural movement kinematics. The resulting controllers are demonstrated to cope with a plausible range of reflex delays, predict the use of velocity-error feedback for the fastest movements, and suggest that experimentally observed triphasic muscle bursts are an emergent feature rather than centrally planned. Also, control schemes which allow for simultaneous control of movement duration and distance are identified. Lastly, it is shown that the generic formulation of the EP hypothesis fails to account for the interaction torques arising in multijoint movements. Extensions are proposed which address this shortcoming while maintaining its two basic assumptions: control signals in positional rather than force-based frames of reference; and the primacy of control properties intrinsic to the body over internal models. It is concluded that the EP hypothesis cannot be rejected for single- or multijoint reaching movements based on claims that predicted movement kinematics are unrealistic