Optimal control simulations reveal mechanisms by which arm movement improves standing long jump performance

Optimal control simulations of the standing long jump were developed to gain insight into the mechanisms of enhanced performance due to arm motion. The activations that maximize standing long jump distance of a joint torque actuated model were determined for jumps with free and restricted arm movement. The simulated jump distance was 40 cm greater when arm movement was free (2.00 m) than when it was restricted (1.60 m). The majority of the performance improvement in the free arm jump was due to the 15% increase (3.30 vs. 2.86 m/s) in the take-off velocity of the center of gravity. Some of the performance improvement in the free arm jump was attributable to the ability of the jumper to swing the arms backwards during the flight phase to alleviate excessive forward rotation and position the body segments properly for landing. In restricted arm jumps, the excessive forward rotation was avoided by "holding back" during the propulsive phase and reducing the activation levels of the ankle, knee, and hip joint torque actuators. In addition, swinging the arm segments allowed the lower body joint torque actuators to perform 26 J more work in the free arm jump. However, the most significant contribution to developing greater take-off velocity came from the additional 80 J work done by the shoulder actuator in the jump with free arm movement.     

Iterative learning control applied to a hybrid rehabilitation exoskeleton system powered by PAM and FES

Currently upper limb exoskeleton rehabilitation robots powered by electric motors used in the hospitals are usually cumbersome, bulky and unmovable. Our developed RUPERT is a low-cost lightweight portable exoskeleton rehabilitation robot that can encourage stroke patients with high stiffness in arm flexor muscles to receive frequent intensive rehabilitation trainings in the community or home, but its joints are unidirectionally actuated by pneumatic artificial muscles (PAMs). RUPERT with one PAM of each joint is not suitable for stroke patients with weak muscles in the flaccid paralysis period. Functional electrical stimulation (FES) uses current with low frequency to activate paralyzed muscles, which can produce muscle torque and compensate the unidirectional drawbacks of RUPERT, so as to realize the two-way motion of its joints for passive reaching trainings. As both the exoskeleton robot driven by PAMs and neuromuscular skeletal system under FES possess the highly nonlinear and time-varying characteristics, which adds control difficulty to the hybrid dynamic system, iterative learning control (ILC) is chosen to control this newly designed hybrid rehabilitation system to realize repetitive task trainings.     

Mathematical Modeling of Pneumatic Artificial Muscle Actuation via Hydrogen Driving Metal Hydride-LaNi5

Quantitative understanding of mechanical actuation of intricate Pneumatic Artificial Muscle (PAM) actuators is technically required in control system design for effective real-time implementation.This paper presents mathematical modeling of the PAM driven by hydrogen-gas pressure due to absorption and desorption of metal hydride.Empirical models of both mechanical actuation of industrial PAM and chemical reaction of the metal hydride-LaNi5 are derived systematically where their interactions comply with the continuity principle and energy balance in describing actual dynamic behaviors of the PAM actuator (PAM and hydriding/dehydriding-reaction bed).Simulation studies of mechanical actuation under various loads are conducted so as to present dynamic responses of the PAM actuators.From the promising results,it is intriguing that the heat input for the PAM actuator can be supplied to,or pumped from the reaction bed,in such a way that absorption and desorption of hydrogen gas take place,respectively,in controlling the pressure of hydrogen gas within the PAM actuator.Accordingly,this manipulation results in desired mechanical actuation of the PAM actuator in practical uses.     

Application of EMG signals for controlling exoskeleton robots.

Exoskeleton robots are mechanical constructions attached to human body parts, containing actuators for influencing human motion. One important application area for exoskeletons is human motion support, for example, for disabled people, including rehabilitation training, and for force enhancement in healthy subjects. This paper surveys two exoskeleton systems developed in our laboratory. The first system is a lower-extremity exoskeleton with one actuated degree of freedom in the knee joint. This system was designed for motion support in disabled people. The second system is an exoskeleton for a human hand with 16 actuated joints, four for each finger. This hand exoskeleton will be used in rehabilitation training after hand surgeries. The application of EMG signals for motion control is presented. An overview of the design and control methods, and first experimental results for the leg exoskeleton are reported.     

Balance control during an arm raising movement in bipedal stance: which biomechanical factor is controlled?

In order to obtain new insight into the control of balance during arm raising movements in bipedal stance, we performed a biomechanical analysis of kinematics and dynamical aspects of arm raising movements by combining experimental work, large-scale models of the body, and techniques simulating human behavior. A comparison between experimental and simulated joint kinematics showed that the minimum torque change model yielded realistic trajectories. We then performed an analysis based on computer simulations. Since keeping the center of pressure (CoP) and the projection of the center of mass (CoM) inside the support area is essential for equilibrium, we modeled an arm raising movement where displacement of one or the other variable is limited. For this optimization model, the effects of adding equilibrium constraints on movement trajectories were investigated. The results show that: (a) the choice of the regulated variable influences the strategy adopted by the system and (b) the system was not able to regulate the CoM for very fast movements without compromising its balance. Consequently, we suggest that the system is able to maintain balance while raising the arm by only controlling the CoP. This may be done mainly by using hip mechanisms and controlling net ankle torque.     

Trajectory formation based on physiological characteristics of skeletal muscles

Human arm trajectories in natural unrestricted reaching movements were studied. They have particular properties such that a hand path is a rather simple straight or curved line, and a tangential velocity profile of hand is bell-shaped. Also these properties are invariant, independent of movement duration and hand-held load. In this study, trajectory formation is investigated on the basis of physiological characteristics of skeletal muscles, and a criterion prescribed by a derivative of isometric muscle torque is proposed. Subsequently, optimal trajectories are formulated under various conditions of movement to account for a planning strategy of human arm trajectories. In addition to such a theoretical approach, human arm trajectories are experimentally observed by a measuring system which provides a visual sensor and a target tracking device, enabling totally unrestricted movements. Then, optimal trajectories are quantitatively evaluated in comparison with experimental data in which essential properties of human arm trajectories are demonstrated. These results support the idea that human arm trajectories are planned in order to minimize the proposed criterion which is determined from physiological aspects. Finally, the physiological advantages of human arm trajectories are discussed with regard to the analysis of observed and optimal trajectories. Received: 2 December 1997 / Accepted in revised form: 20 March 1998     

Virtual trajectory and stiffness ellipse during multijoint arm movement predicted by neural inverse models

We predict the virtual trajectories and stiffness ellipses during multijoint arm movements by computer simulations. A two-link manipulator with four single-joint muscles and two double-joint muscles is used as a model of the human arm. Physical parameters of the model are derived from several experimental data. Among them, special emphasis is put on low values of the dynamic hand stiffness recently measured during single joint and multijoint movements. The feedback-error-learning scheme to acquire the inverse dynamics model and the inverse statics model is utilized for this prediction. The virtual trajectories are much more complex than the actual trajectories. This indicates that planning the virtual trajectory is as difficult as solving the inverse dynamics problem for medium and fast movements, and simply falsifies the advocated computational advantage of the virtual trajectory control hypothesis. Thus, we conclude that learning inverse models is essential even in the virtual trajectory control framework. Finally, we propose a new computational model to learn the complicated shape of the virtual trajectories by integrating the virtual trajectory control and the feedback-error-learning scheme.     

Analysis of an optimal control model of multi-joint arm movements

 In this paper, we propose a model of biological motor control for generation of goal-directed multi-joint arm movements, and study the formation of muscle control inputs and invariant kinematic features of movements. The model has a hierarchical structure that can determine the control inputs for a set of redundant muscles without any inverse computation. Calculation of motor commands is divided into two stages, each of which performs a transformation of motor commands from one coordinate system to another. At the first level, a central controller in the brain accepts instructions from higher centers, which represent the motor goal in the Cartesian space. The controller computes joint equilibrium trajectories and excitation signals according to a minimum effort criterion. At the second level, a neural network in the spinal cord translates the excitation signals and equilibrium trajectories into control commands to three pairs of antagonist muscles which are redundant for a two-joint arm. No inverse computation is required in the determination of individual muscle commands. The minimum effort controller can produce arm movements whose dynamic and kinematic features are similar to those of voluntary arm movements. For fast movements, the hand approaches a target position along a near-straight path with a smooth bell-shaped velocity. The equilibrium trajectories in X and Y show an ‘N’ shape, but the end-point equilibrium path zigzags around the hand path. Joint movements are not always smooth. Joint reversal is found in movements in some directions. The excitation signals have a triphasic (or biphasic) pulse pattern, which leads to stereotyped triphasic (or biphasic) bursts in muscle control inputs, and a dynamically modulated joint stiffness. There is a fixed sequence of muscle activation from proximal muscles to distal muscles. The order is preserved in all movements. For slow movements, it is shown that a constant joint stiffness is necessary to produce a smooth movement with a bell-shaped velocity. Scaled movements can be reproduced by varying the constraints on the maximal level of excitation signals according to the speed of movement. When the inertial parameters of the arm are altered, movement trajectories can be kept invariant by adjusting the pulse height values, showing the ability to adapt to load changes. These results agree with a wide range of experimental observations on human voluntary movements. Received: 4 December 1995 / Accepted in revised form: 17 September 1996     

The inactivation principle: mathematical solutions minimizing the absolute work and biological implications for the planning of arm movements

An important question in the literature focusing on motor control is to determine which laws drive biological limb movements. This question has prompted numerous investigations analyzing arm movements in both humans and monkeys. Many theories assume that among all possible movements the one actually performed satisfies an optimality criterion. In the framework of optimal control theory, a first approach is to choose a cost function and test whether the proposed model fits with experimental data. A second approach (generally considered as the more difficult) is to infer the cost function from behavioral data. The cost proposed here includes a term called the absolute work of forces, reflecting the mechanical energy expenditure. Contrary to most investigations studying optimality principles of arm movements, this model has the particularity of using a cost function that is not smooth. First, a mathematical theory related to both direct and inverse optimal control approaches is presented. The first theoretical result is the Inactivation Principle, according to which minimizing a term similar to the absolute work implies simultaneous inactivation of agonistic and antagonistic muscles acting on a single joint, near the time of peak velocity. The second theoretical result is that, conversely, the presence of non-smoothness in the cost function is a necessary condition for the existence of such inactivation. Second, during an experimental study, participants were asked to perform fast vertical arm movements with one, two, and three degrees of freedom. Observed trajectories, velocity profiles, and final postures were accurately simulated by the model. In accordance, electromyographic signals showed brief simultaneous inactivation of opposing muscles during movements. Thus, assuming that human movements are optimal with respect to a certain integral cost, the minimization of an absolute-work-like cost is supported by experimental observations. Such types of optimality criteria may be applied to a large range of biological movements.     

Motor control of voluntary arm movements

The motor control of pointing and reaching-to-grasp movements was investigated using two different approaches (kinematic and modelling) in order to establish whether the type of control varies according to modifications of arm kinematics. Kinematic analysis of arm movements was performed on subjects' hand trajectories directed to large and small stimuli located at two different distances. The subjects were required either to grasp and to point to each stimulus. The kinematics of the subsequent movement, during which subject's hand came back to the starting position, were also studied. For both movements, kinematic analysis was performed on hand linear trajectories as well as on joint angular trajectories of shoulder and elbow. The second approach consisted in the parametric identification of the black box (ARMAX) model of the controller driving the arm movement. Such controller is hypothesized to work for the correct execution of the motor act. The order of the controller ARMAX model was analyzed with respect to the different experimental conditions (distal task, stimulus size and distance). Results from kinematic analysis showed that target distance and size influenced kinematic parameters both of angular and linear displacements. Nevertheless, the structure of the motor program was found to remain constant with distane and distal task, while it varied with precision requirements due to stimulus size. The estimated model order of the controller confirmed the invariance of the control law with regard to movement amplitude, whereas it was sensitive to target size.     

Biomechanical modeling and optimal control of human posture

The present work describes the biomechanical modeling of human postural mechanics in the saggital plane and the use of optimal control to generate open-loop raising-up movements from a squatting position. The biomechanical model comprises 10 equivalent musculotendon actuators, based on a 40 muscles model, and three links (shank, thigh and HAT-Head, Arms and Trunk). Optimal control solutions are achieved through algorithms based on the Consistent Approximations Theory (Schwartz and Polak, 1996), where the continuous non-linear dynamics is represented in a discrete space by means of a Runge-Kutta integration and the control signals in a spline-coefficient functional space. This leads to non-linear programming problems solved by a sequential quadratic programming (SQP) method. Due to the highly non-linear and unstable nature of the posture dynamics, numerical convergence is difficult, and specific strategies must be implemented in order to allow convergence. Results for control (muscular excitations) and angular trajectories are shown using two final simulation times, as well as specific control strategies are discussed.     

Piezoelectrically Actuated Biomimetic Self-Contained Quadruped Bounding Robot

This paper presents the development of a mesoscale self-contained quadruped mobile robot that employs two pieces ofpiezocomposite actuators for the bounding locomotion.The design of the robot leg is inspired by legged insects and animals,and the biomimetic concept is implemented in the robot in a simplified form,such that each leg of the robot has only one degreeof freedom.The lack of degree of freedom is compensated by a slope of the robot frame relative to the horizontal plane.For theimplementation of the self-contained mobile robot,a small power supply circuit is designed and installed on the robot.Experimentalresults show that the robot can locomote at about 50 mm·s^-1with the circuit on board,which can be considered as asignificant step toward the goal of building an autonomous legged robot actuated by piezoelectric actuators.     

Humanoid robot Lola: Design and walking control

In this paper we present the humanoid robot LOLA, its mechatronic hardware design, simulation and real-time walking control. The goal of the LOLA-project is to build a machine capable of stable, autonomous, fast and human-like walking. LOLA is characterized by a redundant kinematic configuration with 7-DoF legs, an extremely lightweight design, joint actuators with brushless motors and an electronics architecture using decentralized joint control. Special emphasis was put on an improved mass distribution of the legs to achieve good dynamic performance. Trajectory generation and control aim at faster, more flexible and robust walking. Center of mass trajectories are calculated in real-time from footstep locations using quadratic programming and spline collocation methods. Stabilizing control uses hybrid position/force control in task space with an inner joint position control loop. Inertial stabilization is achieved by modifying the contact force trajectories.     

Development of a Biomimetic Quadruped Robot

This paper presents the design and prototype of a small quadruped robot whose walking motion is realized by two piezocomposite actuators. In the design, biomimetic ideas are employed to obtain the agility of motions and sustainability of a heavy load. The design of the robot legs is inspired by the leg configuration of insects, two joints （hip and knee） of the leg enable two basic motions, lifting and stepping. The robot frame is designed to have a slope relative to the horizontal plane, which makes the robot move forward. In addition, the bounding locomotion of quadruped animals is implemented in the robot. Experiments show that the robot can carry an additional load of about 100 g and run with a fairly high velocity. The quadruped prototype can be an important step towards the goal of building an autonomous mobile robot actuated by piezocomposite actuators.     

Prediction of Three-Dimensional Arm Trajectories Based on ECoG Signals Recorded from Human Sensorimotor Cortex

Brain-machine interface techniques have been applied in a number of studies to control neuromotor prostheses and for neurorehabilitation in the hopes of providing a means to restore lost motor function. Electrocorticography (ECoG) has seen recent use in this regard because it offers a higher spatiotemporal resolution than non-invasive EEG and is less invasive than intracortical microelectrodes. Although several studies have already succeeded in the inference of computer cursor trajectories and finger flexions using human ECoG signals, precise three-dimensional (3D) trajectory reconstruction for a human limb from ECoG has not yet been achieved. In this study, we predicted 3D arm trajectories in time series from ECoG signals in humans using a novel preprocessing method and a sparse linear regression. Average Pearson’s correlation coefficients and normalized root-mean-square errors between predicted and actual trajectories were 0.44∼0.73 and 0.18∼0.42, respectively, confirming the feasibility of predicting 3D arm trajectories from ECoG. We foresee this method contributing to future advancements in neuroprosthesis and neurorehabilitation technology.     

A musculoskeletal model of the human lower extremity: the effect of muscle, tendon, and moment arm on the moment-angle relationship of musculotendon actuators at the hip, knee, and ankle

We have developed a musculoskeletal model of the human lower extremity for computer simulation studies of musculotendon function and muscle coordination during movement. This model incorporates the salient features of muscle and tendon, specifies the musculoskeletal geometry and musculotendon parameters of 18 musculotendon actuators, and defines the active isometric moment of these actuators about the hip, knee, and ankle joints in the sagittal plane. We found that tendon slack length, optimal muscle-fiber length, and moment arm are different for each actuator, thus each actuator develops peak isometric moment at a different joint angle. The joint angle where an actuator produces peak moment does not necessarily coincide with the joint angle where: (1) muscle force peaks, (2) moment arm peaks, or (3) the in vivo moment developed by maximum voluntary contractions peaks. We conclude that when tendon is neglected in analyses of musculotendon force or moment about joints, erroneous predictions of human musculotendon function may be stated, not only in static situations as studied here, but during movement as well.     

Kinematic invariants during cyclical arm movements

It has been observed that the motion of the arm end-point (the hand, fingertip or the tip of a pen) is characterized by a number of regularities (kinematic invariants). Trajectory is usually straight, and the velocity profile has a bell shape during point-to-point movements. During drawing movements, a two-thirds power law predicts the dependence of the end-point velocity on the trajectory curvature. Although various principles of movement organization have been discussed as possible origins of these kinematic invariants, the nature of these movement trajectory characteristics remains an open question. A kinematic model of cyclical arm movements derived in the present study analytically demonstrates that all three kinematic invariants can be predicted from a two-joint approximation of the kinematic structure of the arm and from sinusoidal joint motions. With this approach, explicit expressions for two kinematic invariants, the two-thirds power law during drawing movements and the velocity profile during point-to-point movements are obtained as functions of arm segment lengths and joint motion parameters. Additionally, less recognized kinematic invariants are also derived from the model. The obtained analytical expressions are further validated with experimental data. The high accuracy of the predictions confirms practical utility of the model, showing that the model is relevant to human performance over a wide range of movements. The results create a basis for the consolidation of various existing interpretations of kinematic invariants. In particular, optimal control is discussed as a plausible source of invariant characteristics of joint motions and movement trajectories.     

A simulation study of a programme generator for centrally programmed fast two-joint arm movements: responses to single- and double-step target displacements

From earlier experimental results we concluded that a sudden displacement of a target causes the internal representation of the target to shift gradually from the first to the second target location. This internal target is used as an input to the motor programme generator. The aim of the present simulation study is to investigate whether the CNS can programme fast arm movements towards the internal representation of the target without taking into account velocity-dependent mechanical interactions between the upper arm and forearm and velocity-dependent biomechanical properties of the muscles. The simulations of single- and double-step responses show that on the basis of the assumptions mentioned above, movement trajectories and velocity profiles are in fair agreement with experimental results. However, at the end of fast arm movements a stiffness and viscosity control is needed to halt the movement at the target location.     

Simulating Discrete and Rhythmic Multi-joint Human Arm Movements by Optimization of Nonlinear Performance Indices

An optimization approach applied to mechanical linkage models is used to simulate human arm movements. Predicted arm trajectories are the result of minimizing a nonlinear performance index that depends on kinematic or dynamic variables of the movement. A robust optimization algorithm is presented that computes trajectories which satisfy the necessary conditions with high accuracy. It is especially adapted to the analysis of discrete and rhythmic movements. The optimization problem is solved by parameterizing each generalized coordinate (e.g., joint angular displacement) in terms of Jacobi polynomials and Fourier series, depending on whether discrete or rhythmic movements are considered, combined with a multiple shooting algorithm. The parameterization of coordinates has two advantages. First, it provides an initial guess for the multiple shooting algorithm which solves the optimization problem with high accuracy. Second, it leads to a low dimensional representation of discrete and rhythmic movements in terms of expansion coefficients. The selection of a suitable feature space is an important prerequisite for comparison, recognition and classification of movements. In addition, the separate computational analysis of discrete and rhythmic movements is motivated by their distinct neurophysiological realizations in the cortex. By investigating different performance indices subject to different boundary conditions, the approach can be used to examine possible strategies that humans adopt in selecting specific arm motions for the performance of different tasks in a plane and in three-dimensional space.     

Supervised and Dynamic Neuro-Fuzzy Systems to Classify Physiological Responses in Robot-Assisted Neurorehabilitation

This paper presents the application of an Adaptive Resonance Theory (ART) based on neural networks combined with Fuzzy Logic systems to classify physiological reactions of subjects performing robot-assisted rehabilitation therapies. First, the theoretical background of a neuro-fuzzy classifier called S-dFasArt is presented. Then, the methodology and experimental protocols to perform a robot-assisted neurorehabilitation task are described. Our results show that the combination of the dynamic nature of S-dFasArt classifier with a supervisory module are very robust and suggest that this methodology could be very useful to take into account emotional states in robot-assisted environments and help to enhance and better understand human-robot interactions.