A nonlinear modelling approach to quantify sitting control in individuals with sensorimotor impairments

Few biomechanical models of sitting stability have been proposed over the last decades and most of them control the trunk position through a lumbar torque. Unfortunately, this type of model is not valid for individuals living with a complete thoracic spinal cord injury (SCI) who generally experience paralysis of their abdominal and lower back muscles. Instead, individuals with SCI often engage their upper limbs as a compensatory strategy to control their sitting position. A new nonlinear biomechanical model is introduced to take into consideration the influence of the upper limbs for sitting control study of people living with SCI. The inherent nonlinearity of the model is taken into account via the Takagi–Sugeno (T-S) framework. To estimate the internal controlling torques without measurements, an unknown input observer (UIO) is created. Its convergence is expressed by linear matrix inequalities (LMI), which are solved by convex optimization techniques. Numerical simulations with perturbations are used to assess the adequacy of the methodology and preliminary experimental data of one person living with SCI performing a sitting stabilization exercise is used to estimate internal torques of the upper limbs. The main contribution of this work is to provide a way to estimate human joint torques without invasive measurements; the results highlight the validity of both goals of this article, the nonlinear biomechanical modelling and the UIO methodology.     

Two recurrent neural networks for local joint torque optimizationof kinematically redundant manipulators

This paper presents two neural network approaches to real-time joint torque optimization for kinematically redundant manipulators. Two recurrent neural networks are proposed for determining the minimum driving joint torques of redundant manipulators for the eases without and with taking the joint torque limits into consideration, respectively. The first neural network is called the Lagrangian network and the second one is called the primal-dual network. In both neural-network-based computation schemes, while the desired accelerations of the end-effector for a specific task are given to the neural networks as their inputs, the signals of the minimum driving joint torques are generated as their outputs to drive the manipulator arm. Both proposed recurrent neural networks are shown to be capable of generating minimum stable driving joint torques. In addition, the driving joint torques computed by the primal-dual network are shown never exceeding the joint torque limits.     

Gait Pattern Adaptation for an Active Lower-Limb Orthosis Based on Neural Networks

This work deals with neural network (NN)-based gait pattern adaptation algorithms for an active lower-limb orthosis. Stable trajectories with different walking speeds are generated during an optimization process considering the zero-moment point (ZMP) criterion and the inverse dynamic of the orthosis–patient model. Additionally, a set of NNs is used to decrease the time-consuming analytical computation of the model and ZMP. The first NN approximates the inverse dynamics including the ZMP computation, while the second NN works in the optimization procedure, giving an adapted desired trajectory according to orthosis–patient interaction. This trajectory adaptation is added directly to the trajectory generator, also reproduced by a set of NNs. With this strategy, it is possible to adapt the trajectory during the walking cycle in an on-line procedure, instead of changing the trajectory parameter after each step. The dynamic model of the actual exoskeleton, with interaction forces included, is used to generate simulation results. Also, an experimental test is performed with an active ankle–foot orthosis, where the dynamic variables of this joint are replaced in the simulator by actual values provided by the device. It is shown that the final adapted trajectory follows the patient intention of increasing the walking speed, so changing the gait pattern.     

Initial System Evaluation of an Overground Rehabilitation Gait Training Robot (NaTUre-gaits)

For decades, robotic devices have been suggested to enhance motor recovery by replicating clinical manual-assisted training. This paper presents an overground gait rehabilitation robot, which consists of a pair of robotic orthoses, the connected pelvic arm in parallel and a mounted mobile platform. The overground walking incorporates pelvic control together with active joints on the lower limb. As a preliminary evaluation, system trials have been conducted on healthy subjects and a spinal cord injury (SCI) subject, respectively. Electromyography signals were recorded from muscles of the lower limb for each subject. Three experiments were carried out: (i) health volunteers walking at self-preferred walking speed, (ii) a SCI subject walking with the help of three helpers and (iii) the same SCI subject walking with the assistance provided by the gait device. In the experiment, the muscle activation of overground walking was compared between the manual-assisted and robotic-assisted methods. The initial results show that the performance of the device can provide impact-less overground walking and it is comparable to the performance obtained by manual assistance in gait rehabilitation training.     

Backward walking simulation of humans using optimization

The objective of this study is to formulate, simulate and study the backward walking motion of a full-body skeletal digital human model using an optimization approach. Predictive dynamics is used to simulate the task in which joint angle profiles are treated as primary unknowns in the formulation. The joint torques are treated as dependent variables that are evaluated directly from the equations of motion. For the performance measure, the normalized dynamic effort represented by the integral of the squares of all the normalized joint torques is minimized subject to the associated physical constraints. Backward walking at different speeds is simulated and analyzed. The backward walking is validated with motion capture data and the available data in the literature. The results of the backward walking motion are compared to those of the forward walking motion in order to study the differences between the two walking patterns. It is seen that the joint torque profiles for hip and knee of backward walk are quite similar to those of forward walk with reverse sequence, but with different time duration of flexion and extension activations. These findings can impact many fields, such as improvement of human performance, rehabilitation from injuries, and others.     

Keyswitch orientation can reduce finger joint torques during tapping on a computer keyswitch

OBJECTIVE: To examine the effects of keyswitch orientation on joint torques. BACKGROUND: The fingertip produces primarily vertical forces during single-finger tapping on a computer keyswitch. However, horizontal force components within the sagittal plane of the finger could reduce net joint torques. METHOD: Eleven participants tapped on a keyswitch oriented in three directions: vertical, tilted 30 degrees such that when pressed it moved away from the user (similar to a positive-tilt keyboard), and tilted 30 degrees such that when pressed it moved toward the user (similar to a negative-tilt keyboard). Participants also tapped on a prototype cantilever keyswitch design in which the key cap moves along the arc of a bending beam gradually away from the user. Miniature electro-optical goniometers measured the finger posture, and a two-axis force sensor measured fingertip forces. RESULTS: Tapping on a keyswitch oriented such that it moves away from the user when pressed reduced net joint torques by 47% relative to tapping on a vertically orientated keyswitch and by 56% relative to tapping on a keyswitch oriented toward the user, whereas the cantilever design resulted in 14% decreases in net joint torque relative to the vertical orientation. CONCLUSION: Reductions of torques resulted from decreasing the moment arm of the fingertip force about the joints. APPLICATION: Keyboard design should incorporate keyswitch mechanism angles along with other postural and geometric constraints to reduce exposure of the finger joints and muscles to force during typing.     

Adaptive control of an actuated ankle foot orthosis for paretic patients

This paper deals with the control of an active ankle foot orthosis (AAFO) to assist the gait of paretic patients. The AAFO system is driven by both, the residual human torque delivered by the muscles spanning the ankle joint and the AAFO’s actuator’s torque. A model reference adaptive control is proposed to assist dorsiflexion and plantar-flexion movements of the ankle joint during level walking. Unlike most classical model-based controllers, the proposed one does not require any prior estimation of the system’s (AAFO-wearer) parameters. The ankle reference trajectory is updated online based on the main gait cycle events and is adapted with respect to the self-selected speed of the wearer. The adaptive desired ankle trajectory is estimated using cubic spline interpolations between the different key events of the gait cycle. The closed-loop input-to-state stability of the AAFO-wearer system with respect to a bounded human muscular torque is proved by a Lyapunov analysis. Experimental results obtained from three healthy subjects and one paretic patient, show satisfactory results in terms of tracking performance and ankle assistance throughout the full gait cycle. The experiments also show good performance at different walking speeds and with different gait sub-phase duration proportions.     

Animating human locomotion with inverse dynamics

Because the major force components (the internal muscular forces and torques) are not known a priori over time, you cannot use forward dynamics to predict how the human body will walk. The alternative to the apparently intractable problem of specifying the joint torque patterns in advance is to use inverse dynamics to analyze the torques and forces required for the given motion. Such an analysis can show, for example, that the motion induces excessive torque, that the system is out of balance at a certain point, or that the step length is too great. We present a method of using an inverse dynamics computation to dynamically balance the resulting walking motion and to maintain the joint torques within a moderate range imposed by human strength limits. This method corrects or predicts a motion as indicated by the inverse dynamics analysis. Dynamic correctness is a sufficient condition for realistic motion of nonliving objects. In animating a self-actuated system, however, visual realism is another important, separate criterion for determining the success of a technique. Dynamic correctness is not a sufficient condition for this visual realism. An animation of dynamically balanced walking that is also comfortable in the sense of avoiding strength violations can still look quite different from normal human walking. A visually realistic and dynamically sound animation of human locomotion is obtained using an effective combination of kinematic and dynamic techniques     

Optimal impedance via model predictive control for robot-aided rehabilitation

This paper proposes an optimal impedance controller for robot-aided rehabilitation of walking, aiming to increase the patient’s activity during the therapy. In an online procedure, the joint torques produced by the patient during the gait is estimated using the generalized momenta-based disturbance observer and the Extended Kalman filter algorithm. At the same time, a model predictive control is performed to obtain the instantaneous optimal stiffness parameters of the robot’s impedance controller, trying to maximize the patient’s active participation by increasing his/her joint torques. In this feasibility study, experiments with a healthy subject, considering a modular lower limb exoskeleton and a set of user’s behaviors, are performed to evaluate the proposed controller. The results show the robot stiffness converges to a value which increases the user’s active participation.     

A mathematical framework to study fast walking of human

The body of a walking human is an elaborated dynamic system that operates adaptively in various conditions such as fast walking. Due to dynamic redundancies, the individual motor control strategies for speeding up the walking can be different among normal subjects. However, in reality, we see that the pattern of motion is quite similar among people and it is only the profile of hip joint motion along its path which determines the speed. The objective of the current paper is to develop a mathematical framework to investigate time optimal motion of a human during walking. To this end, a nine-link planar biped model is used. The motion is considered to take place in sagittal plane and to follow a normal pattern of motion. The solution is obtained using a phase plane method to solve minimum time problem which is subjected to inequality constraints of variable maximum joint torques and stability conditions. The solution method can be used to find the maximum possible speed of a human with specific body characteristics and to obtain a hip joint trajectory which could produce that speed. The proposed method can be utilized to study quantitative effect of different parameters such as joint strength in fast walking.     

Redundant robot control using task based performance measures

The joint velocities required to move the end-effector of a redundant robot with a desired linear and angular velocity depend on its configuration. Similarly, the joint torques produced due to the force and moment at the end-effector also depend on its configuration. When the robot is near a singular configuration, the joint velocities required to attain the end-effector velocity in certain directions are extremely high. Similarly, in some configurations the joint torque produced at certain joints may be high for a relatively small magnitude of external force. An infinite number of trajectories in the joint space can be used to achieve a desired end-effector trajectory for redundant robots. However, a joint trajectory resulting in robot configurations requiring lower joint velocities or joint torques is desired. This may be achieved through a proper utilization of redundancy. Local performance measures for redundant robots are defined in this article as indicators of their ability to follow a desired end-effector trajectory and their ability to apply desired forces at the end-effector. Thus, these performance measures depend on the task to be performed. Control algorithms which can be efficiently applied to redundant robots to improve these performance measures are presented. These control algorithms are based on the gradient projection method. Gradients of the performance measures used in the control schemes result in simple symbolic expressions for “real world” robots'. Feasibility and effectiveness of these control schemes is demonstrated through the simulation of a seven-degree-of-freedom redundant robot derived from the PUMA geometry.     

Generation of natural motions for redundant multi‐joint systems: A differential‐geometric approach based upon the principle of least actions

This article challenges Bernstein's problem of redundant degrees of freedom (DOF) that remains unsolved from both the standpoints of physiology and robotics. A rather simpler but difficult control problem of movements of human‐like multi‐joint reaching with excess DOF is analyzed from Newtonian mechanics and differential geometry. It is shown that, regardless of ill‐posedness of inverse kinematics for such a redundant system, a simpler control signal composed of a well‐tuned (synergistic) combination of task‐space position feedback (corresponding to spring‐like forces) and joint velocity feedback (viscous‐like forces) leads to a skilled motion of reaching in a natural way without solving inverse kinematics or dynamics. Fundamental characteristics of human skilled multi‐joint movements such as (1) generation of a quasi‐straight line trajectory of the endpoint and (2) a little “variability” in task space but notable “variability” in joint space are analyzed from the concepts of “stability on an EP (equilibrium‐point) manifold” and “transferability to an EP submanifold.” It is claimed that the control signal exerts torques on joints of the whole arm just like a single virtual‐spring drawing the endpoint of the arm to the target while giving a specified viscosity to each joint. This leads to an interpretation that skilled reaching movements emerge through formation of a set of neuro‐motor signals exerting relevant group of muscles to generate a total potential energy equivalent to that of the spring. Discussions are presented on how such control signals in case of human reaching can be generated in a feedforward manner with capability of anticipatory adjustments of stiffness. © 2005 Wiley Periodicals, Inc.     

Toward lower limbs movement restoration with input-output feedback linearization and model predictive control through functional electrical stimulation

Functional electrical stimulation (FES) is used to excite paralyzed muscles that are no longer controlled by patients with spinal cord injuries (SCI). Appropriate stimulation patterns are chosen to stimulate intact muscles, in order to extend their overall performance, postponing thus the muscular fatigue during the daily activities such as standing, standing up, sitting down and walking. This paper presents the modeling and the control of a knee joint actuated by the quadriceps muscles. Appropriate stimulation patterns are computed as a function of the desired lower-limb knee joint movements. Parameters of the biomechanical model are identified based on experimental kinematic data. Model predictive control (MPC) is applied to the input-output feedback linearized (IOFL) system. IOFL allows linearization by inverting the system dynamics through a nonlinear feedback transformation. The described control approach is validated through different simulation scenarios for knee flexion-extension. Internal dynamics stability is mathematically proved and performances are compared to those produced by classical pole placements method. The controller has shown satisfactory results in terms of regulation, stability and robustness with respect to external disturbances.     

柔性冗余度机器人力矩优化的研究

本文首先应用模态理论，对柔性冗余度机器人振动的控制问题的原理与策略进行了研究．在此基础上通过对满足抑振要求的自运动的选取进行分析，指出柔性冗余度机器人在通过优化其自运动实现振动抑制的同时还具有二次优化的能力，并给出了在满足抑振的前提下实现关节力矩优化的方法．最后对一个末杆为柔杆的平面三杆机械手的振动控制与力矩优化进行了仿真，结果验证了该方法的可行性．     

A novel formulation for determining joint constraint loads during optimal dynamic motion of redundant manipulators in DH representation

The kinematic representations of general open-loop chains in many robotic applications are based on the Denavit–Hartenberg (DH) notation. However, when the DH representation is used for kinematic modeling, the relative joint constraints cannot be described explicitly using the common formulation methods. In this paper, we propose a new formulation of solving a system of differential-algebraic equations (DAEs) where the method of Lagrange multipliers is incorporated into the optimization problem for optimal motion planning of redundant manipulators. In particular, a set of fictitious joints is modeled to solve for the joint constraint forces and moments, as well as the optimal dynamic motion and the required actuator torques of redundant manipulators described in DH representation. The proposed method is formulated within the framework of our earlier study on the generation of load-effective optimal dynamic motions of redundant manipulators that guarantee successful execution of given tasks in which the Lagrangian dynamics for general external loads are incorporated. Some example tasks of a simple planar manipulator and a high-degree-of-freedom digital human model are illustrated, and the results show accurate calculation of joint constraint loads without altering the original planned motion. The proposed optimization formulation satisfies the equivalent DAEs.     

正弦驱动与传感反馈结合的双足机器人仿生行走控制

提出了一种正弦驱动与传感反馈结合的双足机器人仿生行走控制方法．所有关节由正弦振荡器驱动, 较之相互耦合的神经元振荡器更加简单;控制参数具有明晰的物理意义,便于对运动模式进行调节．传感反馈表征 了机器人的运动状态,对于保证机器人的稳定行走起着至关重要的作用．将机器人碰地、碰膝等关键运动状态作为 相位反馈,对控制力矩进行相位重置,协调各关节动作,进而实现控制器、机器人、环境的耦合．同时,从节省能量 和仿生的角度,考虑了关节运动的被动特性,确定了各关节力矩的作用区间．仿真结果表明,该控制方法能实现机 器人稳定行走,并具有良好的能效性和自稳定性.     

sEMG-based continuous estimation of joint angles of human legs by using BP neural network

In this paper, we propose an mth order nonlinear model to describe the relationship between the surface electromyography (sEMG) signals and the joint angles of human legs, in which a simple BP neural network is built for the model estimation. The inputs of the model are sEMG time series that have been processed, and the outputs of the model are the joint angles of hip, knee, and ankle. To validate the effectiveness of the BP neural network, six able-bodied people and four spinal cord injury (SCI) patients participated in the experiment. Two movement modes including the treadmill exercise and the leg extension exercise at different speeds and different loads were respectively conducted by the able-bodied individuals, and only the treadmill exercise was selected for the SCI patients. Seven channels of sEMG from seven human leg muscles were recorded and three joint angles including the hip joint, knee joint and the ankle joint were sampled simultaneously. The results present that this method has a good performance on joint angles estimation by using sEMG for both able-bodied subjects and SCI patients. The average angle estimation root-mean-square (rms) error for leg extension exercise is less than 9°, and the average rms error for treadmill exercise is less than 6° for all the able-bodied subjects. The average angle estimation rms error of the SCI patients is even smaller (less than 5°) than that of the able-bodied people because of a smaller movement range. This method would be used to rehabilitation robot or functional electrical stimulation (FES) for active rehabilitation of SCI patients or stroke patients based on sEMG signals.     

3D walking biped: optimal swing of the arms

A ballistic walking gait is designed for a 3D biped with two identical two-link legs, a torso, and two identical one-link arms. In the single support phase, the biped moves due to the existence of a momentum, produced mechanically, without applying active torques in the interlink joints. This biped is controlled with impulsive torques at the instantaneous double support to obtain a cyclic gait. The impulsive torques are applied in the seven interlink joints. Then an infinity of solutions exists to find the impulsive torques. An effort cost functional of these impulsive torques is minimized to determine a unique solution. Numerical results show that for a given time period and a given length of the walking gait step, there is an optimal swinging amplitude of the arms. For this optimal motion of the arms, the cost functional is minimum.     

Optimization-based analysis of push recovery during walking motions to support the design of rigid and compliant lower limb exoskeletons

Abstract

Lower limb exoskeletons provide a promising approach to allow disabled people to walk again in the future. Designing such exoskeletons and tuning the required actuators is challenging, since the full dynamics of the combined human-exoskeleton system have to be taken into account. In particular, it is important to not only consider nominal walking motions but also extreme situations such as the recovery from large perturbations. In this paper, we present an approach based on push recovery experiments while walking, multibody system models, and least-squares optimal control to analyze the required torques to be generated by the exoskeleton, assuming that the human provides no torque. We consider seven different trials with varying push locations and push magnitudes applied on the back of the subject. In a first study, we investigate the dependency of these total joint torques on the exoskeleton mass – and compare the torques required for a human without exoskeleton to the ones for the human with two different exoskeleton configurations. In a second study, we investigate how optimally chosen passive spring-damper elements can support the required torques in the exoskeleton joints. It can be shown that the active torques can be reduced significantly in the different joints and cases.     

Task-based configuration control of redundant manipulators

This article establishes new goals for redundancy resolution based on manipulator dynamics and end-effector characteristics. These goals can be accomplished by employing the recently developed configuration control approach. Redundancy resolution is achieved by controlling the joint inertia matrix or the end-effector mass matrix that affect the inertial torques or by reducing the joint torques due to gravity loading and payload. The manipulator mechanical advantage and velocity ratio are also used as performance measures to be improved by proper utilization of redundancy. Furthermore, end-effector compliance, sensitivity, and impulsive force at impact are introduced as redundancy-resolution criteria. The new goals for redundancy resolution presented in this article allow a more efficient utilization of the redundant joints based on the desired task requirements. Simple case studies using computer simulations are described for illustration.