Virtual Spring-damper Hypothesis Research Articles

Flexible Control Strategy for Upper-Limb Rehabilitation Exoskeleton Based on Virtual Spring Damper Hypothesis

The focus of this work is to design a control strategy with the dynamic characteristics of spring damping to realize the virtual flexibility and softness of a rigid-joint exoskeleton without installing real, physical elastic devices. The basic idea of a “virtual softening control strategy” for a single rigid joint is that a virtual spring damper (VSD) is installed between the motor and the output shaft. By designing the control signal of the motor, the torque output of the joint actuator is softened so that the output has the characteristics of elasticity and variable stiffness. The transfer velocity profile of human limbs reaching from one posture to another always presents as bell-shaped. According to this characteristic, we constructed a trajectory planning method for a point-to-point position-tracking controller based on a normal distribution function, and it was successfully applied to the control of 5-DoF upper-limb rehabilitation exoskeleton. A multi-joint cooperative flexible controller based on the virtual spring damper hypothesis (VSDH) was successfully applied to solve the constrained control problem of the exoskeletons and the self-motion problem caused by redundant degrees of freedom (DoFs). The stability of the closed-loop controlled system is theoretically proven by use of the scalar energy function gradient method and the Riemann metric convergence analysis method.

Experimental Study on Cartesian-Space PD Control for Hydraulic Manipulator

 Abstract—This paper presents Cartesian-space PD control of a hydraulic manipulator. The approach based upon Virtual spring-damper hypothesis is composed of virtual spring effects and virtual damper effects in task space. It has been applied to electrically driven robots. This experiment shows the comparison of Cartesian-space control with typical joint-space control in the performance of straight-line motion for the hydraulic manipulator that easily generate movements of manipulator without spending a huge amount of computational cost.

"仮想バネ・ダンパー仮説"に基づいた筋内力と手先粘性の関係に関する考察

"仮想バネ・ダンパー仮説"に基づいた筋内力と手先粘性の関係に関する考察

Nonlinear Reference Shaping with Endpoint Position Feedback for Large Acceleration Avoidance in Reaching Movement

The nonlinear reference shaping for manipulators used in ordinary living environments is proposed. It generates an intermediate reference position, and it is combined with control based on the virtual springdamper hypothesis. Initial acceleration is moderated by the reference position inserted between the original target and current endpoint position and by a secondorder lag filter. The endpoint position is fed back to prevent from excessive trailing force and large acceleration, resulting in smooth reaching movement and flexible behavior against external force. The feasibility of the concept of the proposed controller is confirmed through computer simulation on a planar 4-DOF manipulator.

Reaching Movements of a Redundant Musculoskeletal Arm: Acquisition of an Adequate Internal Force by Iterative Learning and Its Evaluation through a Dynamic Damping Ellipsoid

This paper presents a proposal of an iterative learning control method for a musculoskeletal arm to acquire adequate internal force in order to realize human-like natural movements. Additionally, a dynamic damping ellipsoid at the end-point is introduced to evaluate internal forces obtained through the iterative learning scheme. Our previous works presented that a human-like smooth reaching movement using a musculoskeletal redundant arm model can be achieved by introducing a nonlinear muscle model and 'the virtual spring–damper hypothesis'. However, to date, the internal forces have been determined heuristically. As described in this paper, to determine internal forces more systematically, an iterative learning control method is used for acquisition of an adequate dynamic damping ellipsoid according to a given task. It is presented that the learning control method can perform effectively to realize given tasks, even though strong nonlinear characteristics of the muscles exist. After acquiring a given task, the dynamic damping ellipsoid is introduced to evaluate the relation between a damping effect generated by the acquired internal forces and a trajectory of the end-point. Some numerical simulations are performed and the usefulness of the learning control strategy, despite strong nonlinearity, is demonstrated through these results.

On control of reaching movements for musculo-skeletal redundant arm model

This paper focuses on a dynamic sensory-motor control mechanism of reaching movements for a musculo-skeletal redundant arm model. The formulation of a musculo-skeletal redundant arm system, which takes into account non-linear muscle properties obtained by some physiological understandings, is introduced and numerical simulations are perfomed. The non-linear properties of muscle dynamics make it possible to modulate the viscosity of the joints, and the end point of the arm converges to the desired point with a simple task-space feedback when adequate internal forces are chosen, regardless of the redundancy of the joint. Numerical simulations were performed and the effectiveness of our control scheme is discussed through these results. The results suggest that the reaching movements can be achieved using only a simple task-space feedback scheme together with the internal force effect that comes from non-linear properties of skeletal muscles without any complex mathematical computation such as an inverse dynamics or optimal trajectory derivation. In addition, the dynamic damping ellipsoid for evaluating how the internal forces can be determined is introduced. The task-space feedback is extended to the 'virtual spring-damper hypothesis' based on the research by Arimoto et al. 2006 to reduce the muscle output forces and heterogeneity of convergence depending on the initial state and desired position. The research suggests a new direction for studies of brain-motor control mechanism of human movements.

On Control of Reaching Movements for Musculo-Skeletal Redundant Arm Model

This paper focuses on a dynamic sensory-motor control mechanism of reaching movements for a musculo-skeletal redundant arm model. The formulation of a musculo-skeletal redundant arm system, which takes into account non-linear muscle properties obtained by some physiological understandings, is introduced and numerical simulations are perfomed. The non-linear properties of muscle dynamics make it possible to modulate the viscosity of the joints, and the end point of the arm converges to the desired point with a simple task-space feedback when adequate internal forces are chosen, regardless of the redundancy of the joint. Numerical simulations were performed and the effectiveness of our control scheme is discussed through these results. The results suggest that the reaching movements can be achieved using only a simple task-space feedback scheme together with the internal force effect that comes from non-linear properties of skeletal muscles without any complex mathematical computation such as an inverse dynamics or optimal trajectory derivation. In addition, the dynamic damping ellipsoid for evaluating how the internal forces can be determined is introduced. The task-space feedback is extended to the ‘virtual spring-damper hypothesis’ based on the research by Arimoto et al. (2006) to reduce the muscle output forces and heterogeneity of convergence depending on the initial state and desired position. The research suggests a new direction for studies of brain-motor control mechanism of human movements.

仮想バネ・ダンパー仮説に基づいた冗長関節ロボットアーム制御方の実験的検証

A simple control method for redundant multi-joint arm was proposed recently by gaining a physical insight into human multi-joint reaching movements in redundancy of DOFs. Differently from the traditional approaches, the method need neither introduce any artificial performance index to resolve ill-posedness of inverse kinematics nor calculate the pseudo-inverse of the Jacobian matrix of task coordinates with respect to joint coordinates. This novel approach is based upon an idea of “Virtual spring-damper hypothesis, ” and the control signal is composed of linear superposition of three terms (1) joint-damping, and (2) virtual damper effects in parallel to (3) virtual spring effects in task space. This paper shows through experiments by using an industrial robot arm (PA-10) with redundant multi-joints that the control signal can generate smooth reaching movements without incurring any annoying selfmotion. It is shown further that virtual damper effects in task space enable endpoint trajectories of the robot arm to be rectilinear and the effects can be enhanced by compensating the viscosity inherent in the robot.

On the Parametrization of the Three-Dimensional Rotation Group

Parameterization of group of rotations of Euclidean three-dimensional space applied to integration of rigid body motion equations