Muscle Co-Contraction Modulates Damping and Joint Stability in a Three-Link Biomechanical Limb

Computational models of neuromotor control require forward models of limb movement that can replicate the natural relationships between muscle activation and joint dynamics without the burdens of excessive anatomical detail. We present a model of a three-link biomechanical limb that emphasizes the dynamics of limb movement within a simplified two-dimensional framework. Muscle co-contraction effects were incorporated into the model by flanking each joint with a pair of antagonist muscles that may be activated independently. Muscle co-contraction is known to alter the damping and stiffness of limb joints without altering net joint torque. Idealized muscle actuators were implemented using the Voigt muscle model which incorporates the parallel elasticity of muscle and tendon but omits series elasticity. The natural force-length-velocity relationships of contractile muscle tissue were incorporated into the actuators using ideal mathematical forms. Numerical stability analysis confirmed that co-contraction of these simplified actuators increased damping in the biomechanical limb consistent with observations of human motor control. Dynamic changes in joint stiffness were excluded by the omission of series elasticity. The analysis also revealed the unexpected finding that distinct stable (bistable) equilibrium positions can co-exist under identical levels of muscle co-contraction. We map the conditions under which bistability arises and prove analytically that monostability (equifinality) is guaranteed when the antagonist muscles are identical. Lastly we verify these analytic findings in the full biomechanical limb model

Bio-inspired robotic joint and manipulator : from biomechanical experimentation and modeling to human-like compliant finger design and control

textOne of the greatest challenges in controlling robotic hands is grasping and manipulating objects in unstructured and uncertain environments. Robotic hands are typically too rigid to react against unexpected impacts and disturbances in order to prevent damage. The human hands have great versatility and robustness due, in part, to the passive compliance and damping. Designing mechanical elements that are inspired by the nonlinear joint compliance of human hands is a promising solution to achieve human-like grasping and manipulation. However, the exact role of biomechanical elements in realizing joint stiffness is unknown. We conducted a series of experiments to investigate nonlinear stiffness and damping of the metacarpophalangeal (MCP) joint at the index finger. We designed a custom-made mechanism to integrate electromyography sensors (EMGs) and a motion capture system to collect data from 19 subjects. We investigated the relative contributions of muscle-tendon units and the MCP capsule ligament complex to joint stiffness with subject-specific modeling. The results show that the muscle-tendon units provide limited contribution to the passive joint compliance. This findings indicate that the parallel compliance, in the form of the capsule-ligament complex, is significant in defining the passive properties of the hand. To identify the passive damping, we used the hysteresis loops to investigate the energy dissipation function. We used symbolic regression and principal component analysis to derive and interpret the damping models. The results show that the nonlinear viscous damping depends on the cyclic frequency, and fluid and structural types of damping also exist at the MCP joint. Inspired by the nonlinear stiffness of the MCP joint, we developed a miniaturized mechanism that uses pouring liquid plastic to design energy storing elements. The key innovations in this design are: a) a set of nonlinear elasticity of compliant materials, b) variable pulley configurations to tune the stiffness profile, and c) pretension mechanism to scale the stiffness profile. The design exhibits human-like passive compliance. By taking advantage of miniaturized joint size and additive manufacturing, we incorporated the novel joint design in a novel robotic manipulator with six series elastic actuators (SEA). The robotic manipulator has passive joint compliance with the intrinsic property of human hands. To validate the system, we investigated the Cartesian stiffness of grasping with low-level force control. The results show that that the overall system performs a great force tracking with position feedback. The parallel compliance decreases the motor efforts and can stabilize the system.Mechanical Engineerin

Neuromuscular Reflex Control for Prostheses and Exoskeletons

Recent powered lower-limb prosthetic and orthotic (P/O) devices aim to restore legged mobility for persons with an amputation or spinal cord injury. Though various control strategies have been proposed for these devices, specifically finite-state impedance controllers, natural gait mechanics are not usually achieved. The goal of this project was to invent a biologically-inspired controller for powered P/O devices. We hypothesize that a more muscle-like actuation system, including spinal reflexes and vestibular feedback, can achieve able-bodied walking and also respond to outside perturbations. The outputs of the Virtual Muscle Reflex (VMR) controller are joint torque commands, sent to the electric motors of a P/O device. We identified the controller parameters through optimizations using human experimental data of perturbed walking, in which we minimized the error between the torque produced by our controller and the standard torque trajectories observed in the able-bodied experiments. In simulations, we then compare the VMR controller to a four-phase impedance controller. For both controllers the coefficient of determination R^2 and root-mean-square (RMS) error were calculated as a function of the gait cycle. When simulating the hip, knee, and ankle joints, the RMS error and R^2 across all joints and all trials is 15.65 Nm and 0.28 for the impedance controller, respectively, and for the VMR controller, these values are 15.15 Nm and 0.29, respectively. With similar performance, it was concluded that the VMR controller can reproduce characteristics of human walking in response to perturbations as effectively as an impedance controller. We then implemented the VMR controller on the Parker Hannifin powered exoskeleton and performed standard isokinetic and isometric knee rehabilitation exercises to observe the behavior of the virtual muscle model. In the isometric results, RMS error between the measured and commanded extension and flexion torques are 3.28 Nm and 1.25 Nm, respectively. In the isokinetic trials, we receive RMS error between the measured and commanded extension and flexion torques of 0.73 Nm and 0.24 Nm. Since the onboard virtual muscles demonstrate similar muscle force-length and force-velocity relationships observed in humans, we conclude the model is capable of the same stabilizing capabilities as observed in an impedance controller

Neuromuscular Reflex Control for Prostheses and Exoskeletons

Recent powered lower-limb prosthetic and orthotic (P/O) devices aim to restore legged mobility for persons with an amputation or spinal cord injury. Though various control strategies have been proposed for these devices, specifically finite-state impedance controllers, natural gait mechanics are not usually achieved. The goal of this project was to invent a biologically-inspired controller for powered P/O devices. We hypothesize that a more muscle-like actuation system, including spinal reflexes and vestibular feedback, can achieve able-bodied walking and also respond to outside perturbations. The outputs of the Virtual Muscle Reflex (VMR) controller are joint torque commands, sent to the electric motors of a P/O device. We identified the controller parameters through optimizations using human experimental data of perturbed walking, in which we minimized the error between the torque produced by our controller and the standard torque trajectories observed in the able-bodied experiments. In simulations, we then compare the VMR controller to a four-phase impedance controller. For both controllers the coefficient of determination R^2 and root-mean-square (RMS) error were calculated as a function of the gait cycle. When simulating the hip, knee, and ankle joints, the RMS error and R^2 across all joints and all trials is 15.65 Nm and 0.28 for the impedance controller, respectively, and for the VMR controller, these values are 15.15 Nm and 0.29, respectively. With similar performance, it was concluded that the VMR controller can reproduce characteristics of human walking in response to perturbations as effectively as an impedance controller. We then implemented the VMR controller on the Parker Hannifin powered exoskeleton and performed standard isokinetic and isometric knee rehabilitation exercises to observe the behavior of the virtual muscle model. In the isometric results, RMS error between the measured and commanded extension and flexion torques are 3.28 Nm and 1.25 Nm, respectively. In the isokinetic trials, we receive RMS error between the measured and commanded extension and flexion torques of 0.73 Nm and 0.24 Nm. Since the onboard virtual muscles demonstrate similar muscle force-length and force-velocity relationships observed in humans, we conclude the model is capable of the same stabilizing capabilities as observed in an impedance controller

Neuromuscular Reflex Control for Prostheses and Exoskeletons

Recent powered lower-limb prosthetic and orthotic (P/O) devices aim to restore legged mobility for persons with an amputation or spinal cord injury. Though various control strategies have been proposed for these devices, specifically finite-state impedance controllers, natural gait mechanics are not usually achieved. The goal of this project was to invent a biologically-inspired controller for powered P/O devices. We hypothesize that a more muscle-like actuation system, including spinal reflexes and vestibular feedback, can achieve able-bodied walking and also respond to outside perturbations. The outputs of the Virtual Muscle Reflex (VMR) controller are joint torque commands, sent to the electric motors of a P/O device. We identified the controller parameters through optimizations using human experimental data of perturbed walking, in which we minimized the error between the torque produced by our controller and the standard torque trajectories observed in the able-bodied experiments. In simulations, we then compare the VMR controller to a four-phase impedance controller. For both controllers the coefficient of determination R^2 and root-mean-square (RMS) error were calculated as a function of the gait cycle. When simulating the hip, knee, and ankle joints, the RMS error and R^2 across all joints and all trials is 15.65 Nm and 0.28 for the impedance controller, respectively, and for the VMR controller, these values are 15.15 Nm and 0.29, respectively. With similar performance, it was concluded that the VMR controller can reproduce characteristics of human walking in response to perturbations as effectively as an impedance controller. We then implemented the VMR controller on the Parker Hannifin powered exoskeleton and performed standard isokinetic and isometric knee rehabilitation exercises to observe the behavior of the virtual muscle model. In the isometric results, RMS error between the measured and commanded extension and flexion torques are 3.28 Nm and 1.25 Nm, respectively. In the isokinetic trials, we receive RMS error between the measured and commanded extension and flexion torques of 0.73 Nm and 0.24 Nm. Since the onboard virtual muscles demonstrate similar muscle force-length and force-velocity relationships observed in humans, we conclude the model is capable of the same stabilizing capabilities as observed in an impedance controller

On the role of stability in animal morphology and neural control

Mechanical stability is vital for the fitness and survival of animals and is a crucial aspect of robot design and control. Stability depends on multiple factors, including the body\u27s intrinsic mechanical response and feedback control. But feedback control is more fragile than the body\u27s innate mechanical response or open-loop control strategies because of sensory noise and time-delays in feedback. This thesis examines the overarching hypothesis that stability demands have played a crucial role in how animal form and function arise through natural selection and motor learning. In two examples, finger contact and overall body stability, we investigated the relationship between morphology, open-loop control, and stability. By studying the stability of the internal degrees of freedom of a finger when pushing on a hard surface, we find that stability limits the force that we can produce and is a dominant aspect of the neural control of the finger\u27s muscles. In our study on whole body lateral stability during locomotion in terrestrial animals, we find that the overall body aspect ratio has evolved to ensure passive lateral stability on the uneven terrain of natural environments. Precisely gripping an object with the fingertips is a hallmark of human hand dexterity. In Chapter 2, we show how human fingers are intrinsically prone to a buckling-type postural instability and how humans use careful neural orchestration of our muscles so that the elastic response of our muscles can suppress the intrinsic instability. In Chapter 3, we extend these findings further to examine the nature of neuromuscular variability and how the nervous system deals with the need for muscle-induced stability. We find that there is structure to neuromuscular variability so that most of the variability lies within the subspace that does not affect stability. Inspired by the open-loop stable control of our index fingers, in Chapter 4, we derive open-loop stability conditions for a general mechanical linkage with arbitrary joint torques subjected to holonomic constraints. The solution that we derive is physically realizable as cable-driven active mechanical linkages. With a user-prescribed cable layout, we pose the problem of actuating the system to maintain stability while subject to goals like energy minimization as a convex optimization problem. We are thus able to use efficient optimization methods available for convex problems and demonstrate numerical solutions in examples inspired by the finger. Chapter 5 presents a general formulation of the stability criteria for active mechanical linkages subject to Pfaffian holonomic and non-holonomic constraints. Active mechanical linkages subject to multiple constraints represent the mechanics of systems spanning many domains and length scales, such as limbs and digits in animals and robots, and elastic networks like actin meshes in microscopic systems. We show that a constrained mechanical linkage with regular stiffness and damping, and circulation-free feedback, can only destabilize by static buckling when subject to holonomic constraints. In contrast, the same mechanical linkage, subject to a non-holonomic constraint, such as a skate contact, can exhibit either static buckling or flutter instability. Chapter 6 moves away from neural control and studies the shape of animal bodies and their relationship to stability in locomotion. We investigate why small land animals tend to have a crouched or sprawled posture, whereas larger animals are generally more upright. We propose a new hypothesis that the scaling of body aspect ratio with size is driven by the scale-dependent unevenness of natural terrain. We show that the scaling law arising from the need for stability on rough natural terrain correctly predicts the frontal aspect ratio scaling law across 335 terrestrial vertebrates and invertebrates, spanning eight orders of magnitude in mass so that smaller animals have a wider aspect ratio. We also carry out statistical analyses that consider the phylogenetic relationship among the species in our dataset to show that the scaling is not due to gradual changes of the traits over time. Thus, stability demands on natural terrain may have driven the macroevolution of body aspect ratio across terrestrial animals. Interrogating unstable and marginally stable behaviors has helped us identify the morphological and control features that allow animals to perform robustly in noisy environments where perfect sensory feedback cannot be assumed. Although the thesis identifies the `what\u27 and `why,\u27 further studies are needed to understand `how\u27 mechanics and development intertwine to give rise to control and form in growing and adapting biological organisms

Steering disturbance rejection using a physics-based neuromusculoskeletal driver model

This is an Accepted Manuscript of an article published by Taylor & Francis in Vehicle System Dynamics on 2016-06-17, available online: https://dx.doi.org/10.1080/00423114.2015.1050403The aim of this work is to develop a comprehensive yet practical driver model to be used in studying driver–vehicle interactions. Drivers interact with their vehicle and the road through the steering wheel. This interaction forms a closed-loop coupled human–machine system, which influences the driver's steering feel and control performance. A hierarchical approach is proposed here to capture the complexity of the driver's neuromuscular dynamics and the central nervous system in the coordination of the driver's upper extremity activities, especially in the presence of external disturbance. The proposed motor control framework has three layers: the first (or the path planning) plans a desired vehicle trajectory and the required steering angles to perform the desired trajectory; the second (or the musculoskeletal controller) actuates the musculoskeletal arm to rotate the steering wheel accordingly; and the final layer ensures the precision control and disturbance rejection of the motor control units. The physics-based driver model presented here can also provide insights into vehicle control in relaxed and tensed driving conditions, which are simulated by adjusting the driver model parameters such as cognition delay and muscle co-contraction dynamics.Ontario Centres of Excellence (OCE)Natural Sciences and Engineering Research Council of Canada (NSERC)ToyotaMaplesof

Inertial Load Compensation by a Model Spinal Circuit During Single Joint Movement

Office of Naval Research (N00014-92-J-1309); CONACYT (Mexico) (63462

Understanding motor control in humans to improve rehabilitation robots

Recent reviews highlighted the limited results of robotic rehabilitation and the low quality of evidences in this field. Despite the worldwide presence of several robotic infrastructures, there is still a lack of knowledge about the capabilities of robotic training effect on the neural control of movement. To fill this gap, a step back to motor neuroscience is needed: the understanding how the brain works in the generation of movements, how it adapts to changes and how it acquires new motor skills is fundamental. This is the rationale behind my PhD project and the contents of this thesis: all the studies included in fact examined changes in motor control due to different destabilizing conditions, ranging from external perturbations, to self-generated disturbances, to pathological conditions. Data on healthy and impaired adults have been collected and quantitative and objective information about kinematics, dynamics, performance and learning were obtained for the investigation of motor control and skill learning. Results on subjects with cervical dystonia show how important assessment is: possibly adequate treatments are missing because the physiological and pathological mechanisms underlying sensorimotor control are not routinely addressed in clinical practice. These results showed how sensory function is crucial for motor control. The relevance of proprioception in motor control and learning is evident also in a second study. This study, performed on healthy subjects, showed that stiffness control is associated with worse robustness to external perturbations and worse learning, which can be attributed to the lower sensitiveness while moving or co-activating. On the other hand, we found that the combination of higher reliance on proprioception with \u201cdisturbance training\u201d is able to lead to a better learning and better robustness. This is in line with recent findings showing that variability may facilitate learning and thus can be exploited for sensorimotor recovery. Based on these results, in a third study, we asked participants to use the more robust and efficient strategy in order to investigate the control policies used to reject disturbances. We found that control is non-linear and we associated this non-linearity with intermittent control. As the name says, intermittent control is characterized by open loop intervals, in which movements are not actively controlled. We exploited the intermittent control paradigm for other two modeling studies. In these studies we have shown how robust is this model, evaluating it in two complex situations, the coordination of two joints for postural balance and the coordination of two different balancing tasks. It is an intriguing issue, to be addressed in future studies, to consider how learning affects intermittency and how this can be exploited to enhance learning or recovery. The approach, that can exploit the results of this thesis, is the computational neurorehabilitation, which mathematically models the mechanisms underlying the rehabilitation process, with the aim of optimizing the individual treatment of patients. Integrating models of sensorimotor control during robotic neurorehabilitation, might lead to robots that are fully adaptable to the level of impairment of the patient and able to change their behavior accordingly to the patient\u2019s intention. This is one of the goals for the development of rehabilitation robotics and in particular of Wristbot, our robot for wrist rehabilitation: combining proper assessment and training protocols, based on motor control paradigms, will maximize robotic rehabilitation effects