Computation of inverse functions in a model of cerebellar and reflex pathways allows to control a mobile mechanical segment

A system-level mathematical model of Basal Ganglia motor-circuit for kinematic planning of arm movements

In this paper, a novel system-level mathematical model of the Basal Ganglia (BG) for kinematic planning, is proposed. An arm composed of several segments presents a geometric redundancy. Thus, selecting one trajectory among an infinite number of possible ones requires overcoming redundancy, according to some kinds of optimization. Solving this optimization is assumed to be the function of BG in planning. In the proposed model, first, a mathematical solution of kinematic planning is proposed for movements of a redundant arm in a plane, based on minimizing energy consumption. Next, the function of each part in the model is interpreted as a possible role of a nucleus of BG. Since the kinematic variables are considered as vectors, the proposed model is presented based on the vector calculus. This vector model predicts different neuronal populations in BG which is in accordance with some recent experimental studies. According to the proposed model, the function of the direct pathway is to calculate the necessary rotation of each joint, and the function of the indirect pathway is to control each joint rotation considering the movement of the other joints. In the proposed model, the local feedback loop between Subthalamic Nucleus and Globus Pallidus externus is interpreted as a local memory to store the previous amounts of movements of the other joints, which are utilized by the indirect pathway. In this model, activities of dopaminergic neurons would encode, at short-term, the error between the desired and actual positions of the end-effector. The short-term modulating effect of dopamine on Striatum is also modeled as cross product. The model is simulated to generate the commands of a redundant manipulator. The performance of the model is studied for different reaching movements between 8 points in a plane. Finally, some symptoms of Parkinson's disease such as bradykinesia and akinesia are simulated by modifying the model parameters, inspired by the dopamine depletion.

Fuzzy neuronal model of motor control inspired by cerebellar pathways to online and gradually learn inverse biomechanical functions in the presence of delay

Contrary to forward biomechanical functions, which are deterministic, inverse biomechanical functions are generally not. Calculating an inverse biomechanical function is an ill-posed problem, which has no unique solution for a manipulator with several degrees of freedom. Studies of the command and control of biological movements suggest that the cerebellum takes part in the computation of approximate inverse functions, and this ability can control fast movements by predicting the consequence of current motor command. Limb movements toward a goal are defined as fast if they last less than the total duration of the processing and transmission delays in the motor and sensory pathways. Because of these delays, fast movements cannot be continuously controlled in a closed loop by use of sensory signals. Thus, fast movements must be controlled by some open loop controller, of which cerebellar pathways constitute an important part. This article presents a system-level fuzzy neuronal motor control circuit, inspired by the cerebellar pathways. The cerebellar cortex (CC) is assumed to embed internal models of the biomechanical functions of the limb segments. Such neural models are able to predict the consequences of motor commands and issue predictive signals encoding movement variables, which are sent to the controller via internal feedback loops. Differences between desired and expected values of variables of movements are calculated in the deep cerebellar nuclei (DCN). After motor learning, the whole circuit can approximate the inverse function of the biomechanical function of a limb and acts as a controller. In this research, internal models of direct biomechanical functions are learned and embedded in the connectivity of the cerebellar pathways. Two fuzzy neural networks represent the two parts of the cerebellum, and an online gradual learning drives the acquisition of the internal models in CC and the controlling rules in DCN. As during real learning, exercise and repetition increase skill and speed. The learning procedure is started by a simple and slow movement, controlled in the presence of delays by a simple closed loop controller comparable to the spinal reflexes. The speed of the movements is then increased gradually, and output error signals are used to compute teaching signals and drive learning. Repetition of movements at each speed level allows to properly set the two neural networks, and progressively learn the movement. Finally, conditions of stability of the proposed model as an inverter are identified. Next, the control of a single segment arm, moved by two muscles, is simulated. After proper setting by motor learning, the circuit is able to reject perturbations.

A cortically-inspired model for inverse kinematics computation of a humanoid finger with mechanically coupled joints

The human hand's versatility allows for robust and flexible grasping. To obtain such efficiency, many robotic hands include human biomechanical features such as fingers having their two last joints mechanically coupled. Although such coupling enables human-like grasping, controlling the inverse kinematics of such mechanical systems is challenging. Here we propose a cortical model for fine motor control of a humanoid finger, having its two last joints coupled, that learns the inverse kinematics of the effector. This neural model functionally mimics the population vector coding as well as sensorimotor prediction processes of the brain's motor/premotor and parietal regions, respectively. After learning, this neural architecture could both overtly (actual execution) and covertly (mental execution or motor imagery) perform accurate, robust and flexible finger movements while reproducing the main human finger kinematic states. This work contributes to developing neuro-mimetic controllers for dexterous humanoid robotic/prosthetic upper-extremities, and has the potential to promote human-robot interactions.

Cerebellum-inspired neural network solution of the inverse kinematics problem

The demand today for more complex robots that have manipulators with higher degrees of freedom is increasing because of technological advances. Obtaining the precise movement for a desired trajectory or a sequence of arm and positions requires the computation of the inverse kinematic (IK) function, which is a major problem in robotics. The solution of the IK problem leads robots to the precise position and orientation of their end-effector. We developed a bioinspired solution comparable with the cerebellar anatomy and function to solve the said problem. The proposed model is stable under all conditions merely by parameter determination, in contrast to recursive model-based solutions, which remain stable only under certain conditions. We modified the proposed model for the simple two-segmented arm to prove the feasibility of the model under a basic condition. A fuzzy neural network through its learning method was used to compute the parameters of the system. Simulation results show the practical feasibility and efficiency of the proposed model in robotics. The main advantage of the proposed model is its generalizability and potential use in any robot.

A biomechanical model for encoding joint dynamics: applications to transfemoral prosthesis control

This paper presents and tests a framework for encoding joint dynamics into energy states using kinematic and kinetic knee joint sensor data and demonstrates how to use this information to predict the future energy state (torque and velocity requirements) of the joint without a priori knowledge of the activity sequence. The intended application is for enhancing micro-controlled prosthetics by making use of the embedded sensory potential of artificial limbs and classical mechanical principles of a prosthetic joint to report instantaneous energy state and most probable next energy state. When applied to the knee during preferred and fast speed walking in 8 human subjects (66 preferred-speed trials and 50 fast-speed trials), it was found that joint energy states could be consistently sequenced (75% consensus) according to mechanical energy transference conditions and subsequences appeared to reflect the stability and energy dissipation requirements of the knee during gait. When simple constraints were applied to the energy transfer input conditions (their signs), simulations indicated that it was possible to predict the future energy state with an accuracy of >80% when 2% cycle in advance (∼20 ms) of the switch and >60% for 4% (∼40 ms) in advance. This study justifies future research to explore whether this encoding algorithm can be used to identify submodes of other human activity that are relevant to TFP control, such as chair and stair activities and their transitions from walking, as well as unexpected perturbations.

Integration of gravitational torques in cerebellar pathways allows for the dynamic inverse computation of vertical pointing movements of a robot arm

BACKGROUND

Several authors suggested that gravitational forces are centrally represented in the brain for planning, control and sensorimotor predictions of movements. Furthermore, some studies proposed that the cerebellum computes the inverse dynamics (internal inverse model) whereas others suggested that it computes sensorimotor predictions (internal forward model).

METHODOLOGY/PRINCIPAL FINDINGS

This study proposes a model of cerebellar pathways deduced from both biological and physical constraints. The model learns the dynamic inverse computation of the effect of gravitational torques from its sensorimotor predictions without calculating an explicit inverse computation. By using supervised learning, this model learns to control an anthropomorphic robot arm actuated by two antagonists McKibben artificial muscles. This was achieved by using internal parallel feedback loops containing neural networks which anticipate the sensorimotor consequences of the neural commands. The artificial neural networks architecture was similar to the large-scale connectivity of the cerebellar cortex. Movements in the sagittal plane were performed during three sessions combining different initial positions, amplitudes and directions of movements to vary the effects of the gravitational torques applied to the robotic arm. The results show that this model acquired an internal representation of the gravitational effects during vertical arm pointing movements.

CONCLUSIONS/SIGNIFICANCE

This is consistent with the proposal that the cerebellar cortex contains an internal representation of gravitational torques which is encoded through a learning process. Furthermore, this model suggests that the cerebellum performs the inverse dynamics computation based on sensorimotor predictions. This highlights the importance of sensorimotor predictions of gravitational torques acting on upper limb movements performed in the gravitational field.

A model of the cerebellar sensory--motor control applied to fast human forearm movements

To address the problem of how the cerebellum processes the premotor orders that control fast movements of the forearm, a model of the cerebellar control is proposed: a cybernetic circuit composed of a model of the cerebellar premotor pathways driving a biomechanical model of the human forearm. Experiments consist of recording electromyographic (EMG) activities and cinematic variables of the human forearm during fast, single joint, point-to-point movements performed in horizontal and vertical directions with and without mass. The biomechanical model of the forearm is first validated by comparing actual movements and movements simulated by using, as inputs to this model, the synthesized EMG signals and of real EMG activities recorded during the experiments. Then the entire control model is validated by comparing actual movements to the desired ones simulated by the model of the cerebellar pathways whose inputs are velocity signals with Gaussian time-courses. The results show that approximate inverse functions can be computed by means of inner models of direct functions placed in feedback loops, and suggest that the orientation of any member segment with respect to gravity is computed as a cinematic variable in the Central Nervous System (CNS).

Head and neck position sense

Traumatic minor cervical strains are common place in high-impact sports (e.g. tackling) and premature degenerative changes have been documented in sports people exposed to recurrent impact trauma (e.g. scrummaging in rugby) or repetitive forces (e.g. Formula 1 racing drivers, jockeys). While proprioceptive exercises have been an integral part of rehabilitation of injuries in the lower limb, they have not featured as prominently in the treatment of cervical injuries. However, head and neck position sense (HNPS) testing and re-training may have relevance in the management of minor sports-related neck injuries, and play a role in reducing the incidence of ongoing pain and problems with function. For efficacious programmes to be developed and tested, fundamental principles associated with proprioception in the cervical spine should be considered. Hence, this article highlights the importance of anatomical structures in the cervical spine responsible for position sense, and how their interaction with the CNS affects our ability to plan and execute effective purposeful movements. This article includes a review of studies examining position sense in subjects with and without pathology and describes the effects of rehabilitation programmes that have sought to improve position sense. In respect to the receptors providing proprioceptive information for the CNS, the high densities and complex arrays of spindles found in cervical muscles suggest that these receptors play a key role. There is some evidence suggesting that ensemble encoding of discharge patterns from muscle spindles is relayed to the CNS and that a pattern recognition system is used to establish joint position and movement. Sensory information from neck proprioceptive receptors is processed in tandem with information from the vestibular system. There are extensive anatomical connections between neck proprioceptive inputs and vestibular inputs. If positional information from the vestibular system is inaccurate or fails to be appropriately integrated in the CNS, errors in head position may occur, resulting in an inaccurate reference for HNPS, and conversely if neck proprioceptive information is inaccurate, then control of head position may be affected. The cerebellum and cortex also play a role in control of head position, providing feed-forward and modulatory influences depending on the task requirements. Position-matching tasks have been the most popular means of testing position sense in the cervical spine. These allow the appreciation of absolute, constant and variable errors in positioning and have been shown to be reliable. The results of such tests indicate that errors are relatively low (2-5 degrees). It is apparent that error is not consistently affected by age, a finding similar to studies undertaken in peripheral joints. Furthermore, the range of motion in which subjects are tested does not consistently affect accuracy in a predictable manner. However, it is evident that impairments in position sense are observed in individuals who have experienced whiplash-type injuries and individuals with chronic head and neck pain of non-traumatic origin (e.g. cervical spondylosis). While researchers advocate comprehensive retraining protocols, which include eye and neck motion targeting tasks and coordination exercises, as well as co-contraction exercises to reduce such impairments, some studies show that more general exercises and manipulation may be of benefit. Overall, there is limited information concerning the efficacy of treatment programmes.

Force Control Strategies While Driving Electric Powered Wheelchairs With Isometric and Movement-Sensing Joysticks

Innovations to control interfaces for electric powered wheelchairs (EPWs) could benefit 220000 current users and over 125000 individuals who desire mobility but cannot use a conventional motion sensing joystick (MSJ). We developed a digital isometric joystick (IJ) with sophisticated signal processing and two control functions. In a prior study, subjects' driving accuracy with our IJ was comparable to using an MSJ. However, we observed subjects using excessive force on the IJ possibly because its rigid post provides no positional feedback. Thus, this paper examines the time-series data recorded in the previous study to characterize subjects' force control strategies since weakness is a concern. Eleven EPW users with upper limb impairments drove an EPW using an IJ with two different control functions and an MSJ in a Fitts' law paradigm. Subjects relied upon positional feedback from the MSJ and used appropriate force. In contrast, subjects using the IJ with either control function applied significantly higher force than necessary (p < 0.0001 and p = 0.0058). Using higher average force was correlated with quicker trial times but not associated with accuracy. Lack of positional feedback may result in use of excess isometric force. Modifying control functions, adjusting gain, or providing additional training or feedback might address this problem.

Motor planning of arm movements is direction-dependent in the gravity field

In the present study we analyzed kinematic and dynamic features of arm movements in order to better elucidate how the motor system integrates environmental constraints (gravity) into motor planning and control processes. To reach this aim, we experimentally manipulated the mechanical effects of gravity on the arm while maintaining arm inertia constant (i.e. the distribution of the mass around the shoulder joint). Six subjects performed single-joint arm movements (rotation around the shoulder joint) in both sagittal (upward, U, versus downward, D) and horizontal (left, L, versus right, R) planes, at different amplitudes and from different initial positions. Under these conditions, shoulder gravitational torques (SGTs) significantly varied when arm movements were performed in the sagittal but not in the horizontal plane. Contrary to SGTs, arm inertia remained constant and similar for both horizontal and sagittal planes since subjects performed arm movements with only one degree of freedom. All subjects, whatever the movement direction, appropriately scaled shoulder joint kinematic parameters according to movement amplitude. Furthermore, peak velocity and movement duration were equivalent for both horizontal and sagittal planes. Interestingly, some kinematic parameters significantly differed according to U/D but not L/R directions. Specifically, acceleration duration was greater for D than U movements, while the opposite was true for peak acceleration. Consequently, although vertical and horizontal arm movements shared a general common strategy (i.e. scaling law), the kinematic asymmetries between U and D arm movements, especially those that reflect central planning process (i.e. peak acceleration), indicated different motor intentions regarding the direction of the upcoming movement. These findings indicate that the interaction of the arm with the dynamics of the environment is internally represented during the generation of arm trajectories.