Modeling of Equilibrium Point Trajectory Control

MODELING OF EQUILIBRIUM POINT TRAJECTORY CONTROL IN HUMAN ARM MOVEMENTS by Kai Chen The underlying concept of the Equilibrium Point Hypothesis (EPH) is that the CNS provides a virtual trajectory of joint motion, representing spacing and timing, with actual movement dynamics being produced by interactions of limb inertia, muscle viscosity and speed/position feedback from muscle spindles. To counter criticisms of the EPH, investigators have proposed the use of complex virtual trajectories, non-linear damping, stiffness and time varying stiffness to the EPH model. While these features allow the EPH to adequately produce human joint velocities, they conflict with the EPH’s premise of simple pre-planned monotonic control of movement trajectory. As a result, this study proposed an EPH based method, which provides a simpler mechanism in motor control without conflict with the core advantages of the original approach. This work has proposed relative damping as an addition to the EPH model to predict the single and two joint arm movements. This addition results in simulated data that not only closely match experimental angle data, but also match the experimental joint torques. In addition, it is suggested that this modified model can be used to predict the multi-joint angular trajectories with fast and normal velocities, without the need for time varying or non-linear stiffness and damping, but with simple monotonic virtual trajectories. In the following study, this relative damping model has been further enhanced with an EMG-based determination of the virtual trajectory and with physiologically realistic neuromuscular delays. The results of unobstructed voluntary movement studies suggest that the EPH models use realistic impedance values and produce desired joint trajectories and joint torques in unperturbed voluntary arm movement. A subsequent study of obstructed voluntary arm movement extended the relative damping concept, and incorporated the influential factors of the mechanical behavior of the neural, muscular and skeletal system in the control and coordination of arm posture and movement. A significant problem of the study is how this information should be used to modify control signals to achieve desired performance. This study used an EPH model to examine changes of controlling signals for arm movements in the context of adding perturbation/load in the form of forces/torques. The mechanical properties and reflex actions of muscles of the elbow joint were examined. Brief unexpected torque/force pulses of identical magnitude and time duration were introduced at different stages of the movement in a random order by a pre-programmed 3 degree of freedom (DOF) robotic arm (MOOG FCS HapticMaster). The results show that the subjects may maintain the same control parameters (virtual trajectory, stiffness and damping) regardless of added perturbations that cause substantial changes in EMG activity and kinematics. MODELING OF EQUILIBRIUM POINT TRAJECTORY CONTROL IN HUMAN ARM MOVEMENTS