No abstract

A reductionist approach was presented to investigate which level of detail of the physiological muscle is required for stable locomotion. Periodic movements of a simplified one-dimensional hopping model with a Hill-type muscle (one contractile element, neither serial nor parallel elastic elements) were analyzed. Force-length and force-velocity relations of the muscle were varied in three levels of approximation (constant, linear and Hill-shaped nonlinear) resulting in nine different hopping models of different complexity. Stability of these models was evaluated by return map analysis and the performance by the maximum hopping height. The simplest model (constant force-length and constant force-velocity relations) outperformed all others in the maximum hopping height but was unstable. Stable hopping was achieved with linear and Hill-shaped nonlinear characteristic of the force-velocity relation. The characteristics of the force-length relation marginally influenced hopping stability. The results of this approach indicate that the intrinsic properties of the contractile element are responsible for stabilization of periodic movements. This connotes that (a) complex movements like legged locomotion could benefit from stabilizing effects of muscle properties, and (b) technical systems could benefit from the emerging stability when implementing biological characteristics into artificial muscles.

Parallel passive-elastic elements can reduce the energy consumption and torque requirements for motors in powered legged systems. However, the hardware design for such combined actuators is challenged by the need to engage and disengage the parallel elasticity depending on the gait phase. Although clutches in the drive train are often proposed, compact and low cost solutions of clutched parallel elastic actuators have so far not been established. Here we present the design and control of an initial prototype for a parallel elastic actuator. The actuator combines a DC motor with a parallel spring that is engaged and disengaged by a commercially available, compact and low-cost electric clutch. In experiments that mimic the torque and motion patterns of knee extensor muscles in human rebounding tasks we find that the parallel spring in the prototype reduces the energy consumption of the actuator by about 80% and the peak torque requirement for the DC motor by about 66%. In addition, we find that a simple trigger-based control can reliably engage and disengage the electric clutch during the motion, allowing the spring to support the motor in rebound, to remove stored energy from the system as necessary for stopping, and to virtually disappear at the actuator output level. On the other hand, the hardware experiments also reveal that our initial design limits the precision in the torque control, and we propose specific improvements to overcome these limitations.

It was hypothesized that a tight integration of feed-forward and feedback-driven muscle activation with the characteristic intrinsic muscle properties is a key feature of locomotion in challenging environments. In this simulation study it was investigated whether a combination of feed-forward and feedback signals improves hopping stability compared with those simulations with one individual type of activation. In a reduced one-dimensional hopping model with a Hill-type muscle (one contractile element, neither serial nor parallel elastic elements), the level of detail of the muscle's force -length -velocity relation and the type of activation generation (feed-forward, feedback and combination of both) were varied to test their influence on periodic hopping. The stability of the hopping patterns was evaluated by return map analysis. It was found that the combination of feed-forward and proprioceptive feedback improved hopping stability. Furthermore, the nonlinear Hill-type representation of intrinsic muscle properties led to a faster reduction of perturbations than a linear approximation, independent of the type of activation. The results emphasize the ability of organisms to exploit the stabilizing properties of intrinsic muscle characteristics.