Motor Control: Emulating Muscle

Motivation

From a bottom-up perspective, it is important to focus on the biomechanics, not only because it is the outmost layer of the motor control system, but also because the intrinsic visco-elastic properties of muscle solve a great part of the motion control problem long before the nervous system comes into play. Additionally, the efficiency and power to weight ratio of the actuator -muscles- has enormous metabolic and behavioral implications for its host, thus if we seek to recreate the performance of living creatures we must build actuators that match the performance of natural muscle.

The development of a muscle-like actuator will provide biologically-realistic motor output for neuromorphic systems, facilitating the future implementation of neuromorphic motor controllers and serving as a foundation for truly biomimetic robots. Furthermore this technology may also serve to actuate prosthetic limbs and may even be implantable in the long run.

Project Status

This project has evolved into the use of electroactive polymers to build muscle-like actuators. Shoot me an email if you are interested about the details. Here I present an previous approach using standard DC motors, which achieves (in simulation) similar mechanical properties to its model system, the fast twitching feline muscle-tendon caudofemoralis (CF). This actuation device is based on a commercial DC Motor and is capable of outputting comparable mechanical power in an equivalent size as its biological counterpart.

The device is somewhere between a direct drive motor and a modified Series Elastic Actuator (SEA). Here, the bulky and heavy ball-screw of the SEA is substituted by a compact winch-like mechanism (cable drive) with a reel of small radius. The winch limits the actuation to pure tension, like natural muscle, and the small radius provides a large torque-to-force amplification factor which in turn allows for a very low-ratio gear-train. The low-ratio gear-train is lighter, more efficient, less non-linear and easier to backdrive than a higher-ratio transmission, allowing for the intrinsic 'viscous' properties of the electrical motor to appear at the output. Elasticity is achieved by adding a tension spring on the winch's cable. The spring constant is chosen to match that of the biological tendon. Finally, a variable damper, theoretically based on MagnetoRheological Fluids (MRF), is connected in parallel with the motor to absorb energy during active extension and thus allow for a lower-powered motor. The properties of MRF also allow 'locking' of the device and thus produce force while holding a static position without consuming electrical energy at the motor.

 

Actuator and Muscle Model Schematic
a) Conceptual Diagram of muscle-like actuator device. b) Schematic representation of Brown and colleagues' (1996) original muscle model for caudofemoralis with focus on the contractile element subdivided into an active and a dampening element. If the Passive Element in b), whose contribution is very small, is neglected the device's schematic matches that of the natural muscle model.

Using Virtual Muscle, a mathematical model of muscle force production implemented in Simulink by Gerard Loeb and his collaborators, I compare the muscle-like device with CF. This comparison is done with the muscle-like device operating in open-loop (applying a fixed voltage to the motor's terminals). At some velocities the muscle-like actuator produces more force than CF; at these levels a closed-loop controller could be used to tone down the actuator to match the biology. At other velocities the muscle-like actuator produces less force than CF; at these levels the actuator fails, as it cannot output enough mechanical power to match the biology.

 Force vs length and Velocity
Force production versus length (a) and velocity (b) for feline caudofemoralis (dark blue lines) and muscle-like device (red and light blue lines). The muscle-like device is operating with a fixed voltage at the motor terminals, both with and without dampening. Lo=5.8cm and Fo=15.4N.

Next I compare the actuator with CF for small perturbation tests. These involve holding the muscle or actuator at a fixed length and then measuring the force when applying a small step change in length. The tests demonstrate that the actuator's intrinsic mechanical properties account for the muscle-like behavior and that its time constant is similar to that of CF. The addition of a closed-loop PID controller for force further improves the match between the actuator's response and its natural model.

Small Perturbation Tests
Small Perturbation tests comparing caudofemoralis with open-loop and closed-loop, critically dampened (a) and undampened (b) muscle-like actuator.

The results show that the muscle-like actuator (in simulation) can produce the same stress (Force over cross sectional area) and strain (percentile deformation) as its natural counterpart and that their dimensions are very similar. Force versus velocity plots show that the mechanical power output is also very similar. The main drawback however is the power to weight ratio, as the motor and its gearhead alone are almost twice as heavy as biology's actuator.

Comparison between CF and Muscle-Like Actuator
Dimensional comparison of Feline Caudofemoralis and Muscle-Like Actuator.