Distributed motor control system with transmission time delay

The multi-link system such as the musculoskeletal mechanism has a recursive dynamics representation. In order to control the body by the parallel calculation of the recursive algorithms of the inverse dynamics, the time delays of information transmission between the distributed calculation elements are required. These time delays are important to model and analyze the biological motor control as a distributed system, because the neural signal speeds are limited and the time delays are not negligible in the quick movement. And some time delays in the control loop make the moment unstable generally, but the biological motor control are stable and can handle the delays. In this paper, we focus on the function of the renshaw cell in the spinal cord of the biological motor control system. The renshaw cell forms the negative feedback loop of the motor neuron output, then we model the renshaw cell as the low-pass filter of torque output. And we propose a hierarchical distributed motor control system including the time delays for 3-dimensional movements, and the reaching simulation results that the time delay makes the movement unstable and the low-pass filter of torque output could contribute toward stabilizing the time delay loop in the distributed control system.