Compensating for a sensorimotor delay requires a predictor that convolves over a memory buffer of efference copies

Effective motor control requires sensory feedback but is seriously complicated by the sensorimotor delay (SMD), which is the time delay between the state of the body at feedback generation and the arrival in the bodys muscles of the feedback-informed motor command. I describe and evaluate three SMD compensation mechanisms: gain scaling, the convolution predictor, and the Smith predictor. These mechanisms are implemented using control theory results for linear dynamical systems, which are well motivated for balance control. These mechanisms are investigated theoretically and by simulations of balance control, both free standing and while riding a bicycle. I demonstrate that compensating for a SMD requires a convolution predictor, which involves a convolution over a memory buffer of efference copies and an initial condition obtained from a state observer that is based on a delayed-input forward model. The performance of a convolution predictor does not crucially depend on its exact computational implementation because a similar performance is obtained with an approximate convolution using a boxcar kernel. I also demonstrate that gain scaling is an effective SMD compensation mechanism but is not sufficient to compensate for a neurobiological SMD. Finally, I demonstrate that the Smith predictor is an ineffective and neurobiologically implausible SMD compensation mechanism for an unstable mechanical system.