An optimality principle for locomotor central pattern generators

Two types of neural circuits contribute to legged locomotion: central pattern generators (CPGs) that produce rhythmic motor commands (even in the absence of feedback, termed “fictive locomotion”), and reflex circuits driven by sensory feedback. Each circuit alone serves a clear purpose, and the two together are understood to cooperate during normal locomotion. The difficulty is in explaining their relative balance objectively within a control model, as there are infinite combinations that could produce the same nominal motor pattern. Here we propose that optimization in the presence of uncertainty can explain how the circuits should best be combined for locomotion. The key is to re-interpret the CPG in the context of state estimator-based control: an internal model of the limbs that predicts their state, using sensory feedback to optimally balance competing effects of environmental and sensory uncertainties.


Fig: Three ways to control bipedal walking. (A) The central pattern generator (CPG) comprises neural oscillators that can produce rhythmic motor commands, even in the absence of sensory feedback. Rhythm can be produced by mutually inhibiting neural half-center oscillators (shaded circles). (B) In normal animal locomotion, the CPG is thought to combine an intrinsic rhythm with sensory feedback, so that the periphery can influence the motor rhythm. (C) In principle, sensory feedback can also control and stabilize locomotion through reflexes, without need for neural oscillators. The extreme of (A) CPG control without feedback is referred to here as pure feedforward control, and the opposite extreme (C) with no oscillators as pure feedback control. Any of these schemes could potentially produce the same nominal locomotion pattern, but some (B) combination of feedforward and feedback appears advantageous.

We demonstrate use of optimally predicted state to drive a simple model of bipedal, dynamic walking, which thus yields minimal energetic cost of transport and best stability. The internal model may be implemented with neural circuitry compatible with classic CPG models, except with neural parameters determined by optimal estimation principles. Fictive locomotion also emerges, but as a side effect of estimator dynamics rather than an explicit internal rhythm. Uncertainty could be key to shaping CPG behavior and governing optimal use of feedback.

Ryu, H.X., Kuo, A.D. An optimality principle for locomotor central pattern generators. Sci Rep 11, 13140 (2021).

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