Abstract
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. 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.
Highlights
Two types of neural circuits contribute to legged locomotion: central pattern generators (CPGs) that produce rhythmic motor commands, and reflex circuits driven by sensory feedback
The CPG controller produced a periodic gait with a model of human-like dynamic walking (Fig. 2A)
Pre-determined timing is problematic for optimal control in unpredictable situations[63], leading some to question why CPG oscillators should dictate timing[62,64]
Summary
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. The other is the reflex circuit, which produces motor patterns triggered by sensory feedback (Fig. 1C) They normally work together, each is capable of independent action. The gain or weight of sensory input determines whether it slowly entrains the CPG15, or whether it resets the phase entirely[16,17] Controllers of this type have demonstrated legged locomotion in bipedal[18] and quadrupedal robots[19,20], and even swimming and other behaviors[21]. Reinforcement learning and other robust optimization approaches (e.g., dynamic programming32,33) are typically expressed solely in terms of state, and do not even have provision for time as an explicit input They have no need for, nor even benefit from, an internally generated rhythm. Feedforward is clearly important in biological CPGs, suggesting that some insight is missing from these optimal control models
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