(en) Walking is never perfectly repetitive: even under steady conditions, stride duration fluctuates slightly from one cycle to the next. These fluctuations exhibit a specific temporal structure: they display long-range autocorrelations (LRA), meaning that fluctuations at any given time remain statistically dependent, following a power-law relationship, on fluctuations occurring many strides earlier. Both the magnitude and the temporal structure of gait variability have been associated with the stability and adaptability of locomotor control, and their alteration in several pathologies, such as Parkinson's disease, has been linked to an increased risk of falling. Yet, the origin and functional significance of LRA remain debated.
This thesis addresses this question by extending a stochastic optimal control model suggesting that LRA arise from the flexible, coordinated regulation of stride duration and length to maintain a stable velocity. Combining this model with experimental data, the results show that the reduced LRA observed in Parkinson's disease can result from stronger, less flexible corrections, and that robotic assistance can help restore healthy patterns of variability. Extending the framework to rhythmic cueing, it further shows that young and older healthy adults adjust their gait control almost instantaneously following a change of task. Patients with Parkinson's disease retain a comparable capacity for control adjustment, despite altered dynamics, suggesting that the basal ganglia are not solely responsible for this flexibility. Finally, because conventional measures of LRA require long recordings, this thesis introduces a geometric approach to characterize stride-to-stride regulation over shorter time series. Together, these results support the view that gait variability reflects the continuous, flexible regulation of a redundant locomotor system and offer new perspectives for developing sensitive markers of gait control.