Unified three-dimensional bipedal locomotion control via ground reaction force-based joint compliance modulation

Human walking is inherently three-dimensional, requiring coordinated control in multiple planes of motion. Among these, controls in the sagittal and frontal planes play central roles in propulsion and balance. While sagittal plane control has been extensively modelled, the control mechanisms underlying frontal plane stability remain less understood. In this study, we hypothesize that frontal plane control can be achieved through a simple yet biologically inspired strategy: modulating hip compliance in response to ground reaction forces (GRFs). To validate this, we extend our previously proposed bipedal walking control framework, termed Concerted Control, to three dimensions and implement this control law at both the joint and muscle levels in bipedal models. Across a wide range of walking speeds (0.7-1.8 m s-1), both implementations yield dynamically stable three-dimensional gaits without any movement constraints, and their hip abduction-adduction torque profiles closely match human data, achieving cross-correlation values above 0.86 in most conditions. These results demonstrate that GRF-based hip compliance modulation is a parsimonious and robust control principle for frontal plane stability. More broadly, our findings highlight the potential of GRF-driven compliance control as a unifying strategy for neuromechanical modelling and bio-inspired bipedal locomotion.