Analytic Centroidal Control with Mass Distribution Models for Humanoid Robots

With rapid advances in humanoid robotics hardware and control algorithms, it is becoming a tangible reality that such robots will function alongside humans. In light of these developments, it is essential to address the challenges of achieving high efficiency and performance while ensuring their accessibility, transparency, and safety. This thesis presents a hardware and software co-design approach for achieving balanced whole-body control and locomotion in humanoid robots. Coordinating such motion remains difficult due to the high dimensionality and nonlinearity of the control problem, stemming from underactuation and complex multibody dynamics. The challenge is further amplified when observability and controllability are limited by reduced sensing, low torque capacity, or missing degrees of freedom. Computing resources are often shared, making efficient and predictable computation critical. To address these issues, we introduce a compact, yet descriptive five-mass model of a humanoid robot, enabling precise, analytic, and fast methods for inverse kinematics, state estimation, and both feedforward and feedback control. The formulation of these methods was shaped by the properties of the NimbRo-OP2X platform, which served as a target for their implementation and evaluation, and was developed within this thesis as an accessible and capable adult-sized humanoid robot. Two direct inverse kinematics methods are proposed for whole-body task-space control. Both rely on a triangle-based parameterization that maps limb configurations to their associated mass positions. Together with the torso, the resulting five masses are then distributed in space to shape desired system quantities such as the center of mass position or inertia, which are then interpolated to produce continuous motion. The mass-based kinematics provide a translation layer between the full kinematic model and a reduced-order template that captures system dynamics. This model is then used to compute reference trajectories from a footstep plan, with performance further enhanced with real-time controls operating on the centroidal state. Finally, we develop centroidal state estimation along with feedforward and feedback control techniques that improve robustness against limited sensing, sensorimotor delays, and structural compliance. These methods substantially enhance balance and enable seamless integration of task-driven motions, such as an impulse-maximizing kicking behavior developed for humanoid robot soccer. We showcase their effectiveness in simulation and real-world experiments. Our approaches allow low-cost hardware to achieve high-fidelity dynamic movement while remaining extremely computationally efficient. Through progressive integration into the control software of Team NimbRo, the methods contributed to winning numerous RoboCup world championships.