Trajectory Generation for Humanoid Backflips and Jumps Based on Whole-Body Dynamics Optimization with Consideration of KKT Residual Convergence

Abstract

For trajectory generation of whole-body jumping motions such as humanoid backflips, it is crucial to simultaneously optimize the takeoff, flight, and landing phases while considering full-body dynamics and kinematics. Although such methods have been proposed for standard jumping motions, they have not been applied to more dynamic actions such as frontflips, backflips, and yaw twist jumps, where strong nonlinearity and high sensitivity to certain parameters (e.g., rotor inertia and torque cost weights) pose significant challenges. To address these challenges, we apply a two-stage optimization strategy to an existing full-body dynamics optimization method that simultaneously optimizes the takeoff, flight, and landing phases. In our approach, the same initialization and reference trajectory generation rules are shared across motions, and the solution from the first optimization is used not only as an initial guess but also as a reference in the second optimization. This strategy improves the convergence of the KKT residuals across various jump types and mitigates sensitivity to parameters such as rotor inertia and torque cost weights. As a result, our method achieves unified trajectory generation for frontflips, backflips, yaw twist jumps, and standard jumps using the same initialization, cost weights, and constraints. We also analyze the sensitivity to rotor inertia and show that exceeding a certain threshold can lead to a sharp deterioration in KKT residual convergence.