Balance-Constrained Recursive Inverse Kinematics for Task-Space Tracking of Two-Wheeled Legged Robots

Abstract

Two-wheeled legged robots (TWLRs) combine high mobility with versatile whole-body motion capability. However, stable torso motion control remains challenging because of their underactuated wheeled inverted pendulum dynamics and closed-loop parallel mechanism structure, particularly under dynamic center-of-mass (CoM) variations. To address this problem, this paper presents a balance-constrained inverse kinematics framework integrating kinematic constraints with dynamic equilibrium conditions. For real-time implementation, a recursive solution framework combining the Levenberg–Marquardt (LM) method and an extended Kalman filter (EKF) is proposed. The LM solution is treated as a measurement input to the EKF, enabling recursive correction of joint-state errors with respect to the desired trajectory. The proposed LM–EKF framework improves temporal continuity and numerical robustness while maintaining real-time computational performance. Numerical results demonstrate stable and accurate task-space trajectory tracking, validating the effectiveness of the proposed approach for whole-body manipulation of TWLR systems.