Impact Dynamics for Humanoid Robot

Abstract

Research on biped robots focuses on replicating human behavior such as walking, jumping, and kicking. The kicking motion, in particular, poses significant challenges due to the need for precise balance and coordination of joint movements and the optimization of joint variables critical for effective kicking. Existing kicking techniques generally rely on kinematic models and predictive model assumptions without incorporating the full dynamics of the robot. Most models use keyframe-based and Inverse Kinematics (IK)-based techniques for joint trajectories and apply feedback control methods such as Dynamic Movement Primitives (DMP), Zero Moment Point (ZMP) control, and reinforcement learning-based control for stability and walking motion. These methods can produce a kicking motion but do not account for the kicking dynamics. Moreover, these techniques are limited to fully actuated robots. This thesis introduces a dynamically inspired, underactuated biped robot operating in a sagittal plane capable of walking and kicking. The model’s dynamics are derived using the Euler-Lagrange method and controlled through a Hybrid Zero Dynamics (HZD)-based Input-Output Linearization (IOL) strategy to achieve precise trajectory tracking. These trajectories are parameterized by the underactuated joint and optimized via Sequential Quadratic Programming (SQP), ensuring that torque remains within permissible limits. This approach incorporates impact dynamics to maintain stability during the walking and kicking phases. The model’s effectiveness is validated using the NAO robot platform in a 3D physics simulator. Our results demonstrate that the robot executes kicks faster, with an average kicking time of 0.75 seconds, and achieves long-range kicks, with an average kicking distance of approximately 6.1 meters. These capabilities surpass the performance of the current state-of-the-art Q-learning-based kicking engines.