A 3-Step Optimization Framework with Hybrid Models for a Humanoid Robot's Jump Motion

TL;DR

This paper addresses generating high-dynamic forward jumps for humanoid robots by introducing a three-step optimization framework that balances posture and centroidal angular momentum (CAM) through inertia shaping. It leverages an SRMP-based launching optimization for momentum, a QP-based joint-space mapping for rapid coarse trajectories, and a final whole-body optimization to refine the plan, enabling offline computations under 10 seconds. The approach is validated through simulation and experiments achieving up to 1.0 m jump distance and 0.5 m height, with inertia shaping guiding landing posture and foot placement. The framework offers a practical, efficient route to agile humanoid jumping in unstructured environments, with potential extensions to continuous jumping and improved model fidelity.

Abstract

High dynamic jump motions are challenging tasks for humanoid robots to achieve environment adaptation and obstacle crossing. The trajectory optimization is a practical method to achieve high-dynamic and explosive jumping. This paper proposes a 3-step trajectory optimization framework for generating a jump motion for a humanoid robot. To improve iteration speed and achieve ideal performance, the framework comprises three sub-optimizations. The first optimization incorporates momentum, inertia, and center of pressure (CoP), treating the robot as a static reaction momentum pendulum (SRMP) model to generate corresponding trajectories. The second optimization maps these trajectories to joint space using effective Quadratic Programming (QP) solvers. Finally, the third optimization generates whole-body joint trajectories utilizing trajectories generated by previous parts. With the combined consideration of momentum and inertia, the robot achieves agile forward jump motions. A simulation and experiments (Fig. \ref{Fig First page fig}) of forward jump with a distance of 1.0 m and 0.5 m height are presented in this paper, validating the applicability of the proposed framework.

Figures (14)

• Figure 1: Illustration of a forward jump experiment.
• Figure 2: Overview of the framework in this paper
• Figure 3: The robot platform used in this paper: (a) actual platform, (b) simulation model, (c) simplified link model
• Figure 4: Diagram of the reaction mass pendulum (RMP) model. The CoM of the inverted pendulum (left-hand side) $C_0$ is divided into a barbell on the sagittal dimension, and the mass is separated to two pieces evenly ($C_1$ and $C_2$) on the endpoint of the barbell. The geometrical characters and dynamical characters are illustrated in (a) and (b), respectively. The length of the pendulum's support segment is represented by $\phi$, and the radius of the barbell is represented by $\varphi$.
• Figure 5: Diagram of the jump motion with the inverted pendulum model. $C_x$ and $C_z$ represent the position of the CoM in the x-axis and z-axis, respectively. $v_{c_0\_x}$ and $v_{c_0\_z}$ represent the velocity of the CoM in the x-axis and z-axis, respectively, at the same moment. $\theta$ represent the launching and landing angle. $l_g$ and $l_f$ are distance in the x-axis distinguished by whether the robot's feet touch the ground.