A Co-Design Framework for Energy-Aware Monoped Jumping with Detailed Actuator Modeling

TL;DR

The paper tackles energy-aware co-design for monoped jumping by jointly optimizing mechanical design, gearbox parameters, and control to maximize jump height while minimizing mechanical energy. It introduces a three-stage framework: Stage 1 optimizes actuator gear parameters to map gear ratio to actuator mass; Stage 2 uses CMA-ES to co-design gear ratios, link lengths, and control parameters; Stage 3 automatically generates a parameterized CAD model for fabrication. Key contributions include explicit gearbox modeling within co-design, realistic actuator and link mass models, and automated CAD templating to bridge simulation and hardware. Experimental results show about a 50% reduction in mechanical energy and a jump height of 0.8 m, with Case-C achieving the best energy savings while maintaining competitive height, demonstrating practical impact in rapid design-to-fabrication for energy-efficient monopeds.

Abstract

A monoped's jump height and energy consumption depend on both, its mechanical design and control strategy. Existing co-design frameworks typically optimize for either maximum height or minimum energy, neglecting their trade-off. They also often omit gearbox parameter optimization and use oversimplified actuator mass models, producing designs difficult to replicate in practice. In this work, we introduce a novel three-stage co-design optimization framework that jointly maximizes jump height while minimizing mechanical energy consumption of a monoped. The proposed method explicitly incorporates realistic actuator mass models and optimizes mechanical design (including gearbox) and control parameters within a unified framework. The resulting design outputs are then used to automatically generate a parameterized CAD model suitable for direct fabrication, significantly reducing manual design iterations. Our experimental evaluations demonstrate a 50 percent reduction in mechanical energy consumption compared to the baseline design, while achieving a jump height of 0.8m. Video presentation is available at http://y2u.be/XW8IFRCcPgM

Figures (8)

• Figure 1: Overview of the proposed methodology
• Figure 2: Mass modeling of actuators and leg links. (a) Actuator mass model for ISSPG and ESSPG: motor dimensions and gear parameters determine all component dimensions, yielding total mass. (b) Leg-link mass model: link lengths $l_1$ and $l_2$ define remaining part dimensions to compute total leg-link mass.
• Figure 3: Link-length to mass mapping, derived from the leg link mass model described in Section \ref{['monoped arch']}.
• Figure 4: The system is modeled as a parallel linear spring–damper of length $l$, the distance from the base center to the foot. A torsional spring models angular deflection about the world-frame y-axis from a fixed vertical (z-axis). The robot’s mass is assumed concentrated at the base.
• Figure 5: Overview of the three-stage co-design framework. Stage-1: Actuator Optimization computes optimal gear parameters for a given motor, mapping gear ratio to actuator mass. Stage-2: Co-design Optimization uses CMA-ES to optimize gear ratios, link lengths, and control parameters. Stage-3: Template CAD Generation auto-generates a parametric CAD model for visualization and prototyping.