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Design of a 3-DOF Hopping Robot with an Optimized Gearbox: An Intermediate Platform Toward Bipedal Robots

JongHun Choe, Gijeong Kim, Hajun Kim, Dongyun Kang, Min-Su Kim, Hae-Won Park

TL;DR

The paper designs a 3-DOF hopping robot with a flat foot and human-like knee-ankle configuration to serve as an intermediate platform toward bipedal robots. It combines a MINLP-optimized 3K compound planetary gearbox to maximize hollow-shaft diameter with custom actuators, drivers, and a tethered electrical system, enabling high-torque, high-velocity performance within tight joint-space constraints. A reinforcement-learning controller trained with barrier-based rewards and PPO demonstrates stable repetitive hopping, front flips, and disturbance rejection in hardware, validating the platform's dynamic capabilities. Together, these contributions establish a solid methodological and hardware foundation for advancing toward robust, dynamic bipedal locomotion.

Abstract

This paper presents a 3-DOF hopping robot with a human-like lower-limb joint configuration and a flat foot, capable of performing dynamic and repetitive jumping motions. To achieve both high torque output and a large hollow shaft diameter for efficient cable routing, a compact 3K compound planetary gearbox was designed using mixed-integer nonlinear programming for gear tooth optimization. To meet performance requirements within the constrained joint geometry, all major components-including the actuator, motor driver, and communication interface-were custom-designed. The robot weighs 12.45 kg, including a dummy mass, and measures 840 mm in length when the knee joint is fully extended. A reinforcement learning-based controller was employed, and robot's performance was validated through hardware experiments, demonstrating stable and repetitive hopping motions in response to user inputs. These experimental results indicate that the platform serves as a solid foundation for future bipedal robot development.

Design of a 3-DOF Hopping Robot with an Optimized Gearbox: An Intermediate Platform Toward Bipedal Robots

TL;DR

The paper designs a 3-DOF hopping robot with a flat foot and human-like knee-ankle configuration to serve as an intermediate platform toward bipedal robots. It combines a MINLP-optimized 3K compound planetary gearbox to maximize hollow-shaft diameter with custom actuators, drivers, and a tethered electrical system, enabling high-torque, high-velocity performance within tight joint-space constraints. A reinforcement-learning controller trained with barrier-based rewards and PPO demonstrates stable repetitive hopping, front flips, and disturbance rejection in hardware, validating the platform's dynamic capabilities. Together, these contributions establish a solid methodological and hardware foundation for advancing toward robust, dynamic bipedal locomotion.

Abstract

This paper presents a 3-DOF hopping robot with a human-like lower-limb joint configuration and a flat foot, capable of performing dynamic and repetitive jumping motions. To achieve both high torque output and a large hollow shaft diameter for efficient cable routing, a compact 3K compound planetary gearbox was designed using mixed-integer nonlinear programming for gear tooth optimization. To meet performance requirements within the constrained joint geometry, all major components-including the actuator, motor driver, and communication interface-were custom-designed. The robot weighs 12.45 kg, including a dummy mass, and measures 840 mm in length when the knee joint is fully extended. A reinforcement learning-based controller was employed, and robot's performance was validated through hardware experiments, demonstrating stable and repetitive hopping motions in response to user inputs. These experimental results indicate that the platform serves as a solid foundation for future bipedal robot development.
Paper Structure (13 sections, 12 equations, 8 figures, 4 tables)

This paper contains 13 sections, 12 equations, 8 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Hardware Design
  3. Mechanical Structure
  4. Electrical Architecture
  5. Custom-Designed Components
  6. Gear Teeth Optimization of 3K Compound Planetary Gearbox
  7. Optimization Variables
  8. Cost Function
  9. Equality Constraints
  10. Inequality Constraints
  11. Reinforcement Learning-based Control
  12. Experiments
  13. Conclusion and Future Work

Figures (8)

  • Figure 1: Conceptual design of the bipedal robot currently under development and the proposed 3-DOF hopping robot as an intermediate prototype. The lower images show the proposed robot performing hopping and flipping motions, and responding to external push disturbances and step terrains.
  • Figure 2: Overview of the proposed hopping robot: (a) design and schematic of the closed-loop parallel mechanism in the ankle joint, (b) key dimensions, major components, and joint configurations, and (c) workspace of the robot.
  • Figure 3: Electrical architecture of the proposed hopping robot
  • Figure 4: Exploded view of the D151 actuator for the knee joint.
  • Figure 5: Photographs of the custom-designed components of the proposed hopping robot: (a) 3K compound planetary gearbox used in the D151 actuator, (b) D110A and D151 motor stators, (c) motor driver, and (d) EtherCAT-CAN converter.
  • ...and 3 more figures