Jump Control Based on Nonlinear Wheel-Spring-Loaded Inverted Pendulum Model: Validation of a Wheeled-Bipedal Robot with Single-Degree-of-Freedom Legs

Jumping is a fundamental capability for wheeled-bipedal robots (WBRs) navigating unstructured terrains, with jump height and stability serving as indicators of the robot’s environmental adaptability. However, existing trajectory planning methods demand high output capacity from the joints and fail t...

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Main Authors: Jingsong Gao, Hongzhe Jin, Liang Gao, Yanhe Zhu, Jie Zhao, Hegao Cai
Format: Article
Language:English
Published: MDPI AG 2025-04-01
Series:Biomimetics
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Online Access:https://www.mdpi.com/2313-7673/10/4/246
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author Jingsong Gao
Hongzhe Jin
Liang Gao
Yanhe Zhu
Jie Zhao
Hegao Cai
author_facet Jingsong Gao
Hongzhe Jin
Liang Gao
Yanhe Zhu
Jie Zhao
Hegao Cai
author_sort Jingsong Gao
collection DOAJ
description Jumping is a fundamental capability for wheeled-bipedal robots (WBRs) navigating unstructured terrains, with jump height and stability serving as indicators of the robot’s environmental adaptability. However, existing trajectory planning methods demand high output capacity from the joints and fail to balance computational load with trajectory tracking performance. This limitation hinders most robots from experimental validation. To address these challenges, this study presents an optimized virtual model, trajectory planning strategy, and control method. These solutions enhance both the height and stability of jumps while ensuring real-time execution on physical robots. Firstly, inspired by the human jumping mechanism, a Nonlinear Wheel-Spring-Loaded Inverted Pendulum (NW-SLIP) model was originally proposed as the virtual model for trajectory planning. The jump height is increased by 3.4 times compared to the linear spring model. Then, cost functions are established based on this virtual model, and the trajectory for each stage is iteratively optimized using Quadratic Programming (QP) and a bisection method. This leads to a 21.5% increase in the maximum jump height while reducing the peak joint torque by 14% at the same height. This significantly eases execution and enhances the robot’s trajectory-tracking ability. Subsequently, a leg statics model is introduced alongside the kinematics model to map the relationship between the virtual model and joint space. This approach improves trajectory tracking performance while circumventing the intricate calculation of the dynamics model, thereby enhancing jump consistency and stability. Finally, the proposed trajectory planning and jump control method is validated through both simulations and real-world experiments, demonstrating its feasibility and effectiveness in practical robotic applications.
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spelling doaj-art-1dc4aeaf9f3c463eb5404e917cb82c462025-08-20T03:14:14ZengMDPI AGBiomimetics2313-76732025-04-0110424610.3390/biomimetics10040246Jump Control Based on Nonlinear Wheel-Spring-Loaded Inverted Pendulum Model: Validation of a Wheeled-Bipedal Robot with Single-Degree-of-Freedom LegsJingsong Gao0Hongzhe Jin1Liang Gao2Yanhe Zhu3Jie Zhao4Hegao Cai5School of Mechatronics Engineering, Harbin Institute of Technology, Harbin 150080, ChinaSchool of Mechatronics Engineering, Harbin Institute of Technology, Harbin 150080, ChinaSchool of Mechatronics Engineering, Harbin Institute of Technology, Harbin 150080, ChinaSchool of Mechatronics Engineering, Harbin Institute of Technology, Harbin 150080, ChinaSchool of Mechatronics Engineering, Harbin Institute of Technology, Harbin 150080, ChinaSchool of Mechatronics Engineering, Harbin Institute of Technology, Harbin 150080, ChinaJumping is a fundamental capability for wheeled-bipedal robots (WBRs) navigating unstructured terrains, with jump height and stability serving as indicators of the robot’s environmental adaptability. However, existing trajectory planning methods demand high output capacity from the joints and fail to balance computational load with trajectory tracking performance. This limitation hinders most robots from experimental validation. To address these challenges, this study presents an optimized virtual model, trajectory planning strategy, and control method. These solutions enhance both the height and stability of jumps while ensuring real-time execution on physical robots. Firstly, inspired by the human jumping mechanism, a Nonlinear Wheel-Spring-Loaded Inverted Pendulum (NW-SLIP) model was originally proposed as the virtual model for trajectory planning. The jump height is increased by 3.4 times compared to the linear spring model. Then, cost functions are established based on this virtual model, and the trajectory for each stage is iteratively optimized using Quadratic Programming (QP) and a bisection method. This leads to a 21.5% increase in the maximum jump height while reducing the peak joint torque by 14% at the same height. This significantly eases execution and enhances the robot’s trajectory-tracking ability. Subsequently, a leg statics model is introduced alongside the kinematics model to map the relationship between the virtual model and joint space. This approach improves trajectory tracking performance while circumventing the intricate calculation of the dynamics model, thereby enhancing jump consistency and stability. Finally, the proposed trajectory planning and jump control method is validated through both simulations and real-world experiments, demonstrating its feasibility and effectiveness in practical robotic applications.https://www.mdpi.com/2313-7673/10/4/246jump controlnonlinear springwheeled-bipedal robottrajectory planning
spellingShingle Jingsong Gao
Hongzhe Jin
Liang Gao
Yanhe Zhu
Jie Zhao
Hegao Cai
Jump Control Based on Nonlinear Wheel-Spring-Loaded Inverted Pendulum Model: Validation of a Wheeled-Bipedal Robot with Single-Degree-of-Freedom Legs
Biomimetics
jump control
nonlinear spring
wheeled-bipedal robot
trajectory planning
title Jump Control Based on Nonlinear Wheel-Spring-Loaded Inverted Pendulum Model: Validation of a Wheeled-Bipedal Robot with Single-Degree-of-Freedom Legs
title_full Jump Control Based on Nonlinear Wheel-Spring-Loaded Inverted Pendulum Model: Validation of a Wheeled-Bipedal Robot with Single-Degree-of-Freedom Legs
title_fullStr Jump Control Based on Nonlinear Wheel-Spring-Loaded Inverted Pendulum Model: Validation of a Wheeled-Bipedal Robot with Single-Degree-of-Freedom Legs
title_full_unstemmed Jump Control Based on Nonlinear Wheel-Spring-Loaded Inverted Pendulum Model: Validation of a Wheeled-Bipedal Robot with Single-Degree-of-Freedom Legs
title_short Jump Control Based on Nonlinear Wheel-Spring-Loaded Inverted Pendulum Model: Validation of a Wheeled-Bipedal Robot with Single-Degree-of-Freedom Legs
title_sort jump control based on nonlinear wheel spring loaded inverted pendulum model validation of a wheeled bipedal robot with single degree of freedom legs
topic jump control
nonlinear spring
wheeled-bipedal robot
trajectory planning
url https://www.mdpi.com/2313-7673/10/4/246
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