# Tunable Leg Stiffness in a Monopedal Hopper for Energy-Efficient Vertical Hopping Across Varying Ground Profiles

arXiv: https://arxiv.org/abs/2508.02873 · HTML: https://mlsanity.com/paper/2508.02873/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Aug 2025.

## Built on by (most cited first, 2 of 2)

- [InSPO: Unlocking Intrinsic Self-Reflection for LLM Preference Optimization](https://mlsanity.com/paper/2512.23126/) (2025)
- [MINT: Minimal Information Neuro-Symbolic Tree for Objective-Driven Knowledge-Gap Reasoning and Active Elicitation](https://mlsanity.com/paper/2602.05048/) (2026)

## Abstract (arXiv)

We present the design and implementation of HASTA (Hopper with Adjustable Stiffness for Terrain Adaptation), a vertical hopping robot with real-time tunable leg stiffness, aimed at optimizing energy efficiency across various ground profiles (a pair of ground stiffness and damping conditions). By adjusting leg stiffness, we aim to maximize apex hopping height, a key metric for energy-efficient vertical hopping. We hypothesize that softer legs perform better on soft, damped ground by minimizing penetration and energy loss, while stiffer legs excel on hard, less damped ground by reducing limb deformation and energy dissipation. Through experimental tests and simulations, we find the best leg stiffness within our selection for each combination of ground stiffness and damping, enabling the robot to achieve maximum steady-state hopping height with a constant energy input. These results support our hypothesis that tunable stiffness improves energy-efficient locomotion in controlled experimental conditions. In addition, the simulation provides insights that could aid in the future development of controllers for selecting leg stiffness.