Improved hopping control on slopes for small robots using spring mass modeling

TL;DR

This paper presents a simple spring-mass model and control strategies to improve the stability of small hopping robots on slopes, enabling reliable landings on uneven terrain with minimal computational effort.

Contribution

It introduces slope-aware adjustments to touchdown angle and torque application, enhancing hopping stability on inclined surfaces without complex sensing.

Findings

Simulation results show significant stability improvements on slopes.

Minimal control adjustments effectively counteract slope-induced rotation.

Method suitable for low-cost robotic platforms.

Abstract

Hopping robots often lose balance on slopes because the tilted ground creates unwanted rotation at landing. This work analyzes that effect using a simple spring mass model and identifies how slope induced impulses destabilize the robot. To address this, we introduce two straightforward fixes, adjusting the bodys touchdown angle based on the slope and applying a small corrective torque before takeoff. Together, these steps effectively cancel the unwanted rotation caused by inclined terrain, allowing the robot to land smoothly and maintain stable hopping even on steep slopes. Moreover, the proposed method remains simple enough to implement on low cost robotic platforms without requiring complex sensing or computation. By combining this analytical model with minimal control actions, this approach provides a practical path toward reliable hopping on uneven terrain. The results from simulation confirm that even small slope aware adjustments can dramatically improve landing stability, making the technique suitable for future autonomous field robots that must navigate natural environments such as hills, rubble, and irregular outdoor landscapes.