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

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.