Humans and terrestrial legged animals can travel with great degree of stability, agility and maneuverability over a large number of terrains such as gravel, grass, sand, rock, mud, snow, asphalt, river-beds and more. They can also perform many locomotive tasks elegantly and seemingly effortlessly, showing their rich structural and dynamic readiness in rejecting even large, rapid and unexpected disturbances.

However, despite significant advances in the robotic legged locomotion field during the last three decades since Raibert introduced the first self-balancing hopping robot, there are not yet any robots that can run over real outdoor rough terrains as humans and animals do.

During rapid locomotion, animals seem to use passive mechanisms such as sprawled posture or tuned mechanical impedances to self-stabilize and reject unexpected disturbances before the neural reflexes take place. These mechanisms allow for immediate response to perturbations, and, in this way, humans and animals are able to move with great stability and maneuverability over various types of terrains.

With the purpose of designing robotic legs with similar passive mechanisms that biological legged systems have embedded, the present work focuses on relating the robotic leg's passive properties to various running performance measures. In particular, curved legs are chosen for this study motivated by the exceptional running performance achieved by some autonomous robots and human amputees using this type of leg. The relevant aspects of running with this type of leg are characterized by using various reduced-order dynamical models. Then, by associating the design parameters of each model to the running performance, these parameters are optimized to obtain new curved leg designs.

The results of the present work reveal that, in the presence of changes in the environmental conditions, the approach of mechanical impedance adaptation is a more effective and realistic strategy than the controller optimization method for stable and efficient running. In addition, this work shows that running with curved legs is more efficient and robust and can recover from perturbations more quickly than with straight legs. These results are justified by the richer running dynamics involved with curved legs than with straight legs such as variable passive compliance and variable rest length due to the rolling motion involved during stance.

In essence, the results obtained in this work show the importance of (actively or passively) tuning the mechanical properties of the leg to achieve stable and efficient running. These approaches do not only apply to robotic platforms with curved legs but can be generalized for any robotic legged system.