Running with compliant curved legs involves the progression of the center of pressure, the changes of both the leg's stiffness and effective rest length, and the shift of the location of the maximum stress point along the leg. These phenomena are product of the geometric and material properties of these legs, and the rolling motion produced during stance. We examine these aspects with several reduced-order dynamical models to relate the leg's design parameters (such as normalized foot radius, leg's effective stiffness, location of the maximum stress point and leg shape) to running performance (such as robustness and efficiency). By using these models, we show that running with compliant curved legs can be more efficient, robust with fast recovery behavior from perturbations than running with compliant straight legs. Moreover, the running performance can be further improved by tuning these design parameters in the context of running with rolling. The results shown in this work may serve as potential guidance for future compliant curved leg designs that may further improve the running performance.

A novel path-planning algorithm is proposed for a tracked mobile robot to traverse uneven terrains, which can efficiently search for stability sub-optimal paths. This algorithm consists of combining two RRT-like algorithms (the Transition-based RRT (T-RRT) and the Dynamic-Domain RRT (DD-RRT) algorithms) bidirectionally and of representing the robot-terrain interaction with the robot's quasi-static tip-over stability measure (assuming that the robot traverses uneven terrains at low speed for safety). The robot's stability is computed by first estimating the robot's pose, which in turn is interpreted as a contact problem, formulated as a linear complementarity problem (LCP), and solved using the Lemke's method (which guarantees a fast convergence). The present work compares the performance of the proposed algorithm to other RRT-like algorithms (in terms of planning time, rate of success in finding solutions and the associated cost values) over various uneven terrains and shows that the proposed algorithm can be advantageous over its counterparts in various aspects of the planning performance.