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Animals are much better at running than robots. The difference in performance arises in the important dimensions of agility, range, and robustness. To understand the underlying causes for this performance gap, we compare natural and artificial technologies in the five subsystems critical for running: power, frame, actuation, sensing, and control. With few exceptions, engineering technologies meet or exceed the performance of their biological counterparts. We conclude that biology’s advantage over engineering arises from better integration of subsystems, and we identify four fundamental obstacles that roboticists must overcome. Toward this goal, we highlight promising research directions that have outsized potential to help future running robots achieve animal-level performance. 

Infinitesimal contraction analysis, wherein global convergence results are obtained from properties of local dynamics, is a powerful analysis tool. In this letter, we generalize infinitesimal contraction analysis to hybrid systems in which state-dependent guards trigger transitions defined by reset maps between modes that may have different norms and need not be of the same dimension. In contrast to existing literature, we do not restrict mode sequence or dwell time. We work in settings where the hybrid system flow is differentiable almost everywhere and its derivative is the solution to a jump-linear-time-varying differential equation whose jumps are defined by a saltation matrix determined from the guard, reset map, and vector field. Our main result shows that if the vector field is infinitesimally contracting, and if the saltation matrix is non-expansive, then the intrinsic distance between any two trajectories decreases exponentially in time. When bounds on dwell time are available, our approach yields a bound on the intrinsic distance between trajectories regardless of whether the dynamics are expansive or contractive. We illustrate our results using two examples: a constrained mechanical system and an electrical circuit with an ideal diode. 

Abstract This paper concerns first-order approximation of the piecewise-differentiable flow generated by a class of nonsmooth vector fields. Specifically, we represent and compute the Bouligand (or B-)derivative of the piecewise-differentiable flow generated by a vector field with event-selected discontinuities. Our results are remarkably efficient: although there are factorially many “pieces” of the derivative, we provide an algorithm that evaluates its action on a tangent vector using polynomial time and space, and verify the algorithm's correctness by deriving a representation for the B-derivative that requires “only” exponential time and space to construct. We apply our methods in two classes of illustrative examples: piecewise-constant vector fields and mechanical systems subject to unilateral constraints.