Related papers: An Input-to-State Stability Perspective on Robust …
Today's complex robotic designs comprise in some cases a large number of degrees of freedom, enabling for multi-objective task resolution (e.g., humanoid robots or aerial manipulators). This paper tackles the stability problem of a…
Stability is a fundamental notion in dynamical systems and control theory that, traditionally understood, describes asymptotic behavior of solutions around an equilibrium point. This notion may be characterized abstractly as continuity of a…
Bipedal walking is one of the most important hallmarks of human that robots have been trying to mimic for many decades. Although previous control methodologies have achieved robot walking on some terrains, there is a need for a framework…
This study presents a theoretical method for planning and controlling agile bipedal locomotion based on robustly tracking a set of non-periodic keyframe states. Based on centroidal momentum dynamics, we formulate a hybrid phase-space…
We present a novel approach to quantifying and optimizing stability in robotic systems based on the Lyapunov exponents addressing an open challenge in the field of robot analysis, design, and optimization. Our method leverages…
Incremental input-to-state stability (delta-ISS) offers a robust framework to ensure that small input variations result in proportionally minor deviations in the state of a nonlinear system. This property is essential in practical…
Biped robots are inherently unstable because of their complex kinematics as well as dynamics. Despite the many research efforts in developing biped locomotion, the performance of biped locomotion is still far from the expectations. This…
We study the existence of asymptotically stable periodic trajectories induced by reset feedback. The analysis is developed for a planar system. Casting the problem into the hybrid setting, we show that a periodic orbit arises from the…
Incremental stability of dynamical systems ensures the convergence of trajectories from different initial conditions towards each other rather than a fixed trajectory or equilibrium point. Here, we introduce and characterize a novel class…
Stable locomotion in precipitous environments is an essential task for quadruped robots, requiring the ability to resist various external disturbances. Recent neural policies enhance robustness against disturbances by learning to resist…
Quadrupedal locomotion over complex terrain has been a long-standing research topic in robotics. While recent reinforcement learning-based locomotion methods improve generalizability and foot-placement precision, they rely on implicit…
A topological approach and understanding to the detection of unstable periodic orbits based on a recently proposed method (PRL 78, 4733 (1997)) is developed. This approach provides a classification of the set of transformations necessary…
This work primarily focuses on synthesizing a controller that guarantees an unknown continuous-time system to be incrementally input-to-state stable ($\delta$-ISS). In this context, the notion of $\delta$-ISS control Lyapunov function…
We establish stability results for PD tracking control laws in bipedal walking robots. Stability of PD control laws for continuous robotic systems is an established result, and we extend this for hybrid robotic systems, an alternating…
Empirically defining some constant probabilistic orbits of f(x) and g(x) iterated high-order functions, the stability of these functions in possible entangled interaction dynamics of the environment through its orbit's connectivity (open…
We reconsider both the global and local stability of solutions of continuously evolving dynamical systems from a geometric perspective. We clarify that an unambiguous definition of stability generally requires the choice of additional…
This paper addresses the robust stability of a boundary controlled system coupling two partial differential equations (PDEs), namely beam and string equations, in the presence of boundary and in-domain disturbances under the framework of…
This paper provides a systematic exposition of Lyapunov stability for compact sets in locally compact metric spaces. We explore foundational concepts, including neighborhoods of compact sets, invariant sets, and the properties of dynamical…
We study the stability properties of a class of time-varying nonlinear systems. We assume that non-strict input-to-state stable (ISS) Lyapunov functions for our systems are given and posit a mild persistency of excitation condition on our…
In the design and operation of complex dynamical systems, it is essential to ensure that all state trajectories of the dynamical system converge to a desired equilibrium within a guaranteed stability region. Yet, for many practical systems…