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This paper establishes a general framework for describing hybrid dynamical systems which is particularly suitable for numerical simulation. In this context, the data structures used to describe the sets and functions which comprise the…
Hybrid dynamical systems, which include continuous flow and discrete mode switching, can model robotics tasks like legged robot locomotion. Model-based methods usually depend on predefined gaits, while model-free approaches lack explicit…
Sensitivity analysis of multibody systems computes the derivatives of general cost functions that depend on the system solution with respect to parameters or initial conditions. This work develops adjoint sensitivity analysis for hybrid…
Rigid bodies, plastic impact, persistent contact, Coulomb friction, and massless limbs are ubiquitous simplifications introduced to reduce the complexity of mechanics models despite the obvious physical inaccuracies that each incurs…
The ability to generate robust walking gaits on bipedal robots is key to their successful realization on hardware. To this end, this work extends the method of Hybrid Zero Dynamics (HZD) -- which traditionally only accounts for locomotive…
For a wide variety of problems, creating detailed continuous models of (continuous) physical systems is, at the very least, impractical. Hybrid models can abstract away short transient behaviour (thus introducing discontinuities) in order…
Hydraulic jumps occur commonly in natural channels and energy dissipation systems of hydraulic structures in the violent transition from supercritical to subcritical flows. They are characterised by large flow aeration, high turbulence and…
Balance control is important for human and bipedal robotic systems. While dynamic balance during locomotion has received considerable attention, quantitative understanding of static balance and falling remains limited. This work presents a…
Controlling hybrid systems is mostly very challenging due to the variety of dynamics these systems can exhibit. Inspired by the concept of differential flatness of nonlinear continuous systems and their inherent invertibility property, the…
This paper provides an analytical methodology to compute the sensitivities with respect to system parameters for any second order hybrid Ordinary Differential Equation (ODE) system. The hybrid ODE system is characterized by discontinuities…
Dynamics model learning deals with the task of inferring unknown dynamics from measurement data and predicting the future behavior of the system. A typical approach to address this problem is to train recurrent models. However, predictions…
Linear time-invariant systems are very popular models in system theory and applications. A fundamental problem in system identification that remains rather unaddressed in extant literature is to leverage commonalities amongst related linear…
The literature is rich with studies, analyses, and examples on parameter estimation for describing the evolution of chaotic dynamical systems based on measurements, even when only partial information is available through observations.…
In this paper, a computationally efficient data-driven hybrid automaton model is proposed to capture unknown complex dynamical system behaviors using multiple neural networks. The sampled data of the system is divided by valid partitions…
This paper focuses on the motion planning problem for the systems exhibiting both continuous and discrete behaviors, which we refer to as hybrid dynamical systems. Firstly, the motion planning problem for hybrid systems is formulated using…
Hybrid dynamical systems have proven to be a powerful modeling abstraction, yet fundamental questions regarding the dynamical properties of these systems remain. In this paper, we develop a novel class of relaxations which we use to recover…
Over times shorter than that required for relaxation of enthalpy, a liquid can exhibit striking heterogeneities. The picture of these heterogeneities is complex with transient patches of rigidity, irregular yet persistent, intersected by…
Hybrid systems are characterized by the hybrid evolution of their state: A part of the state changes discretely, the other part changes continuously over time. Typically, modern control applications belong to this class of systems, where a…
This paper proposes a neural network hybrid modeling framework for dynamics learning to promote an interpretable, computationally efficient way of dynamics learning and system identification. First, a low-level model will be trained to…
We show that, near periodic orbits, a class of hybrid models can be reduced to or approximated by smooth continuous-time dynamical systems. Specifically, near an exponentially stable periodic orbit undergoing isolated transitions in a…