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Using the damped pendulum system we introduce the averaging method to study the periodic solutions of a dynamical system with small perturbation. We provide sufficient conditions for the existence of periodic solutions with small amplitude…
This paper presents the control and stabilization of the rotary inverted pendulum based on a general controller scheme. The proposed scheme has its foundation in classical control theory, and the importance of an integrator in disturbance…
Models of a playground swing have been studied since the 1960s. However, in most of them, the position of the swinger is controlled directly. This simplifies the problem but hides the mechanics of torques applied to keep the swing moving in…
Stable dynamical systems are a flexible tool to plan robotic motions in real-time. In the robotic literature, dynamical system motions are typically planned without considering possible limitations in the robot's workspace. This work…
In this work, we present a method for simulating the large-scale deformation and crumpling of thin, elastoplastic sheets. Motivated by the physical behavior of thin sheets during crumpling, two different formulations of the governing…
In this paper, we prove the exponential stability property of a class of mechanical systems represented in the port-Hamiltonian framework. To this end, we propose a Lyapunov candidate function different from the Hamiltonian of the system.…
This paper presents the development of a new passive assistive handwriting device, which aims to stabilize the motion of people living with movement disorders. Many people living with conditions such as cerebral palsy, stroke, muscular…
Learning from demonstration provides a sample-efficient approach to acquiring complex behaviors, enabling robots to move robustly, compliantly, and with fluidity. In this context, Dynamic Motion Primitives offer built - in stability and…
Obstacle avoidance for DMPs is still a challenging problem. In our previous work, we proposed a framework for obstacle avoidance based on superquadric potential functions to represent volumes. In this work, we extend our previous work to…
This paper proposes a novel wide-area control strategy for modulating the active power injections to damp the critical frequency oscillations in power systems, this includes the inter-area oscillations and the transient frequency swing. The…
In this work, we propose a geometric framework for analyzing mechanical manipulation, for instance, by a robotic agent. Under the assumption of conservative forces and quasi-static manipulation, we use energy methods to derive a metric. In…
This article focuses on the trajectory tracking problem of mobile manipulators (MMs). Firstly, we construct a position and orientation model predictive tracking control (POMPTC) scheme for mobile manipulators. The proposed POMPTC scheme can…
Spring Loaded Inverted Pendulum (SLIP) model has a long history in describing running behavior in animals and humans as well as has been used as a design basis for robots capable of dynamic locomotion. Anchoring the SLIP for lossy physical…
In a dissipative dynamic system driven by an oscillating force, a strong nonlinear highly oscillatory friction force can create a quasi-steady tug, which is always directed opposite to the ponderomotive force induced due to a spatial…
Frequency responses of multi-degree-of-freedom mechanical systems with weak forcing and damping can be studied as perturbations from their conservative limit. Specifically, recent results show how bifurcations near resonances can be…
We show asymptotic, exponential stability of the equilibrium configuration, $\smallL$, of a hollow physical pendulum with its inner part entirely filled with a viscous liquid, corresponding to the center of mass being in the lowest…
If one wants to explore the properties of a dynamical system systematically one has to be able to track equilibria and periodic orbits regardless of their stability. If the dynamical system is a controllable experiment then one approach is…
Numerical simulations of the flow in an extrusion damper are performed using a finite volume method. The damper is assumed to consist of a shaft, with or without a spherical bulge, oscillating axially in a containing cylinder filled with a…
Generating robust locomotion for a humanoid robot in the presence of disturbances is difficult because of its high number of degrees of freedom and its unstable nature. In this paper, we used the concept of Divergent Component of…
In this paper we review recent work on novel computing paradigms using coupled oscillatory dynamical systems. We explore systems of relaxation oscillators based on linear state transitioning devices, which switch between two discrete states…