Related papers: An inverted pendulum with a springy control as a m…
The swinging spring, or elastic pendulum, has a 2:1:1 resonance arising at cubic order in its approximate Lagrangian. The corresponding modulation equations are the well-known three-wave equations that also apply, for example, in…
This paper investigates the behavior of a heavy soft spring in steady circular motion. Since the spring is inhomogeneous due to centrifugal force, one can rigorously prove that it follows the one-dimensional static Willis-form equations.…
A mathematical model of a simply supported Euler-Bernoulli beam with attached spring-mass system is considered. The model is controlled by distributed piezo actuators and lumped force. We address the issue of asymptotic behavior of…
We outline a method for controlling the location of stable and unstable manifolds in the following sense. From a known location of the stable and unstable manifolds in a steady two-dimensional flow, the primary segments of the manifolds are…
This paper examines the quantum mechanical system that arises when one quantises a classical mechanical configuration described by an underdetermined system of equations. Specifically, we consider the well-known problem in classical…
A pendulum prepared perfectly inverted and motionless is a prototype of unstable equilibria and corresponds to an unstable hyperbolic fixed point in the dynamical phase space. Unstable fixed points are central to understanding Hamiltonian…
In this paper, we propose the reduced model for the full dynamics of a bicycle and analyze its nonlinear behavior under a proportional control law for steering. Based on the Gibbs-Appell equations for the Whipple bicycle, we obtain a…
In this paper we introduce a new method to design control laws for non-linear underactuated systems. Our method produces an infinite dimensional family of control laws, whereas most control techniques only produce a finite dimensional…
Intermittent control has a long history in the physiological literature and there is strong experimental evidence that some human control systems are intermittent. Intermittent control has also appeared in various forms in the engineering…
Springs are commonly used in wearable robotic devices to provide assistive joint torque without the need for motors and batteries. However, different tasks (such as walking or running) and different users (such as athletes with strong legs…
We illustrate the potential of neuromorphic control on the simple mechanical model of a pendulum, with both event-based actuation and sensing. The controller and the pendulum are regarded as event-based systems that occasionally interact to…
In this study we experimentally show that a stretched rainbow spring under gravity or extra weight may exhibit unconventional fall motion. Specially, when the rainbow spring is released from a high place, its lower end remains stationary…
Postural stability is one of the most crucial elements in bipedal locomotion. Bipeds are dynamically unstable and need to maintain their trunk upright against the rotations induced by the ground reaction forces (GRFs), especially when…
The climate system is a forced, dissipative, nonlinear, complex and heterogeneous system that is out of thermodynamic equilibrium. The system exhibits natural variability on many scales of motion, in time as well as space, and it is subject…
Low-dimensional models are ubiquitous in the bipedal robotics literature. On the one hand is the community of researchers that bases feedback control design on pendulum models selected to capture the center of mass dynamics of the robot…
The work concerns the spectral, entropy and bifurcation analysis of the dynamics of a reverse-flow system. The existence of chaotic oscillations was demonstrated in a wide range of changes in the parameters of the model. The model of such a…
We propose a hybrid formulation of the linear inverted pendulum model for bipedal locomotion, where the foot switches are triggered based on the center of mass position, removing the need for pre-defined footstep timings. Using a concept…
This study investigates the performance of cascade PID control architecture applied to an inverted pendulum on a cart system through both simulation and experimental implementation. A nonlinear model of the system was developed using…
Dynamic behavior of a weightless rod with a point mass sliding along the rod axis according to periodic law is studied. This is the pendulum with periodically varying length which is also treated as a simple model of child's swing.…
The experience gained with numerous successful applications permits to revisit some points of model-free control. The numerical differentiation of noisy signals may be replaced by a real time parameter identification which is much simpler.…