This paper studies periodic motions of an inverted pendulum with a periodically moving base. A bifurcation tree of period-1 to period-8 motions is predicted through a discrete implicit mapping method. The stable and unstable periodic motions on the bifurcation tree are obtained semi-analytically, ...
A suitable experiment for undergraduates is described which illustrates chaotic motion, i.e., a driven inverted pendulum. By varying the driving frequency, one finds a transition from regular (periodic) motion to chaotic motion. A sonar coupled to a micr
1. The ASLIP consists of a Spring Loaded Inverted Pendulum (SLIP) with the addition of pitch dynamics, and can be used to study the sagittal plane motion of bipedal running. A hybrid controller for the ASLIP is developed that acts on two levels. In the first level, continuous in-stride...
In this paper, a robust nonlinear control design strategy to solve the stabilization problem of an inverted pendulum system subject to parametric uncertainties and unmodeled dynamics is proposed. The control strategy is based on the combination of Amplified Linear Quadratic Regulator (ALQR) control wit...
The high-level control is built on a two-mass linear inverted pendulum (TMLIP) model to generate the appropriate step location such that the robot walker maintains dynamic balance through multiple planned steps. The specified stepping tasks are fed to the low-level control that is based on a ...
To design a teaching platform of the convenient automatic control based on the inverted pendulum, built-in 3 d gyroscope and accelerometer sensors, can realize autonomous vertical control. Platform uses STM32 MCU to track the accelerometer gyroscope of angular velocity and acceleration. Using Calman ...
Inverted pendulum is another common model of legged robot. Unlike equivalent parallel or serial mechanism, the total mass is concentrated in the Center of Mass (CM), inferring the force and torque of the joints by solving dynamic equations based on the inverted pendulum model. DARPA’s biped ro...
In this study, kinematic and kinetic data for 14 test subjects walking on a treadmill were recorded to verify a damped bipedal inverted pendulum (DBIP) model. The verification aim was for the DBIP model to match the step frequency and first harmonic dynamic load factor (DLF1) extracted from...
Given a inverted pendulum governed by Eq. (2) we say that this pendulum is stable during a window of time up to time tmax if given an initial angle −π/2<θ0<π/2, all θt, t=1,2,…tmax, obtained by integration of the motion equations via Runge–Kutta method of fourth or...
Three problems normally associated with periodic motion are generation, stabilization, and trajectory transition. These problems are analyzed and control implementations are provided for the inverted pendulum as the simplest model of a biped. Results of computer simulations are presented....