Dynamics and control of a multi-body planar pendulum

Abstract

The explicit equations of motion for a general n-body planar pendulum are derived in a simple and concise manner. A new and novel approach for obtaining these equations using mathematical induction on the number bodies in the pendulum system is used. Assuming that the parameters of the system are precisely known, a simple method for its control that is inspired by analytical dynamics is developed. The control methodology provides closed-form nonlinear control and makes no approximations/linearizations of the nonlinear system. No a priori structure is imposed on the controller. Globally, asymptotic Lyapunov stability is achieved along with the minimization of a userprovided control cost at each instant of time. This control methodology is then extended to include uncertainties in the parameters of the system through the use of an additional continuous controller. Simulations showing the simplicity and efficacy of the approach are provided for a 10-body pendulum system whose model is only known imprecisely. The ease with which the uncertain system can be controlled to move from any initial

A novel approach for modeling and tracking control of a passive-wheel snake robot

“…On the basis of former researches, Udwadia and colleagues [26][27][28][29][30][31] provided fundamental equation of motion of constraint mechanical systems. Compared to classical dynamic theories, the equation of motion is easily acquired mainly by three steps, without any other variables such as Lagrangian multiplier in Lagrangian equation, which is handy to process.…”

Application of the Udwadia–Kalaba approach to tracking control of mobile robots

“…(40). Figures 2 and 4 show the x coordinate curve and the y coordinate curve as a function of time t of the mass center of the mobile robot when a certain level driving torque generated by the left motor and the right motor to realize the desired trajectory: x d = 3 sin t, y d = −5 cos t. The plot of errorx as a function of time t is presented in Fig.…”

“…Using the fundamental equation, Udwadia et al also successfully addressed the control of nonlinear multibody mechanical systems in the presence of system uncertainties [36][37][38][39][40]. This control methodology now is well known to many researchers in this field.…”

An Approach to the Dynamics and Control of Uncertain Robot Manipulators

“…Unlike most control methods for the control problem of robot manipulators, the present paper does not make any linearizations or approximations. Our methodology is based on the Udwadia-Kalaba equation (UKE) [12][13][14][15][16][17]. The Udwadia-Kalaba equation is obtained by using Gauss's principle rather than the more commonly used principles of Lagrange, Hamilton, Gibbs, and Appell [18].…”

“…Considering the moment of inertial of the robot manipulators are uncertain, a nonlinear controller was adopted to make nonlinear system to track the given trajectory. In the control methodology, this nonlinear controller is augmented by an additional additive controller based on a generalization of the notion of sliding surfaces [15][16][17]29]. It's important to notice that the control obtained relies on recent advances in analytical dynamics rather than on control theory.…”