Udwadia–Kalaba theory for the control of bulldozer link lever

Abstract

We propose to apply Udwadia-Kalaba theory to the bulldozer dynamics analysis. The bulldozer system is divided into several subsystems by this approach, which simplifies the modeling process for multi-link mechanism. Based on this approach, the constraints are classified into structure constraints and performance constraints. Structure constraints are used to set up dynamic model without regard for trajectory. Performance constraints are the desired trajectory. Then, according to the equation of motion of the unconstrained system established by Lagrange approach and system constraints which include structure and performance constraints, an explicit, closed-form analytical expression for the control force can be obtained by solving Udwadia-Kalaba equation. We demonstrate that this approach does not need to solve Lagrange multiplier, which is always difficult to obtain. However, for bulldozer link lever system, the initial conditions are difficult to satisfy the constraints in the actual situation. Thus, the problem of initial condition deviation is taken into consideration. In the end, the numerical simulations are done to prove that the trajectory of the bulldozer satisfies the designed one and the real-time forces are conveniently acquired.

Modeling Flexible Multi-Body Systems Within the Udwadia–Kalaba Framework, a Lumped Parameter Approach

“…The formulation can be used to model a mechanical system as a system of rigid bodies, with geometrical constraint equations governing their physical kinematical motions. Previous investigations of this dynamic modelling approach [6,7,8] showed convincing agreement of simulated system dynamic results with reference data. Udwadia and Phohomsiri in [9] note that alternative analytical formulations of constrained system motion were offered by Gibbs and Appell, Gauss and Dirac, however emphasise that a key feature of the U-K formulation is that it may provide an explicit set of equations for generic constrained systems.…”

“…In the aforementioned studies [6,7,8,14], the U-K formulation was applied to model rigid-body systems. Various studies have discussed and explored methodologies of applying the U-K formulation to deal with flexible systems.…”

Towards development of a nonlinear and flexible multi-body helicopter inceptor model: a resonant frequency tuning study.

“…acceleration constraints brought into play to ensure that the system satisfies the geometric constraints it is subjected to. This dynamic modelling approach has also previously been investigated by Nielsen et al [14], Li et al [15] and Xu et al [16] who all found convincing agreement of simulated system dynamic results with reference data. In 2019, previous work of the authors [7] provided an application study of the Udwadia-Kalaba modelling approach to a rigid nonlinear planar crank-slider linkage mechanism.…”

Robust control design for home pension service mobile robots with passive and servo constraints

“…The applications of the Udwadia control was extensively reported in recent years. [31][32][33][34][35][36] However, Udwadia control does not consider any uncertainty that is inevitable in the actual mechanical systems. Motivated by these reasons, a robust control is designed based on the frame of the Udwadia control in this paper.…”