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.