Direct Kinematic Module Development for Robots with Mixed Rolling, Slipping, and Buoyant Wheels

In several cases, mobile robots are subject to particular constraints such as adhesion or slipping at contact, unilateral contacts, elasticity of materials, and even conditions that may represent the floating of a body on a marine or freshwater surface. In this work, a method to achieve the solution to the direct dynamic problem is applied to an internally driven amphibious robot equipped with wheels that roll in rough terrain or floating on a sea or freshwater surface. In pursuit of this goal, the dynamic problem is first formulated according to classic approach of multibody system dynamics that eliminates the constraint reactions array through the use of Lagrange multipliers. In this regard, it is necessary to define the constraint equation array, where this task is quite easy for holonomic constraints. However, it is also necessary to solve the problem of defining the contact constraints of the wheel with rough terrain or water surface. This problem is addressed herein by introducing an additional array of the Lagrangian components of some reaction forces. This approach can be implemented on a dedicated low-level code that suits real-time applications much better than the general commercially available packages do. The methodology has been applied to a simplified two-dimensional model of the amphibious robot under study, consisting chiefly of a main rolling wheel, an internal master wheel that provides internal traction and a compound pendulum carrier link. The method permits the construction of a forward dynamic block that can be used in control or simulation.