Nonlinear dynamics of an autonomous robot with deformable origami wheels

Autonomous robots have several applications on industry, military and safety fields. The replacement of the conventional wheels by deformable ones improves the maneuverability, allowing it to trespass obstacles that goes from small fissures to step elevations. Besides, path control can be made by directly actuation on the wheel using a small number of actuators, reducing the structure weigh. This paper deals with a dynamical analysis of an autonomous robot with origami wheels actuated by shape memory alloys (SMAs), forming a self-foldable structure. The nonlinear characteristics of the SMAs together with the slender and bi-stable origami aspects provide a complex nonlinear behavior that can be exploited for energetic and maneuverability purposes. Mathematical modeling considers a reduced order model, based on symmetry hypotheses, to describe the origami mechanics. In addition, a polynomial constitutive model is employed to describe the thermomechanical behavior of the SMA actuators. The robot dynamics is described by considering a rigid body system connected to the two origami wheels. Under these assumptions, the robot dynamical model is represented by a 4-degree of freedom system. The yaw rotation, that promotes the route change, is promoted by the origami radius variation. Numerical simulations related to operational conditions are carried out considering different operational conditions represented by distinct thermal and mechanical loads. Results show situations where different external stimulus can promote interesting nonlinear dynamical responses including chaos, transient chaos and synchronization.