Differential Flatness and Its Application to Snake Robots

Abstract

Snake robot is a complicated dynamical system comprised of large number of inputs and generalized coordinates. Moreover, the dynamical equations of motion are highly nonlinear and coupled. The aforementioned complexities make path planning and control system design particularly difficult for this kind of system. The control approaches presented in Chaps. 1, 2, 3 and 4 confirm this observation as they employ a multi-layer control methodology to compute the torque input which is not directly mapped to the output space trajectory of the robot. Furthermore, dynamically capable path planning is still beyond the reach for snake robots. Hence, to address these issues and go beyond the conventional approach, it is required to map the control inputs directly to the output variables. This can be accomplished by adopting a differential-flatness-based approach. Differential flatness is a method of transforming a nonlinear system into a flat system, i.e. a corresponding system of flat outputs by establishing a diffeomorphic relation between the states and the outputs [1, 2, 3]. The flat outputs chosen should be either measurable or be computed from the measured variables. Therefore, trajectories designed as functions of flat outputs become convenient and the tracking control problem becomes simpler as well.