Null-Space-Avoidance-Based Orientation Control Framework for Underactuated, Tail-Inspired Robotic Systems in Flight Phase

In this letter, we propose a unified framework to address underactuated orientation control problems of the tailed robot in flight phase through a 2 DoFs actuated tail. We approach the underactuated control problem from the perspective of an inverse problem of an over-constrained Jacobian matrix. The resulting non-trivial null space can nullify the kinematics control by attracting the system into itself. For this reason, we propose a novel and intuitive null space avoidance control that can always drive the system to states that is perpendicular to its null space, while reaching the desired orientation. Unlike the classic feedforward trajectory tracking approach for nonholonomic systems, the null-space-avoidance-based framework is a real time, feedback control approach with disturbance rejection capability. We verify the generality of the framework in two typical maneuvers:
Body-Only Reorientation
and
Body-Tail Stabilization
. Both the results of the kinematics-level and dynamics-level simulation show that the proposed controllers can track the desired orientation and avoid the null space simultaneously in a free falling condition. Experiments of the body-tail stabilization demonstrate the effectiveness of the proposed framework on a dynamical platform.