Closed Loop Control of a Gravity-assisted Underactuated Snake Robot with Application to Aircraft Wing-Box Assembly

Stable, nonlinear closed-loop control of a gravityassisted underactuated robot arm with 2nd order non-holonomic constraints is presented in this paper. The joints of the hyper articulated arm have no dedicated actuators, but are activated with gravity. By tilting the base link appropriately, the gravitational torque drives the unactuated links to a desired angular position. With simple locking mechanisms, the hyper articulated arm can change its configuration using only one actuator at the base. This underactuated arm design was motivated by the need for a compact snake-like robot that can go into aircraft wings and perform assembly operations using heavy end-effecters. The dynamics of the unactuated links are essentially 2nd order nonholonomic constraints, for which there are no general methods for designing closed loop control. We propose an algorithm for positioning the links of an n-link robot arm inside an aircraft wing-box. This is accomplished by sequentially applying a closed loop point-to-point control scheme to the unactuated links. We synthesize a Lyapunov function to prove the convergence of this control scheme. The Lyapunov function also provides us with lower bounds on the domain of convergence of the control law. The control algorithm is implemented on a prototype 3-link system. Finally, we provide some experimental results to demonstrate the efficacy of the control scheme.