Simultaneous stabilization and trajectory tracking of underactuated mechanical systems with included actuators dynamics

Abstract

The paper deals with a novel control algorithm for simultaneous stabilization and trajectory tracking of underactuated nonlinear mechanical systems (UNMS) with included actuators dynamics. Simultaneous stabilization and trajectory tracking refer to arbitrary chosen actuated and unactuated degrees of freedom (DOF) of the system. The proposed control approach can be applied both to the second-order nonholonomic systems and the systems with input coupling, while a general model of actuators dynamics includes electrical, pneumatic, and hydraulic drives. Control law is based on linear combination of two control signals, where the first signal is designed to separately control only actuated DOF, and second to separately control only unactuated DOF. Simulation example of rotational inverted pendulum driven by electrical DC motor is presented, showing the effectiveness of the proposed approach.

Stabilization and trajectory tracking control for underactuated quadrotor helicopter subject to wind-gust disturbance

“…Hence, the control of a quadrotor becomes quite a complex and difficult mainly due to its underactuated properties and nonlinearities. In literature, different studies have addressed modeling and control of underactuated nonlinear systems and variety of approaches are employed (Zilic et al 2013;Yih 2013;Xu et al 2012;Yang & Yang 2012;Yu et al 2012).…”

Universal Practical Tracking Control of a Planar Underactuated Vehicle

“…Unified/universal control schemes have been proposed in recent years to simultaneously achieve both the fixed-point stabilization and the trajectory tracking for second-order nonholonomic systems [5,6,[22][23][24] and other nonholonomic ones [25][26][27][28]. A negative result was provided in [29] revealing that the feedback laws, able to asymptotically stabilize any feasible reference trajectory, do not exist for nonholonomic systems, which is accordance with the results in [6,22,25,26] where the derived asymptotic tracking laws can only track the specific restricted feasible trajectories (a trajectory is called feasible if it can be generated by the control system dynamics; otherwise, it is non-feasible [28]).…”

“…Control of second‐order nonholonomic systems, such as the planar underactuated vehicle considered in this paper, is quite challenging and significant, and has received increasing interest over more than two decades. In real engineering, second‐order nonholonomic systems may arise from several mechanical models, such as gravity‐assisted underactuated manipulators , planar rotational‐rotational‐rotational (RRR) manipulators (with the last joint un‐actuated) , planar prismatic‐prismatic‐rotational (PPR) manipulators (with the rotational joint un‐actuated) , rotational inverted pendulums , and underactuated surface ships . Second‐order nonholonomic constraints restrict the generalized accelerations and cannot be integrated to first‐order nonholonomic ones, rendering the techniques so far developed for first‐order nonholonomic systems non‐applicable.…”

“…Several approaches have been developed solving the universal practical tracking control problem for second‐order nonholonomic systems. In , based on the linear combination of two control signals, a control algorithm was presented for second‐order nonholonomic underactuated systems. In , Morin et al proposed a systematic transverse function (TF) approach for a class of underactuated mechanical systems.…”

“…By applying the TF approach and back‐stepping technique, Do derived a smooth control law in to achieve practical stabilization of arbitrary reference trajectories for underactuated ships. However, the stability analysis was not given in . The control law in was local and not suitable for large initial tracking errors.…”