A ROS-based swing up control and stabilization of the Pendubot using virtual holonomic constraints

Evaluation of Linearization Methods for Control of the Pendubot

“…This section provides simulation results of implementing control method (6) to the system in a form of (11), and moreover some preliminary experimental results. The aim of presented simulations is to check the performance of the controller applied for the stabilization of Pendubot in the upright equilibrium pose.…”

“…Since the control approach discussed in Section 3.1 does not guarantee stabilization of the closed-loop system at the chosen equilibrium the overall control strategy based on a hybrid approach (6) will be used. For this purpose, firstly a set of feasible initial conditions for which the controller (20) applied for system (11) brings the robot state near the equilibrium point should be obtained.…”

“…Secondly, recalling that the linear approximation of dynamics (11) established at the equilibrium point provides a controllable linear system [18], it is possible to locally stabilize (11) at this point using the following linear feedback…”

“…Recently, an extended state observer based active disturbance rejection control scheme was applied to the Pendubot system for a trajectory tracking tasks in the presence of uncertain dynamics [9]. On the other hand, the stabilization task near the equilibrium pose are mainly supported by linear controllers including LQR-based feedbacks [5,10,11].…”

Orbital Stabilization of Point-to-Point Maneuvers in Underactuated Mechanical Systems

“…For the purpose we consider in this paper, however, namely the design of a continuous (orbitally) stabilizing feedback controller for PtP motions with a known maneuver, one must of course also take into consideration the equilibria located at the boundaries of the motion. On the one hand, this directly excludes regular transverse coordinates-based methods such as [4,12,13], which would then require some form of control switching and/or orbit jumping à la [15,16]. On the other hand, the ideas proposed in regards to maneuver regulations in [1,5] can, as we will see, to some extent be modified as to also handle the equilibria, but suffers from other shortcomings: 1) the choice of projection operator is strictly determined by the tracking controller, thus excluding simpler operators, e.g., operators only depending on the configuration variables; while most importantly, 2) the restriction of constant feedback gains greatly limits its applicability to stabilize (not necessarily PtP) motions of both UMSs and nonlinear systems in general.…”