Underactuated Dynamic System Research Articles

Cascaded VFO Control for Non-Standard N-Trailer Robots

Articulated mobile robots consisting of a tractor and passively off-hooked trailers belong to a class of highly nonlinear, nonholonomic, structurally unstable, differentially non-flat, and underactuated dynamic systems. Due to the mentioned properties of their kinematics, motion control problems related to N-trailer robots (N-trailers) are non-trivial and challenging. Cascaded control strategy presented in this paper provides unified solution to the set-point and trajectory tracking control tasks for articulated robots equipped with arbitrary number of passively off-axle hitched trailers. Practically useful features of the proposed controller come from its high scalability and from application of the Vector-Field-Orientation (VFO) controller in the outer loop, which ensures fast errors convergence and simplicity of control implementation and tuning. Control input limitations of the robot are directly taken into account by utilization of a simple velocity scaling procedure which preserves an instantaneous motion curvature of a tractor. Description and theoretical substantiation of the concept are followed by the results of experimental validation tests conducted with usage of a 3-trailer semi-autonomous vehicle.

Differentially Flat Design of a Closed-Chain Planar Underactuated $\hbox{2}$ -DOF System

This paper demonstrates that for certain choices of mass distribution and addition of springs, an underactuated two-degree-of-freedom (2-DOF) \bm PRRRP system is static feedback linearizable, i.e., differentially flat as well. This paper is original and provides a ground breaking study in underactuated dynamical systems.

A comparison study of nonlinear control techniques for the RTAC system

In this paper, we implement the recently developed energy- and entropy-based hybrid control framework for stabilization of Lagrangian systems on the experimental testbed of the Rotational/Translational Proof-Mass Actuator (RTAC) system. In addition, on the same experimental platform, we implement the sliding mode control framework for stabilization of underactuated dynamical systems and compare the performances of all three controllers. The concept of an energy-based hybrid controller involves a hybrid controller that exploits the feature that the states of the dynamic controller may be reset to enhance the overall energy dissipation in the closed-loop system. We give a detailed description of the hardware layout for the testbed and present the experimental results. The real-time data indicate that the energy- and entropy-based hybrid controllers result in almost the same closed-loop system behavior with the same control effort. However, hybrid controllers use significantly less control effort and stabilize the system in a shorter period of time than the sliding mode controller.

Closed-loop tracking control of a pendulum-driven cart-pole underactuated system

This paper investigates a new modelling and control issue: the tracking control problem of underactuated dynamic systems by using a special example – a pendulum-driven cart-pole system. A dynamic model of a pendulum-driven cart-pole system is firstly presented. Then, a six-step motion strategy of the pendulum-driven cart-pole system is proposed. After that, a desired profile of the pendulum joint velocity is developed based on the proposed six-step motion strategy. The desired joint position and acceleration can be computed using the desired joint velocity profile. A closed-loop control approach is proposed using the partial feedback linearization technique. Finally, extensive simulation studies are conducted to demonstrate the proposed approaches.

Analysis and Control of a Capsubot

In this paper, a special underactuated system – a capsule robot, also called capsubot, is studied to investigate the tracking control issue of underactuated dynamic systems. A seven-step motion strategy of the capsubot is proposed. A trajectory profile is designed based on the proposed motion strategy. By using this profile, the capsubot can move effectively in a desired direction. Three control approaches are investigated: an open-loop control approach, a closed-loop control approach using partial feedback linearization technique, and a simple switch control approach. Extensive simulation studies are conducted to demonstrate the proposed approaches.

Image based visual servo control for a class of aerial robotic systems

An image-based strategy for visual servo control of a class of dynamic systems is proposed. The class of systems considered includes dynamic models of unmanned aerial vehicles capable of quasi-stationary flight (hover and near hover flight). The control strategy exploits passivity-like properties of the dynamic model to derive a Lyapunov control algorithm using backstepping techniques. The paper extends earlier work (Hamel, T., & Mahony, R. (2002). Visual servoing of an under-actuated dynamic rigid-body system: An image based approach. IEEE Transactions on Robotics and Automation, 18(2), 187–198) where partial pose information was used in the construction of the visual error. In this paper the visual error is defined purely in terms of the image features derived from the camera input. Local exponential stability of the system is proved. An estimate of the basin of attraction for the closed-loop system is provided.

Minimum Control-Switch Motions for the Snakeboard: A Case Study in Kinematically Controllable Underactuated Systems

We study the problem of computing an exact motion plan for the snakeboard, an underactuated system subject to nonholonomic constraints, by exploiting its kinematic controllability properties and its decoupling vector fields. Decoupling vector fields allow us to plan motions for the underactuated dynamic system as if it were kinematic, and rest-to-rest paths are the concatenation of integral curves of the decoupling vector fields. These paths can then be time-scaled according to actuator limits to yield fast trajectories. Switches between decoupling vector fields must occur at zero velocity, so, to find fast trajectories, we wish to find paths minimizing the number of switches. In this paper, we solve the minimum-switch path-planning problem for the snakeboard. We consider two problems: 1) finding motion plans achieving a desired position and orientation of the body of the snakeboard and 2) the full problem of motion planning for all five configuration variables of the snakeboard. The first problem is solvable in closed form by geometric considerations, while the second problem is solved by a numerical approach with guaranteed convergence. We present a complete characterization of the snakeboard's minimum-switch paths.

Visual servoing of an under-actuated dynamic rigid-body system: an image-based approach

A new image-based control strategy for visual servoing of a class of under-actuated rigid body systems is presented. The proposed control design applies to eye-in-hand systems where the camera is fixed to a rigid body with actuated dynamics. The control design is motivated by a theoretical analysis of the dynamic equations of motion of a rigid body and exploits passivity-like properties of these dynamics to derive a Lyapunov control algorithm using robust backstepping techniques. The proposed control is novel in considering the full dynamic system incorporating all degrees of freedom (albeit for a restricted class of dynamics) and in not requiring measurement of the relative depths of the observed image points. A motivating application is the stabilization of a scale model autonomous helicopter over a marked landing pad.

Kinematic controllability for decoupled trajectory planning in underactuated mechanical systems

We introduce the notion of kinematic controllability for second-order underactuated mechanical systems. For systems satisfying this property, the problem of planning fast collision-free trajectories between zero velocity states can be decoupled into the computationally simpler problems of path planning for a kinematic system followed by time-optimal time scaling. While this approach is well known for fully actuated systems, until now there has been no way to apply it to underactuated dynamic systems. The results in this paper form the basis for efficient collision-free trajectory planning for a class of underactuated mechanical systems including manipulators and vehicles in space and underwater environments.