Pascal Morin

A Control Approach for Thrust-Propelled Underactuated Vehicles and its Application to VTOL Drones

A control approach is proposed for a class of underactuated vehicles in order to stabilize reference trajectories either in thrust direction, velocity, or position. The basic modeling assumption is that the vehicle is pro-pulsed via a thrust force along a single body-fixed direction and that it has full torque actuation for attitude control (i.e., a typical actuation structure for aircrafts, vertical take-off and landing (VTOL) vehicles, submarines, etc.). Additional assumptions on the external forces applied to the vehicle are also introduced for the sake of control design and stability analyses. They are best satisfied for vehicles which are subjected to an external force field (e.g., gravity) and whose shape induces lift forces with limited amplitude, unlike airplanes but as in the case of many VTOL drones. The interactions of the vehicle with the surrounding fluid are often difficult to model precisely whereas they may significantly influence and perturb its motion. By using a standard Lyapunov-based approach, novel nonlinear feedback control laws are proposed to compensate for modeling errors and perform robustly against such perturbations. Simulation results illustrating these properties on a realistic model of a VTOL drone subjected to wind gusts are reported.

Practical stabilization of driftless systems on Lie groups: the transverse function approach

A general control design approach for the stabilization of controllable driftless nonlinear systems on finite dimensional Lie groups is presented. The approach is based on the concept of bounded transverse functions, the existence of which is equivalent to the systems controllability. Its outcome is the practical stabilization of any trajectory, i.e., not necessarily a solution of the control system, in the state-space. The possibility of applying the approach to an arbitrary controllable smooth driftless system follows in turn from the fact that any controllable homogeneous approximation of this system can be lifted (via a dynamic extension) to a system on a Lie group. Illustrative examples are given.

Time-varying exponential stabilization of a rigid spacecraft with two control torques

Rigid body models with two controls cannot be locally asymptotically stabilized by continuous feedbacks which are functions of the state only. This impossibility no longer holds when the feedback is also a function of time, and time-varying asymptotically stabilizing feedbacks have already been proposed. However, due to the smoothness of the feedbacks, the convergence rate is only polynomial. In this paper, exponential convergence is obtained by considering time-varying feedbacks which are only continuous.

Introduction to feedback control of underactuated VTOLvehicles: A review of basic control design ideas and principles

This article is an introduction to feedback control design for a family of robotic aerial vehicles with vertical take-off and landing (VTOL) capabilities such as quadrotors, ducted-fan tail-sitters, and helicopters. Potential applications for such devices, like surveillance, monitoring, or mapping, are varied and numerous. For these applications to emerge, motion control algorithms that guarantee a good amount of robustness against state measurement/ estimation errors and unmodeled dynamics like, for example, aerodynamic perturbations, are needed. The feedback control methods considered here range from basic linear control schemes to more elaborate nonlinear control solutions. The modeling of the dynamics of these systems is first recalled and discussed. Then several control algorithms are presented and commented upon in relation to implementation issues and various operating modes encountered in practice, from teleoperated to fully autonomous flight. Particular attention is paid to the incorporation of integral-like control actions, often overlooked in nonlinear control studies despite their practical importance to render the control performance more robust with respect to unmodeled or poorly estimated additive perturbations.

Control of Nonholonomic Mobile Robots Based on the Transverse Function Approach

The problem of stabilizing reference trajectories - also referred to as the trajectory tracking problem - for nonholonomic mobile robots is revisited. Theoretical difficulties and impossibilities that set inevitable limits to what is achievable with feedback control are surveyed, and properties of kinematic control models are recalled, with a focus on controllable driftless systems that are invariant on a Lie group. This geometric framework takes advantage of ubiquitous symmetry properties involved in the motion of mechanical bodies. The transverse function approach, a control design method developed by the authors for the past few years, is reviewed. A salient feature of this approach, which singles it out of the abundant literature devoted to the subject, is the obtention of feedback laws that unconditionally achieve the practical stabilization of arbitrary reference trajectories, including fixed points and nonadmissible trajectories. This property is complemented with novel results showing how the more common property of asymptotic stabilization of a large class of admissible trajectories can also be granted with this type of control. Application to unicycle-type and car-like vehicles is presented and illustrated via simulations. Complementary issues (transient maneuvers monitoring, extensions of the approach to systems that are not invariant on a Lie group, etc.) are also addressed with the concern of practicality.

A Characterization of the Lie Algebra Rank Condition by Transverse Periodic Functions

The Lie algebra rank condition plays a central role in nonlinear systems control theory. The present paper establishes that the satisfaction of this condition by a set of smooth control vector fields is equivalent to the existence of smooth transverse periodic functions. The proof here enclosed is constructive and provides an explicit method for the synthesis of such functions.

Application of backstepping techniques to the time-varying exponential stabilisation of chained form systems

It is known that the kinematic model of several nonholonomic systems can be converted into a chained form control system. Asymptotic stabilisation of any equilibrium point of this system cannot be achieved by means of a continuous pure state feedback, but can be obtained by using a time-varying continuous feedback [26]. In the present paper, a backstepping technique is used to derive explicit time-varying feedbacks that ensure exponential stability of the closed-loop system. Two classes of control laws are proposed, with one of them involving a dynamic extension of the original chained system. As in other recent studies on the same topic, exponential convergence is obtained by using the properties associated with homogeneous systems. The control laws so obtained are continuous in both the state and time variables. A complementary and novel feature of the proposed control design technique lies in the estimation ofa lowerbound ofthe asymptotic rate of convergence as a function of a reduced set of control parameters which is independent ofthe systems dimension. Moreover, the fact that this lowerbound may take any positive value indicates that any prespecified exponential rate of convergence can be achieved via a suitable choice ofthe control parameters.

Time-varying exponential stabilization of the attitude of a rigid spacecraft with two controls

Rigid body models with two controls cannot be locally asymptotically stabilized by continuous feedback which are functions of the state only. However, explicit smooth time-varying feedback which locally asymptotically stabilize the attitude of a rigid spacecraft have previously been proposed by the authors (1995). Due to the smoothness of the control law, the stabilization is not exponential and the asymptotical convergence rate to the desired equilibrium is only polynomial in the worst case. Nevertheless, exponential convergence can be obtained by considering time-varying feedback which are only continuous at the equilibrium. This paper proposes explicit feedback control laws of this type.

A Framework for the Control of Nonholonomic Mobile Manipulators

A general framework for the feedback control of mobile manipulators is proposed. Its main originality lies in its capacity to address in a unified manner both cases of omnidirectional and nonholonomic mobile platforms. It also allows for the execution of the desired manipulation task without the manipulator colliding into its joint limits, whenever these two objectives are compatible. This is obtained without having to rely upon trajectory planning. In the nonholonomic case this feature, which is not demonstrated for previous feedback control schemes proposed in the literature, is instrumental for performing reflex maneuvers automatically. It relies upon the concept, used in the control design, of a companion omnidirectional frame associated with the physical platform. The generality of the approach can be appreciated from its applicability to various nonholonomic platforms, for example unicycle-type and car-like.

Trajectory tracking for non-holonomic vehicles: overview and case study

The paper provides an overview of trajectory tracking problems for non-holonomic vehicles. Several control objectives are reviewed and discussed with the viewpoints of control design and robotics applications. In order to illustrate and compare different approaches, explicit control laws and simulation results are provided for a car-like vehicle.