We introduce flat systems, which are equivalent to linear ones via a special type of feedback called endogenous. Their physical properties are subsumed by a linearizing output and they might be regarded as providing another nonlinear extension of Kalman's controllability. The distance to flatness is measured by a non-negative integer, the defect. We utilize differential algebra where flatness- and defect are best defined without distinguishing between input, state, output and other variables. Many realistic classes of examples are flat. We treat two popular ones: the crane and the car with n trailers, the motion planning of which is obtained via elementary properties of plane curves. The three non-flat examples, the simple, double and variable length pendulums, are borrowed from non-linear physics. A high frequency control strategy is proposed such that the averaged systems become flat.

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Flatness and defect of non-linear systems: introductory theory and examples

to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).

This manuscript describes a unique class of locomotive robot: A soft robot, composed exclusively of soft materials (elastomeric polymers), which is inspired by animals (e.g., squid, starfish, worms) that do not have hard internal skeletons. Soft lithography was used to fabricate a pneumatically actuated robot capable of sophisticated locomotion (e.g., fluid movement of limbs and multiple gaits). This robot is quadrupedal; it uses no sensors, only five actuators, and a simple pneumatic valving system that operates at low pressures (< 10 psi). A combination of crawling and undulation gaits allowed this robot to navigate a difficult obstacle. This demonstration illustrates an advantage of soft robotics: They are systems in which simple types of actuation produce complex motion.

Multigait soft robot

Self-driving vehicles are a maturing technology with the potential to reshape mobility by enhancing the safety, accessibility, efficiency, and convenience of automotive transportation. Safety-critical tasks that must be executed by a self-driving vehicle include planning of motions through a dynamic environment shared with other vehicles and pedestrians, and their robust executions via feedback control. The objective of this paper is to survey the current state of the art on planning and control algorithms with particular regard to the urban setting. A selection of proposed techniques is reviewed along with a discussion of their effectiveness. The surveyed approaches differ in the vehicle mobility model used, in assumptions on the structure of the environment, and in computational requirements. The side by side comparison presented in this survey helps to gain insight into the strengths and limitations of the reviewed approaches and assists with system level design choices.

A Survey of Motion Planning and Control Techniques for Self-Driving Urban Vehicles

Provides a summary of recent developments in control of nonholonomic systems. The published literature has grown enormously during the last six years, and it is now possible to give a tutorial presentation of many of these developments. The objective of this article is to provide a unified and accessible presentation, placing the various models, problem formulations, approaches, and results into a proper context. It is hoped that this overview will provide a good introduction to the subject for nonspecialists in the field, while perhaps providing specialists with a better perspective of the field as a whole. The paper is organized as follows: introduction to nonholonomic control systems and where they arise in applications, classification of models of nonholonomic control systems, control problem formulations, motion planning results, stabilization results, and current and future research topics.

Developments in nonholonomic control problems

Most autonomous driving architectures separate planning and control phases in different layers, even though both problems are intrinsically related Due to limitations on the available computational power, their levels of abstraction and modeling differ; in particular, vehicle dynamics are often highly simplified at the planning phase, which may lead to inconsistency between the two layers In this paper, we study the kinematic bicycle model, which is often used for trajectory planning, and compare its results to a 9 degrees of freedom model Modeling errors and limitations of the kinematic bicycle model are highlighted Lastly, this paper proposes a simple and efficient consistency criterion in order to validate the use of this model for planning purposes

The kinematic bicycle model: A consistent model for planning feasible trajectories for autonomous vehicles?

The dynamics of non holonomic mechanical system are described by the classical Euler-Lagrange equations subjected to a set of non-integrable constraints. Non holonomic systems are strongly accessible whatever the structure of the constraints. They cannot be asymptotically stabilized by a smooth pure state feedback. However smooth state feedback control laws can be designed which guarantee the global marginal stability of non holonomic systems.

Controllability and state feedback stabilizability of non holonomic mechanical systems

Smooth time-varying laws can solve the stabilization problem of nonholonomic mechanical systems. The authors show that by means of dynamic state feedback, it is possible for three-wheeled mobile robots to track arbitrary fast trajectories not reduced to equilibrium points. Dynamical modeling of nonholonomic mechanical systems for the case of three-wheeled mobile robots is considered. Dynamic feedback allows solution of the tracking problem for an omnidirectional mobile robot with less motors than degrees of freedom. This is possible by choosing output functions depending on the mass repartition of the robot. >

Dynamic feedback linearization of nonholonomic wheeled mobile robots

This paper deals with the stabilization of a rotating body-beam system with torque control. The system we consider is the one studied by Baillieul and Levi (1987). Xu and Baillieul proved (1993) that, for any constant angular velocity smaller than a critical one, this system can be stabilized by means of a feedback torque control law if there is damping. We prove that this result also holds if there is no damping.

Stabilization of a rotating body beam without damping

A general dynamical model is derived for three-wheel mobile robots with nonholonomic constraints by using a Lagrange formulation and differential geometry. It is shown that a static state feedback allows one to reduce the dynamics of the system to a form in which stabilizing input-output linearizing control is possible. >

Brigitte d'Andréa-Novel

Papers

The kinematic bicycle model: A consistent model for planning feasible trajectories for autonomous vehicles?

Controllability and state feedback stabilizability of non holonomic mechanical systems

Dynamic feedback linearization of nonholonomic wheeled mobile robots

Stabilization of a rotating body beam without damping

Modelling and control of non-holonomic wheeled mobile robots