Philippe Souères

Shortest paths synthesis for a car-like robot

This paper deals with the complete characterization of the shortest paths for a car-like robot. Previous works have shown that the search for a shortest path may be limited to a simple family of trajectories. Our work completes this study by providing a way to select inside this family an optimal path to link any two configurations. We combine the necessary conditions given by Pontryagins maximum principle with a geometric reasoning. This approach enables us to complete the local information with a global analysis of different wave fronts. We construct a partition of the configuration space in regions where the same kind of path is optimal to reach the origin. In other words, we determine a shortest path synthesis by providing, at each point, an optimal control law to steer the robot to the origin.

The Autonomous Blimp Project of LAAS-CNRS: Achievements in Flight Control and Terrain Mapping

In this paper we provide a progress report of the LAAS-CNRS project of autonomous blimp robot development, in the context of field robotics. Hardware developments aimed at designing a generic and versatile experimental platform are first presented. On this base, the flight control and terrain mapping issues, which constitute the main thrust of the research work, are presented in two parts. The first part, devoted to the automatic control study, is based on a rigorous modeling of the airship dynamics. Considering the decoupling of the lateral and longitudinal dynamics, several flight phases are identified for which appropriate control strategies are proposed. The description focuses on the lateral steady navigation. In the second part of the paper, we present work on terrain mapping with lowaltitude stereovision. A simultaneous localization and map building approach based on an extended Kalman filter is depicted, with details on the identification of the various errors involved in the process. Experimental results show that positioning in the three-dimensional space with a centimeter accuracy can be achieved, thus allowing the possibility to build high-resolution digital elevation maps.

Position control of a ducted fan VTOL UAV in crosswind

This paper describes a control strategy to stabilize the position of a vertical takeoff and landing (VTOL) unmanned aerial vehicle (UAV) in crosswind despite unknown aerodynamic effects. The proposed approach overcomes the problem of gyroscopic coupling by taking advantage of both the structure of the thrust mechanism, which is made of two counter rotating propellers, and the control strategy which involves a decoupling of the yaw rate dynamics from the rest of the system dynamics. The controller is designed by means of backstepping techniques that allow the stabilization of the vehicles position while online estimating the unknown aerodynamic effects.

Hovering flight stabilization in wind gusts for ducted fan UAV

This paper describes a control strategy to stabilize the position of a micro air vehicle in wind gusts despite unknown aerodynamic efforts. The proposed approach allows us to overcome the problem of gyroscopic coupling by taking advantage from both the structure of the thrust mechanism, which is made of two counter rotating propellers, and the control strategy which involves a decoupling of the yaw rate dynamics from the rest of the system dynamics. The controller is designed by means of backstepping techniques allowing the stabilization of the vehicles position while on-line estimating the unknown aerodynamic efforts.

Nonlinear attitude and gyroscope's bias estimation for a VTOL UAV

This paper addresses the problem of attitude and heading restitution for a VTOL UAV (Vertical Take Off and Landing Unmanned Aerial Vehicle). In a first step, we propose an observation strategy to restore the attitude starting from a measure of the orientation matrix and angular rate readings polluted by an unknown bias vector. In the second step, we detail the implementation of this algorithm in the HoverEye, a ducted fan VTOL UAV developed by Bertin Technologies, equipped with an inertial measurement unit (IMU) and magnetometers. A measured orientation matrix is calculated from the gravity and the earths magnetic field. Then, an estimated orientation is built by integration of gyroscopic readings, and corrected by the measured ones. The proposed observer, directly designed in the special orthogonal group SO(3), is as efficient as classical Extended Kalman Filtering based observers, but easier to implement in real time. Experiments achieved on the HoverEye illustrate the concept.

Automatic airship control involving backstepping techniques

This paper deals with the autonomous airship control in a case of very low perturbations. A flight decomposition allowing one to define canonical navigation phases from take-off to landing is proposed. For each phase a reduced model is determined and a controller is designed on the base of backstepping techniques. This approach allows one to consider the kinematic and dynamic requirement separately. Due to the decoupling properties, an equilibrium state is reached at the end of each flight phase, allowing one to model easily the transition between them. Simulations of the different controllers are presented for a realistic model of blimp including aerostatic, dynamic and aerodynamic effects.

Robust path following control for wheeled robots via sliding mode techniques

The techniques of filtering and merging data coming from several sensors allow to localize a mobile robot in its environment with a precision which can be evaluated. However, as the localization error cannot be neglected, the design of robust closed-loop controller for wheeled robots constitutes a difficult problem. We present here a path following feedback controller robust with respect to localization error. The model is a dynamic extension of the usual kinematic model of a car, in the sense that the path curvature error is considered as a new state variable. The control inputs are respectively the linear velocity and the derivative of the curvature. We determine a variable structure control with sliding mode to stabilize the vehicles motion around the reference path in the nominal case. Then, we prove that the system remains stable when the state feedback is computed from the estimated values instead of the exact ones. We show that the regulation error is contained in a compact attractive domain when the system has reached its steady state. From this domain, one can easily compute a security margin to guarantee obstacle avoidance during the path following process. Experimental results are presented at the end of the paper.

A Geometric Algorithm to Compute Time-Optimal Trajectories for a Bidirectional Steered Robot

This paper addresses the problem of determining time-optimal trajectories, between two specified configurations, for a nonholonomic bidirectional steered robot. It presents an original geometric reasoning that is grounded on Pontryagins maximum principle, which provides analytical solutions of this problem in a visually clear way and allows for an effective algorithm to compute the exact optimal trajectories between two arbitrarily specified configurations. The proposed geometric reasoning is based on the analysis of the switching functions of the optimal controller and the definition of a switching vector from which it is able to determine a unit vector rotating along a unit circle of an appropriate coordinate system. It is shown that simple geometric rules are sufficient to determine all possible rotations of this unit vector, from which the time-optimal trajectories can be uniquely determined. The proposed algorithm, which is based on this geometric reasoning, is guaranteed to be complete and has a low computational cost. Moreover, the proposed geometric representation provides an interesting insight into the structure of this class of nonholonomic systems, thereby offering a model for further studies.

A hierarchical control strategy for the autonomous navigation of a ducted fan flying robot

This paper describes a control strategy to stabilize the position of a vertical takeoff and landing (VTOL) unmanned aerial vehicle (UAV) in wind gusts. The proposed approach takes advantage of the cascade structure of the system to design a hierarchical controller. The idea is to separate the controller in a high level controller devoted to position control and a low level controller devoted to stabilization and attitude control. Both controllers are designed by means of backstepping techniques that allow the stabilization of the vehicles position while on-line estimation of the unknown aerodynamic forces. The global stability of the connected system is proven, and simulations as well as experimental results are presented

Attitude and gyro bias estimation for a flying UAV

In this paper, a nonlinear complimentary filter (x-estimator) is presented to estimate the attitude of a UAV (unmanned aerial vehicle). The measurements are taken from a low-cost SMU (inertial measurement unit) which consists of 3-axis accelerometers and 3-axis gyroscopes. The gyro bias are estimated online. A second nonlinear complimentary filter (z-estimator) is also designed, it combines 3-axis gyroscope readings with 3-axis magnetometer measurements. From the proposed estimators, the full rotation matrix R will be retrieved. Both estimators use the fact that the orientation matrix, evolving on SO(3), is not locally parameterized and thus could be used to describe any kind of 3D motion. Convergence of the two observers is theoretically proved and simulations as well as experiments are conducted on a real platform in hovering flight conditions.