This paper presents a simple algebraic method to estimate the pose of a camera relative to a planar target from n ≥ 4 reference points with known coordinates in the target frame and their corresponding bearing measurements in the camera frame. The proposed approach follows a hierarchical structure; first, the unit vector normal to the target plane is determined, followed by the camera’s position vector, its distance to the target plane, and finally, the full orientation. To improve the method’s robustness to measurement noise, an averaging methodology is introduced to refine the estimation of the target’s normal direction. The accuracy and robustness of the approach are validated through extensive experiments.

This paper revisits the problem of estimating the attitude, linear velocity and depth of an IMU-Camera with respect to a planar target. The considered solution relies on the measurement of the optical flow (extracted from the continuous homography) complemented with gyrometer and accelerometer measurements. The proposed deterministic observer is accompanied with an observability analysis that points out camera's motion excitation conditions whose satisfaction grants stability of the observer and convergence of the estimation errors to zero. The performance of the observer is illustrated by performing experiments on a testbed IMU-Camera system.

A control approach for a class of underactuated vehicles with the objective of stabilizing reference trajectories either in velocity or position is proposed. The basic modeling assumption is that the vehicle is propulsed 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 whose shape induces lift forces with limited amplitude and which are subjected to an external force field (e.g. gravity), as in the case of VTOL vehicles. The interactions of the vehicle with the surrounding fluid are often difficult to model precisely and they may significantly perturb its motion. Some 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 vehicle are reported.

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.

The paper addresses the problem of controlling the posture of a nonholonomic mobile robot via sensor-based target tracking. The control technique here considered is adapted from the transverse function approach with sensory signals used to calculate an estimate of the relative pose of the robot with respect to the target. An analysis of stability and robustness w.r.t. pose estimation errors is presented and the overall control performance is tested via simulation and experimentation on a unicycle-type mobile robot equipped with a camera

The authors study a certain class of stabilizing laws for a flexible arm either in torsion or in compression. They first choose a discrete-model of this arm, and then the arm is modeled by a classical partial differential equation. A sufficient condition for the stability of both closed-loop systems is given. This sufficient condition requires that the gain of the control law act positively on the eigenfunctions of the autonomous system.>

A preliminary study of the problem of the feedback control of mobile robots is presented. The robot considered is a two-wheel-driven nonholonomic cart. Despite the controllability of the system, pure state feedback stabilization of the cart's configuration around a given terminal configuration is not possible. However, feedback stabilization of the position of any point of the cart is possible. Extension to the problem of trajectory tracking in Cartesian space is then considered, and it is shown that stabilization of the cart's configuration around the configuration of a virtual reference cart becomes possible as long as the reference cart keeps moving. Several simple control laws are proposed, and simulation results are given. Connections with the path planning problem are pointed out.>

When a nonlinear system is not stabilizable by a smooth state feedback, it is common to think of the discontinuous feedback as being the alternative. However, another possibility is to consider a smooth time-varying feedback in which the independent time index plays the role of an extra variable. This possibility is illustrated in the case of two degrees-of-freedom nonholonomic wheeled mobile robot for which the globally stabilizing smooth feedback is derived.>

In this paper, an attempt is made to analyze the fixed point error performance of the normalized ladder algorithm for autoregressive system identification, assuming rounding arithmetic. The paper contains two main results; i) A simplified theoretical expression for predicting the average bias in the estimated reflection coefficients at any stage, and ii) a recursive relation for the average error, arising from finite precision arithmetic, in the squared residuals. The second result illustrates how the errors made in one stage affect the errors in the succeeding stages. Simulations are performed to check the theorical predictions.