T. Hamel

• Professor
• Professor (Full) at University Côte d'Azur

This paper addresses accurate pose estimation (position, velocity, and orientation) for a rigid body using a combination of generic inertial-frame and/or body-frame measurements along with an Inertial Measurement Unit (IMU). By embedding the original state space, $\so \times \R^3 \times \R^3$, within the higher-dimensional Lie group $\sefive$, we r...

An approach to tackle the classical problem of homography decomposition is presented. The key novelty lies in the design of two deterministic Riccati observers tailored specifically the homography decomposition problem, departing from the conventional frame-by-frame solving approach employed in traditional algebraic methods. By leveraging the tempo...

This paper introduces DAF (Dissipative Avoidance Feedback), a novel approach for autonomous robot navigation in unknown, obstacle-filled environments with second-order dynamics. Unlike traditional APF (Artificial Potential Field) methods, which rely on repulsive forces based solely on position, DAF employs a dissipative feedback mechanism that adju...

This paper proposes an observer-based formation tracking control approach for multi-vehicle systems with second-order motion dynamics, assuming that vehicles' relative or global position and velocity measurements are unavailable. It is assumed that all vehicles are equipped with sensors capable of sensing the bearings relative to neighboring vehicl...

Accurately estimating camera motion from image sequences poses a significant challenge in computer vision and robotics. Many computer vision methods first compute the essential matrix associated with a motion and then extract orientation and normalized translation as inputs to pose estimation, reconstructing the scene scale (that is unobservable in...

Motivated by aircraft applications, we revisit the path-following guidance problem in three dimensions. First, by formulating the path-following error directly in the inertial frame, we propose a class of guidance laws for regular parameterized paths that, unlike most approaches existing in the literature, do not require the explicit construction o...

Inertial Navigation Systems (INS) are algorithms that fuse inertial measurements of angular velocity and specific acceleration with supplementary sensors including GNSS and magnetometers to estimate the position, velocity and attitude, or extended pose, of a vehicle. The industry-standard extended Kalman filter (EKF) does not come with strong stabi...

Feature-based homography estimation approaches rely on extensive image processing for feature extraction and matching, and do not adequately account for the information provided by the image. Therefore, developing efficient direct techniques to extract the homography from images is essential. This paper presents a novel nonlinear direct homography...

This letter deals with the problem of state estimation for a class of systems involving linear dynamics with multiple quadratic output measurements. We propose a systematic approach to immerse the original system into a linear time-varying (LTV) system of a higher dimension. The methodology extends the original system by incorporating a minimum num...

Inertial Velocity-Aided Attitude (VAA) is an important problem in the control of Remotely Piloted Aerial Systems (RPAS), and involves estimating the velocity and attitude of a vehicle using gyroscope, accelerometer, and inertial-frame velocity (e.g. GPS velocity) measurements. Existing solutions tend to be complex and provide limited stability guar...

High performance trajectory tracking control of quadrotor vehicles is an important challenge in aerial robotics. Symmetry is a fundamental property of physical systems and offers the potential to provide a tool to design high-performance control algorithms. We propose a design methodology that takes any given symmetry, linearises the associated err...

This paper addresses the problem of time-varying bearing formation control in d (d≥2)-dimensional Euclidean space by exploring Persistence of Excitation (PE) of the desired bearing reference. A general concept of Bearing Persistently Exciting (BPE) formation defined in d-dimensional space is here fully developed. By providing a desired formation th...

This paper explores the properties of Bearing Persistently Exciting (BPE) formations defined in d(d≥2)-dimensional space, a class of time-varying bearing formations whose configuration can be uniquely determined up to a translational Euclidean vector using only bearing and velocity measurements. By analyzing the bearing Laplacian matrix in relation...

Equivariance is a common and natural property of many nonlinear control systems, especially those associated with models of mechatronic and navigation systems. Such systems admit a symmetry, associated with the equivariance, that provides structure enabling the design of robust and high-performance observers. A key insight is to pose the observer s...

This paper develops an equivariant symmetry for second order kinematic systems on matrix Lie groups and uses this symmetry for observer design. The state of a second order kinematic system on a matrix Lie group is naturally posed on the tangent bundle of the group with the inputs lying in the tangent of the tangent bundle known as the double tangen...

The kinematics of many systems encountered in robotics, mechatronics, and avionics are naturally posed on homogeneous spaces; i.e., their state lies in a smooth manifold equipped with a transitive Lie group symmetry. This article proposes a novel filter, the equivariant filter (EqF) , by posing the observer state on the symmetry group, linearizin...

This paper addresses the problem of bearing leader-follower formation control in three-dimensional space by exploring the persistence of excitation (PE) of the desired formation. Using only bearing and relative velocity measurements, distributed control laws are derived for a group of agents with double-integrator dynamics. The key contribution is...

This paper considers the problem of controlling a quadrotor to go through a window and land on a planar target, the landing pad, using an Image-Based Visual Servo (IBVS) controller that relies on sensing information from two on-board cameras and an IMU. The maneuver is divided into two stages: crossing the window and landing on the pad. For the fir...

Visual Simultaneous Localisation and Mapping (VSLAM) is a well-known problem in robotics with a large range of applications. This paper presents a novel approach to VSLAM by lifting the observer design to a novel Lie group VSLAMn(3) on which the system output is equivariant. The perspective gained from this analysis facilitates the design of a non-...

Equivariance is a common and natural property of many nonlinear control systems, especially those associated with models of mechatronic and navigation systems. Such systems admit a symmetry, associated with the equivariance, that provides structure enabling the design of robust and high performance observers. A key insight is to pose the observer s...

The kinematics of many mechanical systems encountered in robotics and other fields, such as single-bearing attitude estimation and SLAM, are naturally posed on homogeneous spaces: That is, their state lies in a smooth manifold equipped with a transitive Lie-group symmetry. This paper shows that any system posed in a homogeneous space can be extende...

Simultaneous Localisation and Mapping (SLAM) is the archetypal chicken and egg problem: Localisation of a robot with respect to a map requires an estimate of the map, while mapping an environment from data acquired by a robot requires an estimate of the robot localisation. The nonlinearity and co-dependence of the SLAM problem has made it an ongoin...

This paper presents the equivariant systems theory and observer design for second order kinematic systems on matrix Lie groups. The state of a second order kinematic system on a matrix Lie group is naturally posed on the tangent bundle of the group with the inputs lying in the tangent of the tangent bundle known as the double tangent bundle. We pro...

This paper considers the problem of controlling a quadrotor to go through a window and land on a planar target, the landing pad, using an Image-Based Visual Servo (IBVS) controller that relies on sensing information from two on-board cameras and an IMU. The maneuver is divided into two stages: crossing the window and landing on the pad. For the fir...

This paper addresses the problem of estimating the attitude and angular velocity of a rigid object by exploiting its second order kinematic model. The approach is particularly useful in cases where angular velocity measurements are not available and the attitude and angular velocity of an object need to be estimated from accelerometers and magnetom...

This paper addresses the problem of time-varying bearing formation control in $d$ $(d\ge 2)$-dimensional Euclidean space by exploring Persistence of Excitation (PE) of the desired bearing reference. A general concept of Bearing Persistently Exciting (BPE) formation defined in $d$-dimensional space is here fully developed. By providing a desired for...

This paper addresses the problem of leader–follower formation control in three dimensional space by exploring persistence of excitation (PE) of the desired formation. Using only bearing and relative velocity measurements, distributed control laws are derived for a group of agents with double-integrator dynamics. The key contribution is that the exp...

This paper addresses the problem of bearing-only formation control in $d~(d\geq 2)$-dimensional space by exploring persistence of excitation (PE) of the desired bearing reference. By defining a desired formation that is bearing PE, distributed bearing-only control laws are proposed, which guarantee exponential stabilization of the desired formation...

The kinematics of many systems encountered in robotics, mechatronics, and avionics are naturally posed on homogeneous spaces, that is, their state lies in a smooth manifold equipped with a transitive Lie-group symmetry. This paper shows that all such systems can be embedded in an equivariant system using a velocity extension. We propose a novel fil...

A homography-based dynamic control approach applied to station keeping of autonomous underwater vehicles (AUVs) without relying on linear velocity measurements is proposed. The homography estimated from images of a planar target scene captured by a downward-looking camera is directly used as feedback information. The full dynamics of the AUV are ex...

This technical communiqu\'e aims at correcting an erroneous statement (Lemma 2.4) in an earlier paper by the same authors concerning a sufficient condition of uniform observability for a Linear Time-Varying (LTV) system. In this earlier paper, the proofs of two other lemmas, about body-pose estimation from range measurements, relied on this erroneo...

This paper addresses the problem of bearing-only formation control in $d~(d\geq 2)$-dimensional space by exploring persistence of excitation (PE) of the desired bearing reference. By defining a desired formation that is bearing PE, distributed bearing-only control laws are proposed, which guarantee exponential stabilization of the desired formation...

This paper addresses the problem of formation control with a leader-follower structure in three dimensional space by exploring persistence of excitation (PE) of the desired bearing reference, which is provided by a possibly moving or time-varying desired formation. Using only bearing measurements, control laws are proposed for a group of agents wit...

A wide range of system models in modern robotics and avionics applications admit natural symmetries. Such systems are termed equivariant and the structure provided by the symmetry is a powerful tool in the design of observers. Significant progress has been made in the last ten years in the design of filters and observers for attitude and pose estim...

Visual Simultaneous Localisation and Mapping (VSLAM) is a well-known problem in robotics with a large range of applications. This paper presents a novel approach to VSLAM by lifting the observer design to a novel Lie group on which the system output is equivariant. The perspective gained from this analysis facilitates the design of a non-linear obs...

Visual Simultaneous Localisation and Mapping (VSLAM) is a key enabling technology for small embedded robotic systems such as aerial vehicles. Recent advances in equivariant filter and observer design offer the potential of a new generation of highly robust algorithms with low memory and computation requirements for embedded system applications. Thi...

Although homography estimation from correspondences of mixed-type features, namely points and lines, has been relatively well studied with algebraic approaches by the computer vision community, this problem has never been addressed with nonlinear observer paradigms. In this paper, a novel nonlinear observer on the Special Linear group SL(3) applied...

Homography estimation is an important task in robotics applications, such as landing on moving platforms, docking and refueling, building inspection, and so on. Nonlinear observers depend on an estimate of the group algebra velocity as a feed-forward term to minimize lag in the filter response. When both the camera and the scene are moving, and for...

This paper addresses the problem of formation control with a leader-follower structure in three dimensional space by exploring persistence of excitation (PE) of the desired bearing reference, which is provided by a possibly moving or time-varying desired formation. Using only bearing measurements, control laws are proposed for a group of agents wit...

Visual Simultaneous Localisation and Mapping (VSLAM) is a key enabling technology for small embedded robotic systems such as aerial vehicles. Recent advances in equivariant filter and observer design offer the potential of a new generation of highly robust algorithms with low memory and computation requirements for embedded system applications. Thi...

This paper addresses the path following control problem for scale-model fixed-wing aircraft. Kinematic guidance and dynamic control laws are developed within a single coherent framework that exploits a simple generic model of aerodynamic forces acting on the aircraft and applies to almost all regular 3D paths. The proposed control solutions are der...

This paper builds on recent work on Simultaneous Localisation and Mapping (SLAM) in the non-linear observer community, by framing the visual localisation and mapping problem as a continuous-time equivariant observer design problem on the symmetry group of a kinematic system. The state-space is a quotient of the robot pose expressed on SE(3) and mul...

This paper revisits dynamic soaring on the basis of a nonlinear point-mass flight dynamics model previously used for scale-model aircraft to design path-following autopilots endowed with theoretically and experimentally demonstrated stability and convergence properties. The energy-harvesting process associated with specific maneuvers of a glider su...

This paper presents a new algorithm for online estimation of a sequence of homographies applicable to image sequences obtained from robotic vehicles equipped with vision sensors. The approach taken exploits the underlying Special Linear group structure of the set of homographies along with gyroscope measurements and direct point‐feature corresponde...

This work proposes a 2D image-based controller to automatically steer a fixed-wing Unmanned Aerial Vehicle (UAV) during the first three stages of landing: alignment, glide-slope, and flare. Observable image features of the runway and its textured ground are exploited to derive a feedback controller for the automatic maneuver. The proposed controlle...

A nonlinear image-based visual servo control approach for pipeline following of fully-actuated Autonomous Underwater Vehicles (AUV) is proposed. It makes use of the binormalized Plücker coordinates of the pipeline borders detected in the image plane as feedback information while the system dynamics are exploited in a cascade manner in the control d...

This paper considers the problem of controlling a quadrotor to go through a window and land on a planar target, using an image-based controller, with only a camera and an Inertial Measurement Unit (IMU) as sensors. The maneuver is divided into two stages: crossing the window and landing on the target plane. For the first stage, a control law is pro...

This paper addresses the path following control problem for scale-model fixed-wing aircraft. Kinematic guidance and dynamic control laws are developed within a single coherent framework that exploits a simple generic model of aerodynamics forces acting on the aircraft and applies to almost all regular 3D paths. The proposed control solutions are de...

This paper revisits the problems of estimating the position of an object moving in ( )-dimensional Euclidean space using velocity measurements and either direction or range measurements of one or multiple source points. The proposed solutions exploit the Continuous Riccati Equation (CRE) to calculate observer gains yielding global uniform exponenti...

This paper revisits the problem of estimating the pose of a body in 3D space with respect to (w.r.t.) an inertial frame by using i) the knowledge of source points positions in the inertial frame, ii) the measurements of the body angular velocity expressed in the body's frame iii) the measurements of the body translational velocity, either in the bo...

We exploit the first-order aerodynamic effects for the feedback control of quadrotors in order to enhance the performance of the closed-loop system. We describe first the origin of these forces and then we show how the complexity of the system dynamics can be transformed by a change of control input into a simpler form, for which the classical hier...

A nonlinear inertial-aided image-based visual servo control approach for the stabilization of (almost) fully actuated autonomous underwater vehicles (AUVs) is proposed. It makes use of the homography matrix between two images of a planar scene as feedback information while the system dynamics are exploited in a cascade manner in a control design: A...

This chapter considers the questions of observability and design of observers for position estimates of an object moving in \(\mathbb {R}^n\). The scenario considered assumes a possibly biased measurement of velocity along with bearing or direction measurements to one or multiple fixed points in the environment. The motivating example is a robot mo...

Motivated by drone autonomous navigation applications we address a novel problem of velocity-aided attitude estimation by combining two linear velocity components measured in a body-fixed frame and a linear velocity component measured in an inertial frame with the measurements of an Inertial Measurement Unit (IMU). The main contributions of the pre...

This paper addresses the landing problem of a vertical take-off and landing vehicle, exemplified by a quadrotor, on a moving platform using image-based visual servo control. Observable features on a flat and textured target plane are exploited to derive a suitable control law. The target plane may be moving with bounded linear acceleration in any d...

We propose a simple nonlinear observer for estimating the attitude and velocity of a rigid body from the measurements of specific acceleration, angular velocity, magnetic field (in body axes), and linear velocity (in body axes). It is uniformly globally exponentially convergent, and also enjoys other nice properties: global decoupling of pitch and...

This paper revisits the problems of estimating the position of an object moving in $n$ ($\geq 2$)-dimensional Euclidean space using velocity measurements and either direction or range measurements of one or multiple source points. The proposed solutions exploit the Continuous Riccati Equation (CRE) to calculate observer gains yielding global expone...

This paper presents a new algorithm for online estimation of a sequence of homographies applicable to image sequences obtained from robotic vehicles equipped with vision sensors. The approach taken exploits the underlying Special Linear group structure of the set of homographies along with gyroscope measurements and direct point-feature corresponde...

This paper proposes a state estimation methodology for invariant systems on Lie groups where outputs of the system are measured with delay. The proposed method is based on cascading an observer and a predictor. The observer uses delayed measurements and provides estimates of delayed states. The predictor uses those estimates together with the curre...

This paper deals with the problem of output regulation for systems defined on matrix Lie-Groups. Reference trajectories to be tracked are supposed to be generated by an exosystem, defined on the same Lie-Group of the controlled system, and only partial relative error measurements are supposed to be available. These measurements are assumed to be in...

The Transverse Function (TF) control approach is applied to the control of a generic motorboat endowed with a surge force along the stern–bow direction and a torque actuation to modify the boat’s orientation. With respect to more conventional methods this approach allows for uniform practical stabilization of any smooth reference pose (i.e. positio...