This paper investigates the problem of pose synchronization for multiple rigid body systems evolving on the matrix Lie group (3). We propose a distributed hybrid feedback control scheme with global asymptotic stability guarantees using relative pose and group velocity measurements. The key idea consists of constructing a new potential function on (3) ×ℝ with a generalized non-diagonal weighting matrix, and a set of auxiliary scalar variables with continuous-discrete hybrid dynamics. Based on the new potential function and the auxiliary scalar variables, a geometric distributed hybrid feedback designed directly on (3) is proposed to achieve global pose synchronization. Numerical simulation results are presented to illustrate the performance of the proposed distributed hybrid control scheme.

We propose a hybrid feedback control framework for autonomous robot navigation in $n$ -dimensional Euclidean spaces with spherical obstacles. The proposed approach ensures safe and global navigation toward a target location by dynamically switching between motion-to-destination and locally optimal obstacle-avoidance modes. It generates continuous velocity inputs, collision-free trajectories, and locally optimal avoidance maneuvers. Compatible with range sensors, the framework enables navigation in both known and unknown environments. Extensive 2-D/3-D simulations and experiments on a TurtleBot 4 platform demonstrate the approach’s effectiveness, yielding shorter paths and smoother trajectories compared to state-of-the-art methods, while remaining efficient and practical.

This paper deals with the leader-follower attitude synchronization problem for a group of heterogeneous rigid body systems on SO(3) under an undirected, connected, and acyclic graph communication topology. The proposed distributed control strategy, endowed with almost global asymptotic stability guarantees, allows the synchronization of the rigid body systems to a constant desired orientation known only to a single rigid body. Some simulation results are also provided to validate the theoretical developments and illustrate the performance of the proposed control strategy.

This paper addresses the problem of Visual-Inertial Odometry (VIO) for rigid body systems evolving in three-dimensional space. We introduce a novel matrix Lie group structure, denoted SE_{3+n}(3), that unifies the pose, gravity, linear velocity, and landmark positions within a consistent geometric framework tailored to the VIO problem. Building upon this formulation, we design an almost globally asymptotically stable nonlinear geometric observer that tightly integrates data from an Inertial Measurement Unit (IMU) and visual sensors. Unlike conventional Extended Kalman Filter (EKF)-based estimators that rely on local linearization and thus ensure only local convergence, the proposed observer achieves almost global stability through the decoupling of the rotational and translational dynamics. A globally exponentially stable Riccati-based translational observer along with an almost global input-to-state stable attitude observer are designed such that the overall cascaded observer enjoys almost global asymptotic stability. This cascaded architecture guarantees robust and consistent estimation of the extended state, including orientation, position, velocity, gravity, and landmark positions, up to the VIO unobservable directions (i.e., a global translation and rotation about gravity). The effectiveness of the proposed scheme is demonstrated through numerical simulations as well as experimental validation on the EuRoC MAV dataset, highlighting its robustness and suitability for real-world VIO applications.

In this article, we address the problem of attitude synchronization for a group of rigid body systems evolving on SO(3). The interaction among these systems is modeled through an undirected, connected, and acyclic graph topology. First, we present an almost global continuous distributed attitude synchronization scheme with rigorously proven stability guarantees. Thereafter, we propose two global distributed hybrid attitude synchronization schemes on SO(3). The first scheme is a hybrid control law that leverages angular velocities and relative orientations to achieve global alignment to a common orientation. The second scheme eliminates the dependence on angular velocities by introducing dynamic auxiliary variables, while ensuring global asymptotic attitude synchronization. This velocity-free control scheme relies exclusively on attitude information. The proposed schemes are applicable to heterogeneous multiagent systems, where agents may have distinct inertia matrices. Simulation results are provided to illustrate the effectiveness of the proposed distributed attitude synchronization schemes.

The problem of constrained stabilization on the n-sphere under star-shaped constraints is considered. We propose a control strategy that allows to almost globally steer the state to a desired location while avoiding star-shaped constraints on the n-sphere. Depending on the state's proximity to the unsafe regions, the state is either guided towards the target location along the geodesic connecting the target to the state or steered towards the antipode of a predefined point lying in the interior of the nearest unsafe region. We prove that the target location is almost globally asymptotically stable under the proposed continuous, time-invariant feedback control law. Nontrivial simulation results on the 2-sphere and the 3-sphere demonstrate the effectiveness of the theoretical results.

We address the tracking problem for a class of uncertain non-affine nonlinear systems with high relative degrees, performing non-repetitive tasks. We propose a rigorously proven, robust adaptive learning control scheme that relies on a gradient descent parameter adaptation law to handle the unknown time-varying parameters of the system, along with a state estimator that estimates the unmeasurable state variables. Furthermore, despite the inherently complex nature of the non-affine system, we provide an explicit iterative computation method to facilitate the implementation of the proposed control scheme. The paper includes a thorough analysis of the performance of the proposed control strategy, and simulation results are presented to demonstrate the effectiveness of the approach.

This paper addresses the autonomous robot navigation problem in a priori unknown $n$-dimensional environments containing disjoint convex obstacles of arbitrary shapes and sizes, with pairwise distances strictly greater than the robot's diameter. We propose a hybrid feedback control scheme that guarantees safe and global asymptotic convergence of the robot to a predefined target location. The proposed control strategy relies on a switching mechanism allowing the robot to operate either in the move-to-target mode or the obstacle-avoidance mode, based on its proximity to the obstacles and the availability of a clear straight path between the robot and the target. In the obstacle-avoidance mode, the robot is constrained to move within a two-dimensional plane that intersects the obstacle being avoided and the target, preventing it from retracing its path. The effectiveness of the proposed hybrid feedback controller is demonstrated through simulations and experimental results.

We consider the constrained stabilization problem of second-order systems evolving on the n-sphere. We propose a control strategy with a constraint proximity-based dynamic damping mechanism that ensures safe and almost global asymptotic stabilization of the target point in the presence of star-shaped constraints on the n-sphere. It is also shown that the proposed approach can be used to deal with the constrained rigid-body attitude stabilization. The effectiveness of the proposed approach is demonstrated through simulation results on the 2-sphere in the presence of star-shaped constraint sets.

This paper proposes a model predictive trajectory tracking approach for quadrotors subject to input constraints. Our proposed approach relies on a hierarchical control strategy with an outer-loop feedback generating the required thrust and desired attitude and an inner-loop feedback regulating the actual attitude to the desired one. For the outer-loop translational dynamics, the generation of the virtual control input is formulated as a constrained model predictive control problem with time-varying input constraints and a control strategy, endowed with uniform global asymptotic stability guarantees, is proposed. For the inner-loop rotational dynamics, a hybrid geometric controller is adopted, achieving semi-global exponential tracking of the desired attitude. Finally, we prove that the overall cascaded system is semi-globally asymptotically stable. Simulation results illustrate the effectiveness of the proposed approach.

We propose a continuous feedback control strategy that steers a point-mass vehicle safely to a destination, in a quasi-optimal manner, in sphere worlds. The main idea consists in avoiding each obstacle via the shortest path on the cone's surface enclosing the obstacle and moving straight toward the target when the vehicle has a clear line of sight to the target location. In particular, almost global asymptotic stability of the target location is achieved in two-dimensional (2D) environments under a particular assumption on the obstacles configuration. We also propose a reactive (sensor-based) approach, suitable for real-time implementations in a priori unknown 2D environments with sufficiently curved convex obstacles, guaranteeing almost global asymptotic stability of the target location. Simulation results are presented to illustrate the effectiveness of the proposed approach.

This paper investigates the estimation problem of the pose (orientation and position) and linear velocity of a rigid body, as well as the landmark positions, using an inertial measurement unit (IMU) and a monocular camera. First, we propose a globally exponentially stable (GES) linear timevarying (LTV) observer for the estimation of body-frame landmark positions and velocity, using IMU and monocular bearing measurements. Thereafter, using the gyro measurements, some landmarks known in the inertial frame and the estimates from the LTV observer, we propose a nonlinear pose observer on SO(3) x R-3. The overall estimation system is shown to be almost globally asymptotically stable (AGAS) using the notion of almost global input-to-state stability (ISS). Interestingly, we show that with the knowledge (in the inertial frame) of a small number of landmarks, we can recover (under some conditions) the unknown positions (in the inertial frame) of a large number of landmarks. Numerical simulation results are presented to illustrate the performance of the proposed estimation scheme.

We consider the problem of distributed attitude estimation of multi-agent systems, evolving on SO(3), relying on individual angular velocity and relative attitude measurements. We propose a nonlinear distributed hybrid attitude estimation scheme guaranteeing global asymptotic convergence of the attitude estimation errors to a common constant orientation, under an undirected, connected and acyclic graph topology. Moreover, in the presence of a leader in the group (knowing its absolute orientation), one can guarantee global asymptotic convergence of the attitude estimation errors to zero. Numerical simulation results are presented to illustrate the performance of our proposed scheme.

This work introduces a single-range-aided navigation observer that reconstructs the full state of a rigid body using only an Inertial Measurement Unit (IMU), a body-frame vector measurement (e.g., magnetometer), and a distance measurement from a fixed anchor point. The design first formulates an extended linear time-varying (LTV) system to estimate body-frame position, body-frame velocity, and the gravity direction. The recovered gravity direction, combined with the body-frame vector measurement, is then used to reconstruct the full orientation on SO(3), resulting in a cascaded observer architecture. Almost Global Asymptotic Stability (AGAS) of the cascaded design is established under a uniform observability condition, ensuring robustness to sensor noise and trajectory variations. Simulation studies on three-dimensional trajectories demonstrate accurate estimation of position, velocity, and orientation, highlighting single-range aiding as a lightweight and effective modality for autonomous navigation.

In this paper, we address the problem of leaderless attitude synchronization for a group of rigid body systems evolving on SO(3), relying on local measurements of some inertial (unit-length) vectors. The interaction graph among agents is assumed to be undirected, acyclic, and connected. We first present a distributed attitude synchronization scheme designed at the kinematic level of SO(3), followed by an extended scheme designed at the dynamic level. Both schemes are supported by a rigorous stability analysis, which establishes their almost global asymptotic stability properties. Finally, numerical simulations demonstrate the effectiveness of both distributed attitude synchronization schemes.

We propose a hybrid feedback control scheme for the autonomous robot navigation problem in three-dimensional environments with arbitrarily-shaped convex obstacles. The proposed hybrid control strategy, which consists in switching between the move-to-target mode and the obstacle-avoidance mode, guarantees global asymptotic stability of the target location in the obstacle-free workspace. We also provide a procedure for the implementation of the proposed hybrid controller in a priori unknown environments and validate its effectiveness through simulation results.

In this paper, we address the problem of attitude synchronization for a group of rigid body systems evolving on SO(3). The interaction among these systems is modeled through an undirected, connected, and acyclic graph topology. First, we present an almost global continuous distributed attitude synchronization scheme with rigorously proven stability guarantees. Thereafter, we propose two global distributed hybrid attitude synchronization schemes on SO(3). The first scheme is a hybrid control law that leverages angular velocities and relative orientations to achieve global alignment to a common orientation. The second scheme eliminates the dependence on angular velocities by introducing dynamic auxiliary variables, while ensuring global asymptotic attitude synchronization. This velocity-free control scheme relies exclusively on attitude information. The proposed schemes are applicable to heterogeneous multi-agent systems, where agents may have distinct inertia matrices. Simulation results are provided to illustrate the effectiveness of the proposed distributed attitude synchronization schemes.

This paper extends first-order motion planners to robots governed by second-order dynamics. Two control schemes are proposed based on the knowledge of a scalar function whose negative gradient aligns with a given first-order motion planner. When such a function is known, the first-order motion planner is combined with a damping velocity vector with a dynamic gain to extend the safety and convergence guarantees of the first-order motion planner to second-order systems. If no such function is available, we propose an alternative control scheme ensuring that the error between the robot’s velocity and the first-order motion planner converges to zero. The theoretical developments are supported by simulation results demonstrating the effectiveness of the proposed approaches.

In this brief, we depict the clock edge triggering control of topology-based logic dynamic systems (TLDSs) often seen in nowadays digital circuits and electronics chips. The state-space equations (SSEs) of TLDSs are firstly derived, and the necessary and sufficient conditions are given for determining the existence of a clock edge triggering control in TLDSs using the properties of the matrices in the SSEs. The effectiveness of the proposed method is then validated in the equivalent TLDS of a practical engineering chip.

We address the problem of constrained stabilization to a desired point on the 2-sphere under geodesically strongly convex constraints. The proposed feedback control law is composed of an attractive vector field that guides the state along a geodesic toward the desired point and a repulsive vector field that drives the state away from the unsafe regions. We show that the target point is almost globally asymptotically stable under the proposed continuous time-invariant control law. Simulation results are provided to illustrate the effectiveness of the theoretical developments.