arXiv subjects

Weijia Yao

Publications and source records attributed to Weijia Yao.

At least 19 recordsLinked to original sources

arXiv2026

Decoupling Physical Speed from Path Parameterization in Singularity-Free Guiding Vector Fields

The existing singularity-free guiding vector field (SF-GVF) with an additional virtual coordinate can eliminate singular points (i.e., points where the vector field vanishes) inherent in conventional GVFs and guarantee global convergence of robot trajectories to closed and self-intersecting desired paths. However, the desired speed given by the GVF along the desired path in the original lower-dimensional space cannot be arbitrarily specified but depends on path parameterizations. One possible workaround is to partially normalize the physical projection of the SF-GVF and assign a user-designed speed. However, we show that this workaround may introduce new singularities since the normalization denominator can become zero. To address this issue, we propose a new SF-GVF with prescribed physical speed (PPS). The integral curves of the new SF-GVF converge exponentially to the desired path from any initial condition in the higher-dimensional space (including virtual dimension); more importantly, the robot's physical speed converges to the PPS, while the path-error dynamics remain invariant under regular reparameterizations of the desired path. We further develop a saturated acceleration control law for second-order kinematic models. Finally, comparative simulations and 3D path-following experiments with a quadrotor under different PPS profiles validate the theoretical results and demonstrate the effectiveness of the proposed approach.

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arXiv2026

Simultaneous Arrival Control for Distributed Multi-Robot Systems with Curvature and Constant-Speed Constraints

The simultaneous arrival of multiple mobile robots at a target point is crucial for cooperation tasks such as cooperative encirclement, disaster relief, and environmental monitoring. Although the simultaneous arrival problem itself is already complex, the problem becomes more challenging when there are constraints on the robot trajectory curvatures and the speeds are required to be constant (possibly different for different robots), and the control law for robots needs to be distributed. These constraints are typical for a multi-robot system consisting of, e.g., fixed-wing UAVs. To address this challenge, this paper proposes a distributed switching control method based on the maximum consensus protocol. By exploiting the geometric properties of Dubins paths along with optimization principles, a virtual time variable is introduced, and a hybrid control law that combines optimal control with saturated proportional control is designed. Under the proposed control law, each robot is driven to approach the maximum virtual time among its neighbors, thereby achieving simultaneous arrival under some mild conditions. Furthermore, we prove that in certain cases the proposed method attains a theoretically optimal arrival time. The approach is scalable and real-time, with low communication overhead. Its effectiveness and robustness are validated through extensive simulations and experiments.

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arXiv2026

Finite-Time Curvature-Constrained Vector Field for Saturation-Free Motion Planning of Nonholonomic Robots

Accurately steering a robot to a target configuration is fundamental in engineering, yet remains challenging for nonholonomic mobile robots. Vector fields (VFs) provide a natural framework by specifying desired motion directions throughout the workspace and enabling direct integration with feedback control. However, most existing VF-based methods cannot explicitly generate trajectories satisfying curvature constraints. Actuator limits are therefore often enforced by input saturation, which may invalidate stability guarantees and degrade closed-loop performance when not considered in controller design. In addition, these methods usually ensure only asymptotic convergence without an explicit settling-time bound. To address these issues, we propose a generalized motion planning and control framework consisting of a finite-time curvature-constrained vector field (FT-C2VF) and a saturation-free control law. Depending on the motion objective, the framework drives the robot to the target configuration in finite time or through it periodically. First, the FT-C2VF is constructed using complementary gains to achieve finite-time convergence while ensuring that the curvature of its integral curves is continuous, bounded, and monotonically decreasing with the radial ratio. Second, an almost globally C1-smooth, saturation-free controller is developed to track the FT-C2VF without Jacobian information, while keeping all control inputs within prescribed actuator limits. Third, dynamical-systems analysis establishes almost-global finite-time stability of the target equilibrium. Numerical simulations show improved performance over representative VF-based methods, and outdoor experiments on an Ackermann-steered vehicle confirm the effectiveness and robustness of the proposed approach.

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arXiv2026

Distributed Safe Cooperative Vector Field for Trajectory Curvature Constrained Multi-Robot Systems

Trajectory curvature constraints are inherent in practical multi-robot systems due to the limited turning capabilities of the robots. Without properly accounting for these constraints, robots may fail to accomplish assigned tasks, and their trajectories may diverge from the intended paths. This paper proposes a distributed safe cooperative vector field approach for multi-robot systems subject to trajectory curvature constraints. The proposed approach is composed of a cooperative vector field and a safety-oriented collision avoidance vector field, aiming to address the problems of cooperative motion and safe collision avoidance in multi-robot path-following tasks. A safety-oriented collision avoidance vector field with adaptively adjustable reactive boundary is developed to accommodate the kinematic curvature constraints of robots, thereby ensuring the physical feasibility of collision avoidance maneuvers. The proposed vector field requires only a single virtual variable from each neighboring robot to achieve cooperative motion and ensure both obstacle avoidance and inter-robot collision avoidance. The effectiveness of the proposed approach is validated through both simulations and real-world experiments on an actual multi-robot platform.

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arXiv2026

Fully distributed and resilient source seeking for robot swarms

Existing source-seeking algorithms for robot swarms typically require either direct gradient measurements or rigid geometric formations, limiting their flexibility and resilience to robot failures. We propose a fully distributed solution that overcomes these limitations by computing an ascending direction through local field measurements and distributed estimation of centroid-relative coordinates. The resulting architecture consists of three exponentially convergent algorithms operating in a slow-fast closed-loop system, enabling simultaneous estimation and motion control without central coordination. Our framework accommodates arbitrary swarm geometries and analyzes how the spatial distribution of robots affects gradient observability, robustness, and resilience to failures. We characterize optimal swarm shapes that guarantee alignment with the true gradient and show how shape morphing can maneuver the collective motion. The approach is developed for kinematic points in $\mathbb{R}^m$ and extended to 2D unicycles with constant speed. Simulations with large-scale swarms validate the methodology.

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arXiv2026

Vector Fields for Path Following on Lie Groups with Application in Robot Control

Many robotic systems allow independent control of position and orientation (pose), including omnidirectional aerial vehicles, underwater robots, and manipulator end-effectors. In many applications, these systems must follow a continuous sequence of poses, leading to either trajectory-tracking or path following formulations. Compared to trajectory-tracking, path following offers important practical advantages. In particular, we focus on the problem of path following on Lie groups. Considering the robots as rigid bodies moving in the 3D space, this path-following problem can be posed as a problem of designing guiding vector fields on the matrix Lie group SE(3). In this paper, we develop a general vector-field framework for path following on connected matrix Lie groups, of which SE(3) is a prominent special case. The proposed vector field guarantees convergence to a desired parametric curve from almost all initial conditions while ensuring continuous motion along the path. Furthermore, another interesting feature is that, as opposed to previous works, the control input is "minimal" in terms of representation and closer to the engineering application (e.g., the body twist in the case SE(3)). After establishing the general case, the framework is then specialized to SE(3), of special interest in robotics, yielding an efficient algorithm suitable for real-time robotic control. Experiments with a robotic manipulator tracking complex pose paths demonstrate the effectiveness of the approach. An open-source implementation is also provided.

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arXiv2026

Structure of Motion under Constraints and non-Holonomic Path-Following on $R^3$

In this paper we study a path-following problem on $R^3$ with a non-holonomic constraint. The geometric structure associated to the velocity constraint is explored, and general principles for constructing guiding vector fields are obtained, fulfilling the path-following requirements on a neighborhood of the desired path while allowing the design of vector fields to be conducted in global coordinates.

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arXiv2026

Vector-field guided constraint-following control for path following of uncertain mechanical systems

This note proposes a general control approach, called vector-field guided constraint-following control, to solve the dynamics control problem of geometric path-following for a class of uncertain mechanical systems. More specifically, it operates at the dynamics level and can handle both fully-actuated and underactuated mechanical systems, heterogeneous (possibly fast) time-varying uncertainties with unknown bounds, and geometric desired paths that may be self-intersecting. Simulations are conducted to demonstrate the effectiveness of the approach.

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arXiv2025

SwordRiding: A Unified Navigation Framework for Quadrotors in Unknown Complex Environments via Online Guiding Vector Fields

Although quadrotor navigation has achieved high performance in trajectory planning and control, real-time adaptability in unknown complex environments remains a core challenge. This difficulty mainly arises because most existing planning frameworks operate in an open-loop manner, making it hard to cope with environmental uncertainties such as wind disturbances or external perturbations. This paper presents a unified real-time navigation framework for quadrotors in unknown complex environments, based on the online construction of guiding vector fields (GVFs) from discrete reference path points. In the framework, onboard perception modules build a Euclidean Signed Distance Field (ESDF) representation of the environment, which enables obstacle awareness and path distance evaluation. The system first generates discrete, collision-free path points using a global planner, and then parameterizes them via uniform B-splines to produce a smooth and physically feasible reference trajectory. An adaptive GVF is then synthesized from the ESDF and the optimized B-spline trajectory. Unlike conventional approaches, the method adopts a closed-loop navigation paradigm, which significantly enhances robustness under external disturbances. Compared with conventional GVF methods, the proposed approach directly accommodates discretized paths and maintains compatibility with standard planning algorithms. Extensive simulations and real-world experiments demonstrate improved robustness against external disturbances and superior real-time performance.

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arXiv2025

Concurrent-Allocation Task Execution for Multi-Robot Path-Crossing-Minimal Navigation in Obstacle Environments

Reducing undesirable path crossings among trajectories of different robots is vital in multi-robot navigation missions, which not only reduces detours and conflict scenarios, but also enhances navigation efficiency and boosts productivity. Despite recent progress in multi-robot path-crossing-minimal (MPCM) navigation, the majority of approaches depend on the minimal squared-distance reassignment of suitable desired points to robots directly. However, if obstacles occupy the passing space, calculating the actual robot-point distances becomes complex or intractable, which may render the MPCM navigation in obstacle environments inefficient or even infeasible. In this paper, the concurrent-allocation task execution (CATE) algorithm is presented to address this problem (i.e., MPCM navigation in obstacle environments). First, the path-crossing-related elements in terms of (i) robot allocation, (ii) desired-point convergence, and (iii) collision and obstacle avoidance are encoded into integer and control barrier function (CBF) constraints. Then, the proposed constraints are used in an online constrained optimization framework, which implicitly yet effectively minimizes the possible path crossings and trajectory length in obstacle environments by minimizing the desired point allocation cost and slack variables in CBF constraints simultaneously. In this way, the MPCM navigation in obstacle environments can be achieved with flexible spatial orderings. Note that the feasibility of solutions and the asymptotic convergence property of the proposed CATE algorithm in obstacle environments are both guaranteed, and the calculation burden is also reduced by concurrently calculating the optimal allocation and the control input directly without the path planning process.

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arXiv2025

MOFM-Nav: On-Manifold Ordering-Flexible Multi-Robot Navigation

This paper addresses the problem of multi-robot navigation where robots maneuver on a desired $m$-dimensional (i.e., $m$-D) manifold in the $n$-dimensional Euclidean space, and maintain a {\it flexible spatial ordering}. We consider $ m\geq 2$, and the multi-robot coordination is achieved via non-Euclidean metrics. However, since the $m$-D manifold can be characterized by the zero-level sets of $n$ implicit functions, the last $m$ entries of the GVF propagation term become {\it strongly coupled} with the partial derivatives of these functions if the auxiliary vectors are not appropriately chosen. These couplings not only influence the on-manifold maneuvering of robots, but also pose significant challenges to the further design of the ordering-flexible coordination via non-Euclidean metrics. To tackle this issue, we first identify a feasible solution of auxiliary vectors such that the last $m$ entries of the propagation term are effectively decoupled to be the same constant. Then, we redesign the coordinated GVF (CGVF) algorithm to {\it boost} the advantages of singularities elimination and global convergence by treating $m$ manifold parameters as additional $m$ virtual coordinates. Furthermore, we enable the on-manifold ordering-flexible motion coordination by allowing each robot to share $m$ virtual coordinates with its time-varying neighbors and a virtual target robot, which {\it circumvents} the possible complex calculation if Euclidean metrics were used instead. Finally, we showcase the proposed algorithm's flexibility, adaptability, and robustness through extensive simulations with different initial positions, higher-dimensional manifolds, and robot breakdown, respectively.

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arXiv2025

Vector Field-Guided Learning Predictive Control for Motion Planning of Mobile Robots with Uncertain Dynamics

In obstacle-dense scenarios, providing safe guidance for mobile robots is critical to improve the safe maneuvering capability. However, the guidance provided by standard guiding vector fields (GVFs) may limit the motion capability due to the improper curvature of the integral curve when traversing obstacles. On the other hand, robotic system dynamics are often time-varying, uncertain, and even unknown during the motion planning process. Therefore, many existing kinodynamic motion planning methods could not achieve satisfactory reliability in guaranteeing safety. To address these challenges, we propose a two-level Vector Field-guided Learning Predictive Control (VF-LPC) approach that improves safe maneuverability. The first level, the guiding level, generates safe desired trajectories using the designed kinodynamic GVF, enabling safe motion in obstacle-dense environments. The second level, the Integrated Motion Planning and Control (IMPC) level, first uses a deep Koopman operator to learn a nominal dynamics model offline and then updates the model uncertainties online using sparse Gaussian processes (GPs). The learned dynamics and a game-based safe barrier function are then incorporated into the LPC framework to generate near-optimal planning solutions. Extensive simulations and real-world experiments were conducted on quadrotor unmanned aerial vehicles and unmanned ground vehicles, demonstrating that VF-LPC enables robots to maneuver safely.

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arXiv2025

Versatile Distributed Maneuvering with Generalized Formations using Guiding Vector Fields

This paper presents a unified approach to realize versatile distributed maneuvering with generalized formations. Specifically, we decompose the robots' maneuvers into two independent components, i.e., interception and enclosing, which are parameterized by two independent virtual coordinates. Treating these two virtual coordinates as dimensions of an abstract manifold, we derive the corresponding singularity-free guiding vector field (GVF), which, along with a distributed coordination mechanism based on the consensus theory, guides robots to achieve various motions (i.e., versatile maneuvering), including (a) formation tracking, (b) target enclosing, and (c) circumnavigation. Additional motion parameters can generate more complex cooperative robot motions. Based on GVFs, we design a controller for a nonholonomic robot model. Besides the theoretical results, extensive simulations and experiments are performed to validate the effectiveness of the approach.

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arXiv2025

Inverse Kinematics on Guiding Vector Fields for Robot Path Following

Inverse kinematics is a fundamental technique for motion and positioning control in robotics, typically applied to end-effectors. In this paper, we extend the concept of inverse kinematics to guiding vector fields for path following in autonomous mobile robots. The desired path is defined by its implicit equation, i.e., by a collection of points belonging to one or more zero-level sets. These level sets serve as a reference to construct an error signal that drives the guiding vector field toward the desired path, enabling the robot to converge and travel along the path by following such a vector field. We start with the formal exposition on how inverse kinematics can be applied to guiding vector fields for single-integrator robots in an m-dimensional Euclidean space. Then, we leverage inverse kinematics to ensure that the level-set error signal behaves as a linear system, facilitating control over the robot's transient motion toward the desired path and allowing for the injection of feed-forward signals to induce precise motion behavior along the path. We then propose solutions to the theoretical and practical challenges of applying this technique to unicycles with constant speeds to follow 2D paths with precise transient control. We finish by validating the predicted theoretical results through real flights with fixed-wing drones.

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arXiv2025

HI-GVF: Shared Control based on Human-Influenced Guiding Vector Fields for Human-multi-robot Cooperation

Human-multi-robot shared control leverages human decision-making and robotic autonomy to enhance human-robot collaboration. While widely studied, existing systems often adopt a leader-follower model, limiting robot autonomy to some extent. Besides, a human is required to directly participate in the motion control of robots through teleoperation, which significantly burdens the operator. To alleviate these two issues, we propose a layered shared control computing framework using human-influenced guiding vector fields (HI-GVF) for human-robot collaboration. HI-GVF guides the multi-robot system along a desired path specified by the human. Then, an intention field is designed to merge the human and robot intentions, accelerating the propagation of the human intention within the multi-robot system. Moreover, we give the stability analysis of the proposed model and use collision avoidance based on safety barrier certificates to fine-tune the velocity. Eventually, considering the firefighting task as an example scenario, we conduct simulations and experiments using multiple human-robot interfaces (brain-computer interface, myoelectric wristband, eye-tracking), and the results demonstrate that our proposed approach boosts the effectiveness and performance of the task.

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arXiv2024

DVRP-MHSI: Dynamic Visualization Research Platform for Multimodal Human-Swarm Interaction

In recent years, there has been a significant amount of research on algorithms and control methods for distributed collaborative robots. However, the emergence of collective behavior in a swarm is still difficult to predict and control. Nevertheless, human interaction with the swarm helps render the swarm more predictable and controllable, as human operators can utilize intuition or knowledge that is not always available to the swarm. Therefore, this paper designs the Dynamic Visualization Research Platform for Multimodal Human-Swarm Interaction (DVRP-MHSI), which is an innovative open system that can perform real-time dynamic visualization and is specifically designed to accommodate a multitude of interaction modalities (such as brain-computer, eye-tracking, electromyographic, and touch-based interfaces), thereby expediting progress in human-swarm interaction research. Specifically, the platform consists of custom-made low-cost omnidirectional wheeled mobile robots, multitouch screens and two workstations. In particular, the mutitouch screens can recognize human gestures and the shapes of objects placed on them, and they can also dynamically render diverse scenes. One of the workstations processes communication information within robots and the other one implements human-robot interaction methods. The development of DVRP-MHSI frees researchers from hardware or software details and allows them to focus on versatile swarm algorithms and human-swarm interaction methods without being limited to fixed scenarios, tasks, and interfaces. The effectiveness and potential of the platform for human-swarm interaction studies are validated by several demonstrative experiments.

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arXiv2024

Resilient source seeking with robot swarms

We present a solution for locating the source, or maximum, of an unknown scalar field using a swarm of mobile robots. Unlike relying on the traditional gradient information, the swarm determines an ascending direction to approach the source with arbitrary precision. The ascending direction is calculated from measurements of the field strength at the robot locations and their relative positions concerning the centroid. Rather than focusing on individual robots, we focus the analysis on the density of robots per unit area to guarantee a more resilient swarm, i.e., the functionality remains even if individuals go missing or are misplaced during the mission. We reinforce the robustness of the algorithm by providing sufficient conditions for the swarm shape so that the ascending direction is almost parallel to the gradient. The swarm can respond to an unexpected environment by morphing its shape and exploiting the existence of multiple ascending directions. Finally, we validate our approach numerically with hundreds of robots. The fact that a large number of robots always calculate an ascending direction compensates for the loss of individuals and mitigates issues arising from the actuator and sensor noises.

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arXiv2024

Coordinated Guiding Vector Field Design for Ordering-Flexible Multi-Robot Surface Navigation

We design a distributed coordinated guiding vector field (CGVF) for a group of robots to achieve ordering-flexible motion coordination while maneuvering on a desired two-dimensional (2D) surface. The CGVF is characterized by three terms, i.e., a convergence term to drive the robots to converge to the desired surface, a propagation term to provide a traversing direction for maneuvering on the desired surface, and a coordinated term to achieve the surface motion coordination with an arbitrary ordering of the robotic group. By setting the surface parameters as additional virtual coordinates, the proposed approach eliminates the potential singularity of the CGVF and enables both the global convergence to the desired surface and the maneuvering on the surface from all possible initial conditions. The ordering-flexible surface motion coordination is realized by each robot to share with its neighbors only two virtual coordinates, i.e. that of a given target and that of its own, which reduces the communication and computation cost in multi-robot surface navigation. Finally, the effectiveness of the CGVF is substantiated by extensive numerical simulations.

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