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.

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.

In this paper, we have proposed a new strategy of using the landmark anchor node instead of a radio-based anchor node to obtain the virtual coordinates (landmarkID, DISTANCE) of moving troops or defense forces that will help in tracking and maneuvering the troops along a safe path within a GPS-denied battlefield environment. The proposed strategy implements landmark recognition using the Yolov5 model and landmark distance estimation using an efficient Stereo Matching Algorithm. We consider that a moving node carrying a low-power mobile device facilitated with a calibrated stereo vision camera that captures stereo images of a scene containing landmarks within the battlefield region whose locations are stored in an offline server residing within the device itself. We created a custom landmark image dataset called MSTLandmarkv1 with 34 landmark classes and another landmark stereo dataset of those 34 landmark instances called MSTLandmarkStereov1. We trained the YOLOv5 model with MSTLandmarkv1 dataset and achieved 0.95 mAP @ 0.5 IoU and 0.767 mAP @ [0.5: 0.95] IoU. We calculated the distance from a node to the landmark utilizing the bounding box coordinates and the depth map generated by the improved SGM algorithm using MSTLandmarkStereov1. The tuple of landmark IDs obtained from the detection result and the distances calculated by the SGM algorithm are stored as the virtual coordinates of a node. In future work, we will use these virtual coordinates to obtain the location of a node using an efficient trilateration algorithm and optimize the node position using the appropriate optimization method.

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.

This paper proposes a distributed guiding-vector-field (DGVF) controller for cross-domain unmanned systems (CDUSs) consisting of heterogeneous unmanned aerial vehicles (UAVs) and unmanned surface vehicles (USVs), to achieve coordinated navigation whereas maneuvering along their prescribed paths. In particular, the DGVF controller provides a hierarchical architecture of an upper-level heterogeneous guidance velocity controller and a lower-level signal tracking regulator. Therein, the upper-level controller is to govern multiple heterogeneous USVs and UAVs to approach and maneuver along the prescribed paths and coordinate the formation simultaneously, whereas the low-level regulator is to track the corresponding desired guidance signals provided by the upper-level module. Significantly, the heterogeneous coordination among neighboring UAVs and USVs is achieved merely by the lightweight communication of a scalar (i.e., the additional virtual coordinate), which substantially decreases the communication and computational costs. Sufficient conditions assuring asymptotical convergence of the closed-loop system are derived in presence of the exponentially vanishing tracking errors. Finally, real-lake experiments are conducted on a self-established cross-domain heterogeneous platform consisting of three M-100 UAVs, two HUSTER-16 USVs, a HUSTER-12C USV, and a WiFi 5G wireless communication station to verify the effectiveness of the present DGVF controller.

We propose coordinating guiding vector fields to achieve two tasks simultaneously with a team of robots: first, the guidance and navigation of multiple robots to possibly different paths or surfaces typically embedded in 2D or 3D; second, their motion coordination while tracking their prescribed paths or surfaces. The motion coordination is defined by desired parametric displacements between robots on the path or surface. Such a desired displacement is achieved by controlling the virtual coordinates, which correspond to the path or surface's parameters, between guiding vector fields. Rigorous mathematical guarantees underpinned by dynamical systems theory and Lyapunov theory are provided for the effective distributed motion coordination and navigation of robots on paths or surfaces from all initial positions. As an example for practical robotic applications, we derive a control algorithm from the proposed coordinating guiding vector fields for a Dubins-car-like model with actuation saturation. Our proposed algorithm is distributed and scalable to an arbitrary number of robots. Furthermore, extensive illustrative simulations and fixed-wing aircraft outdoor experiments validate the effectiveness and robustness of our algorithm.

Full-immersive multiuser Virtual Reality (VR) envisions supporting unconstrained mobility of the users in the virtual worlds, while at the same time constraining their physical movements inside VR setups through redirected walking. For enabling delivery of high data rate video content in real-time, the supporting wireless networks will leverage highly directional communication links that will "track" the users for maintaining the Line-of-Sight (LoS) connectivity. Recurrent Neural Networks (RNNs) and in particular Long Short-Term Memory (LSTM) networks have historically presented themselves as a suitable candidate for near-term movement trajectory prediction for natural human mobility, and have also recently been shown as applicable in predicting VR users' mobility under the constraints of redirected walking. In this work, we extend these initial findings by showing that Gated Recurrent Unit (GRU) networks, another candidate from the RNN family, generally outperform the traditionally utilized LSTMs. Second, we show that context from a virtual world can enhance the accuracy of the prediction if used as an additional input feature in comparison to the more traditional utilization of solely the historical physical movements of the VR users. Finally, we show that the prediction system trained on a static number of coexisting VR users be scaled to a multi-user system without significant accuracy degradation.