Motion planning for large-scale robotic swarms presents significant challenges in terms of scalability and safety assurance in cluttered environments. To address these issues, this manuscript proposes a Closed-loop hierarchical Risk-aware swarm mOtion planner using Conditional ValuE at Risk (C-ROVER) that enables safe and efficient navigation for swarm robotic systems. The hierarchical structure of C-ROVER comprises a macroscopic planning stage that models the swarm state with Gaussian Mixture Models (GMMs) and generates trajectories for the swarm GMM, followed by a microscopic control stage that computes individual robot control using distributed model predictive control to track the GMM trajectories while achieving robot-level collision avoidance. Robot positions are periodically used to update the swarm GMM, closing the hierarchical planning and control loop. To achieve collision risk-awareness between the swarm and environmental obstacles at the macroscopic stage, C-ROVER leverages the stochastic Signed Distance Function to characterize the distance between the swarm GMM and obstacles, which is proven to follow a GMM. Then C-ROVER proposes an analytical expression of Conditional Value-at-Risk (CVaR) of a GMM to enable the swarm collision risk mitigation. Furthermore, C-ROVER designs a novel risk-aware space discretization approach to enhance the ability to navigate constrained spaces. To achieve efficient online motion planning, C-ROVER develops a convergent sequential convex programming approach for macroscopic planning, leveraging the concavity of CVaR constraints. C-ROVER has been evaluated through various simulations and real-world experiments, demonstrating its capability to ensure safe, scalable, and real-time swarm navigation in cluttered scenarios.

Large-scale swarm robotic systems consisting of numerous cooperative agents show considerable promise for performing autonomous tasks across various sectors. Nonetheless, traditional motion planning approaches often face a trade-off between scalability and solution quality due to the exponential growth of the joint state space of robots. In response, this work proposes SwarmPRM, a hierarchical, scalable, computationally efficient, and risk-aware sampling-based motion planning approach for large-scale swarm robots. SwarmPRM utilizes a Gaussian Mixture Model (GMM) to represent the swarm’s macroscopic state and constructs a Probabilistic Roadmap in Gaussian space, referred to as the Gaussian roadmap, to generate a transport trajectory of GMM. This trajectory is then followed by each robot at the microscopic stage. To enhance trajectory safety, SwarmPRM incorporates the conditional value-at-risk (CVaR) in the collision checking process to impart the property of risk awareness to the constructed Gaussian roadmap. SwarmPRM then crafts a linear programming formulation to compute the optimal GMM transport trajectory within this roadmap. Extensive simulations demonstrate that SwarmPRM outperforms state-of-the-art methods in computational efficiency, scalability, and trajectory quality while offering the capability to adjust the risk tolerance of generated trajectories.

Swarm robotics has garnered significant attention due to its ability to accomplish elaborate and synchronized tasks. Existing methodologies for motion planning of swarm robotic systems mainly encounter difficulties in scalability and safety guarantee. To address these limitations, we propose a Risk-aware swarm mOtion planner using conditional ValuE-at-Risk (ROVER) that systematically navigates large-scale swarms through cluttered environments while ensuring safety. ROVER formulates a finite-time model predictive control (FTMPC) problem predicated upon the macroscopic state of the robot swarm represented by a Gaussian Mixture Model (GMM) and integrates conditional value-at-risk (CVaR) to ensure collision avoidance. The key component of ROVER is imposing a CVaR constraint on the distribution of the Signed Distance Function between the swarm GMM and obstacles in the FTMPC to enforce collision avoidance. Utilizing the analytical expression of CVaR of a GMM derived in this work, we develop a computationally efficient solution to solve the non-linear constrained FTMPC through sequential linear programming. Simulations and comparisons with representative benchmark approaches demonstrate the effectiveness of ROVER in flexibility, scalability, and safety guarantee.

Information-driven control can be used to develop intelligent sensors that can optimize their measurement value based on environmental feedback. In object tracking applications, sensor actions are chosen based on the expected reduction in uncertainty also known as information gain. Random finite set (RFS) theory provides a formalism for quantifying and estimating information gain in multi-object tracking problems. However, estimating information gain in these applications remains computationally challenging. This paper presents a new tractable approximation of the RFS expected information gain applicable to sensor control for multi-object search and tracking. Unlike existing RFS approaches, the information gain approximation presented in this paper considers the contributions of non-ideal noisy measurements, missed detections, false alarms, and object appearance/disappearance. The effectiveness of the information-driven sensor control is demonstrated through two multi-vehicle search-while-tracking experiments using real video data from remote terrestrial and satellite sensors.

Spike train decoding is considered one of the grand challenges in reverse-engineering neural control systems as well as in the development of neuromorphic controllers. This paper presents a novel relative-time kernel design that accounts for not only individual spike train patterns, but also the relative spike timing between neuron pairs in the population. The new relative-time-kernel-based spike train decoding method proposed in this paper allows us to map the spike trains of a population of neurons onto a lower-dimensional manifold, in which continuous-time trajectories live. The effectiveness of our novel approach is demonstrated by comparing it with existing kernel-based and rate-based decoders, including the traditional reproducing kernel Hilbert space framework. In this paper, we use the data collected in hawk moth flower tracking experiments to test the importance of relative spike timing information for neural control, and focus on the problem of uncovering the mapping from the spike trains of ten primary flight muscles to the resulting forces and torques on the moth body. We show that our new relative-time-kernel-based decoder improves the prediction of the resulting forces and torques by up to 52.1 %. Our proposed relative-time-kernel-based decoder may be used to reverse-engineer neural control systems more accurately by incorporating precise relative spike timing information in spike trains.

This paper develops a kernel nonlinear system identification approach to dual estimation problems. Given the observation model and the corresponding observation sequence, the unknown state transition function is approximated in the reproducing kernel Hilbert space (RKHS), while the corresponding hidden states are also estimated with the unscented Kalman smoother (UKS). To implement the dual estimation, the optimization solution of the proposed kernel expectation-maximization (EM) cost function is approximated based on the unscented transform (UT). Finally, the kernel nonlinear system identification method is applied to the noisy time-series estimation, where the data are generated by the IKEDA chaotic dynamical system with unknown system parameters. The simulation results show that the noisy data's signal-noise ratio (SNR) is improved significantly and is close to the SNR obtained with the accurate system model. Furthermore, the proposed non-parametric approach is compared with the parametric approach and outperforms obviously the parametric approach, even if the parameterized system model is assumed to be known.

Despite initially made for military purposes, drones have presented themselves to consumers, and the drone industry is expected to witness a significant growth during the forecast period. As the number of drones in the sky keeps growing, a fleet of drones and stationary zone service providers (ZSPs) can form an airborne network which is termed the Internet of Drones (IoD). In order to achieve the objectives of efficient information sharing and superior team performance, routing protocol plays a vital role for reliable communication in the IoD. However, malicious drones may strategically drop any received packets, and traditional mitigation techniques designed specially for mobile/vehicular ad hoc networks are unable to be directly applied in the IoD as a consequence of the intermittent connectivity between drones. In this paper, we propose a distributed countermeasure, also called CounterRomir, to detect and mitigate routing misbehavior in the IoD. In CounterRomir, a drone keeps the previous signed communication invoice and shares it with the next-hop drone so that the next-hop drone can detect whether the drone has dropped any packets or not. In consideration of a malicious drone likely misstating its communication invoice to avoid detection, each drone saves and sends a small number of past communication invoices to the ZSP which can detect the misstating drone. We develop a comprehensive simulation framework and conduct extensive simulation experiments using OMNeT++ for performance evaluation and analysis. After comparing with prior schemes, we come to the conclusion that CounterRomircan provide admirable performance in terms of detection rate, packet delivery ratio, miss/error detection rate, and the number of dropped packets, indicating an applicable approach against routing misbehavior in the IoD.

Even though drones are still in the infancy period in terms of widespread adoption and use, they have already pierced through solid conventional barriers in various domains of industry. As the usage of drones is becoming commonplace, a next generation aerial communication paradigm, Internet of Drones (IoD), has been proposed to further explore drone technology in a broad scope. IoD relies on the mobility of drones and intermittent drone-to-drone (D2D) and drone-to-ground station (D2I) communications for information sharing and exchange. Because of high mobility and resource constraints, IoD is defenseless to flooding attacks where an adversary sends an excessive amount of packets (original or replica) to legitimate drones with the intention of draining the limited IoD resources (i.e., communication bandwidth and drones' storage space). In this paper, we propose a lightweight distributed detection scheme, hereafter referred to as Lids, to defend against flooding attacks in the IoD environment. The basic idea of Lids is that each drone counts the number of packets that it has sent within a predefined time interval and shares the self-counting report with other drones during contacts. The receiving drones store the self-counting reports while flying and send them to nearby ground station which will check the consistency of self-counting reports to detect flooding attacks. For performance evaluation, we implement Lids and its counterparts (i.e., DAFA and LFADefender) in OMNeT++ network simulator and conduct extensive experiments in terms of detection ratio, miss detection ratio, detection latency, as well as energy consumption. Our experimental results indicate the superior performance of Lids to defend against flooding attacks in the IoD environment.

This paper develops a decentralized approach for mapping and information-driven path planning for Very Large Scale Robotic (VLSR) systems. In this approach, obstacle mapping is performed using a continuous probabilistic representation known as a Hilbert map, which formulates the mapping problem as a binary classification task and uses kernel logistic regression to train a discriminative classifier online. A novel Hilbert map fusion method is presented that quickly and efficiently combines the information from individual robot maps. An integrated mapping and path planning algorithm is presented to determine paths of maximum information value, while simultaneously performing obstacle avoidance. Furthermore, the effect of how percentage communication failure effects the overall performance of the system is investigated. The approach is demonstrated on a VLSR system with hundreds of robots that must map obstacles collaboratively over a large region of interest using onboard range sensors and no prior obstacle information. The results show that, through fusion and decentralized processing, the entropy of the map decreases over time and robot paths remain collision-free.

This paper develops a new indirect method for distributed optimal control (DOC) that is applicable to optimal planning for very-large-scale robotic (VLSR) systems in complex environments. The method is inspired by the nested analysis and design method known as generalized reduced gradient (GRG). The computational complexity analysis presented in this paper shows that the GRG method is significantly more efficient than classical optimal control or direct DOC methods. The GRG method is demonstrated for VLSR path planning in obstacle-populated environments in which robots are subject to external forces and disturbances. The results show that the method significantly improves performance compared to the existing direct DOC and stochastic gradient methods.

This paper presents a multi-layer reproducing kernel Hilbert space (RKHS) approach for probability distribution to real and probability distribution to function regressions. The approach maps the distributions into RKHS by distribution embeddings and, then, constructs a multi-layer RKHS within which the multi-kernel distribution regression can be implemented using an existing kernel regression algorithm, such as kernel recursive least squares (KRLS). The numerical simulations on synthetic data obtained via Gaussian mixtures show that the proposed approach outperforms existing probability distribution (DR) regression algorithms by achieving smaller mean squared errors (MSEs) and requiring less training samples.

This paper presents a camera control approach for learning unknown nonlinear target dynamics by approximating information value functions using particles that represent targets' position distributions. The target dynamics are described by a non-parametric mixture model that can learn a potentially infinite number of motion patterns. Assuming that each motion pattern can be represented as a velocity field, the target behaviors can be described by a non-parametric Dirichlet process-Gaussian process (DP-GP) mixture model. The DP-GP model has been successfully applied for clustering time-invariant spatial phenomena due to its flexibility to adapt to data complexity without overfitting. A new DP-GP information value function is presented that can be used by the sensor to explore and improve the DP-GP mixture model. The optimal camera control is computed to maximize this information value function online via a computationally efficient particle-based search method. The proposed approach is demonstrated through numerical simulations and hardware experiments in the RAVEN testbed at MIT.

This paper presents a visibility-based method for planning the motion of a mobile robotic sensor with bounded field-of-view to optimally track a moving target while localizing itself. The target and robot states are estimated from online sensor measurements and a set of a priori known landmarks, using an extended Kalman filter (EKF), and thus the proposed method is applicable to robots without a global positioning system. It is shown that the problem of optimizing the target tracking and robot localization performance is equivalent to optimizing the visibility or probability of detection in the EKF framework under mild assumptions. The control law that maximizes the probability of detection for a robotic sensor with a sector-shaped field-of-view (FoV) is derived as a function of the robot heading and aperture. Simulations have been conducted on synthetic experiments and the results show that the optimized-visibility approach is effective at avoiding target loss, and outperforms a state-of-the-art potential method based on robot trailer models [1].

This paper presents a kernelized version of recurrent systems (KRS) and develops a kernel real-time recurrent learning (KRTRL) algorithm to train KRS. To avoid instabilities during training, the teacher forcing technique is adopted to modify the KRTRL learning. The proposed algorithms compared with the KLMS in Lorenz time series prediction. The prediction performances of the proposed algorithm outperform the KLMS significantly.

This paper proposes a parameter-free kernel that is translation invariant and positive definite. The new kernel is based on the data cumulative distribution function (CDF) that provides all the statistical information about the observed samples. Without an explicit kernel size parameter, this novel kernel is used to define the autocorrentropy function, which is a generalized similarity measure, and spectral density estimator. Numerical examples show that the proposed method provides comparable performance to the existing Gaussian kernel with optimized kernel size.

In this paper, the extended kernel recursive least squares (Ex-KRLS) algorithm is reviewed and analyzed. We point out that the Theorem 1 in [10] is not always correct for general cases. Furthermore, the Ex-KRLS algorithm for tracking model is just a random walk KRLS algorithm. Finally, this algorithm is explained as a special Kalman filter in the reproducing kernel Hilbert space.

In a recent paper, we developed a novel quantized kernel least mean square algorithm, in which the input space is quantized (partitioned into smaller regions) and the network size is upper bounded by the quantization codebook size (number of the regions). In this paper, we propose the quantized kernel least squares regression, and derive the optimal solution. By incorporating a simple online vector quantization method, we derive a recursive algorithm to update the solution, namely the quantized kernel recursive least squares algorithm. The good performance of the new algorithm is demonstrated by Monte Carlo simulations.

In this paper, we propose a quantization approach, as an alternative of sparsification, to curb the growth of the radial basis function structure in kernel adaptive filtering. The basic idea behind this method is to quantize and hence compress the input (or feature) space. Different from sparsification, the new approach uses the "redundant" data to update the coefficient of the closest center. In particular, a quantized kernel least mean square (QKLMS) algorithm is developed, which is based on a simple online vector quantization method. The analytical study of the mean square convergence has been carried out. The energy conservation relation for QKLMS is established, and on this basis we arrive at a sufficient condition for mean square convergence, and a lower and upper bound on the theoretical value of the steady-state excess mean square error. Static function estimation and short-term chaotic time-series prediction examples are presented to demonstrate the excellent performance.

In this paper, a novel methodology is proposed to solve the state estimation problem combining the extended Kalman filter (EKF) with a kernel recursive least squares (KRLS) algorithm (EKF-KRLS). The EKF algorithm estimates hidden states in the input space, while the KRLS algorithm estimates the measurement model. The algorithm works well without knowing the linear or nonlinear measurement model. We apply this algorithm to vehicle tracking, and compare the performances with traditional Kalman filter, EKF and KRLS algorithms. Results demonstrate that the performance of the EKF-KRLS algorithm outperforms these existing algorithms. Especially when nonlinear measurement functions are applied, the advantage of the EKF-KRLS algorithm is very obvious.