Control Barrier Functions (CBFs) have become powerful tools for ensuring safety in nonlinear systems. How-ever, finding valid CBFs that guarantee persistent safety and feasibility remains an open challenge, especially in systems with input constraints. Traditional approaches often rely on manually tuning the parameters of the class$K$functions of the CBF conditions a priori. The performance of CBF-based controllers is highly sensitive to these fixed parameters, potentially leading to overly conservative behavior or safety violations. To overcome these issues, this paper introduces a learning-based optimal control framework for online adaptation of Input Constrained CBF (ICCBF) parameters in discrete-time nonlinear systems. Our method employs a probabilistic ensemble neural network to predict the performance and risk metrics, as defined in this work, for candidate parameters, accounting for both epistemic and aleatoric uncertainties. We propose a two-step verification process using Jensen-Rényi Divergence and distributionally-robust Conditional Value at Risk to identify valid parameters. This enables dynamic re-finement of ICCBF parameters based on current state and nearby environments, optimizing performance while ensuring safety within the verified parameter set. Experimental results demonstrate that our method outperforms both fixed-parameter and existing adaptive methods in robot navigation scenarios across safety and performance metrics. [Project Page]11Project page: https://www.taekyung.me/online-adaptive-cbf [Code] [Video]

In leader-follower consensus, strong$r$-robustness of the communication graph provides a sufficient condition for followers to achieve consensus in the presence of misbehaving agents. Previous studies have assumed that robots can form and/or switch between predetermined network topologies with known robustness properties. However, robots with distancebased communication models may not be able to achieve these topologies while moving through spatially constrained environments, such as narrow corridors, to complete their objectives. This paper introduces a Control Barrier Function (CBF) that ensures robots maintain strong$r$-robustness of their communication graph above a certain threshold without maintaining any fixed topologies. Our CBF directly addresses robustness, allowing robots to have flexible reconfigurable network structure while navigating to achieve their objectives. The efficacy of our method is tested through various simulation and hardware experiments [code] https://github.com/joonlee16/Resilient-Leader-Follower-CBF-QP.

This paper develops a control strategy for pursuit-evasion problems in environments with occlusions. We address the challenge of a mobile pursuer keeping a mobile evader within its field of view (FoV) despite line-of-sight obstructions. The signed distance function (SDF) of the FoV is used to formulate visibility as a control barrier function (CBF) constraint on the pursuer's control inputs. Similarly, obstacle avoidance is formulated as a CBF constraint based on the SDF of the obstacle set. While the visibility and safety CBFs are Lipschitz continuous, they are not differentiable everywhere, necessitating the use of generalized gradients. To achieve non-myopic pursuit, we generate reference control trajectories leading to evader visibility using a sampling-based kinodynamic planner. The pursuer then tracks this reference via convex optimization under the CBF constraints. We validate our approach in CARLA simulations and real-world robot experiments, demonstrating successful visibility maintenance using only onboard sensing, even under severe occlusions and dynamic evader movements.

This paper develop a scheduling protocol for a team of autonomous robots that operate on long-term persistent tasks. The proposed framework, called meSch, accounts for the limited battery capacity of the robots and ensures that the robots return to charge their batteries one at a time at the single charging station. The protocol is applicable to general nonlinear robot models under certain assumptions, does not require robots to be deployed at different times, and can handle robots with different discharge rates. We further consider the case when the charging station is mobile and its state information is subject to uncertainty. The feasibility of the algorithm in terms of ensuring persistent charging is given under certain assumptions, while the efficacy of meSch is validated through simulation and hardware experiments. [Code]a[Video]b

Robot navigation in dynamic, crowded environments poses a significant challenge due to the inherent uncertainties in the obstacle model. In this work, we propose a risk-adaptive approach based on the Conditional Value-at-Risk Barrier Function (CVaR-BF), where the risk level is automatically adjusted to accept the minimum necessary risk, achieving a good performance in terms of safety and optimization feasibility under uncertainty. Additionally, we introduce a dynamic zone-based barrier function which characterizes the collision likelihood by evaluating the relative state between the robot and the obstacle. By integrating risk adaptation with this new function, our approach adaptively expands the safety margin, enabling the robot to proactively avoid obstacles in highly dynamic environments. Comparisons and ablation studies demonstrate that our method outperforms existing social navigation approaches, and validate the effectiveness of our proposed framework. [Paper Page] [Video] [Code].

Planning informative trajectories while considering the spatial distribution of the information over the environment, as well as constraints such as the robot’s limited battery capacity, makes the long-time horizon persistent coverage problem complex. Ergodic search methods consider the spatial distribution of environmental information while optimizing robot trajectories; however, current methods lack the ability to construct the target information spatial distribution for environments that vary stochastically across space and time. Moreover, current coverage methods dealing with battery capacity constraints either assume simple robot and battery models or are computationally expensive. To address these problems, we propose a framework called Eclares, in which our contribution is two-fold. 1) First, we propose a method to construct the target information spatial distribution for ergodic trajectory optimization using clarity, an information measure bounded between [0, 1]. The clarity dynamics allow us to capture information decay due to a lack of measurements and to quantify the maximum attainable information in stochastic spatiotemporal environments. 2) Second, instead of directly tracking the ergodic trajectory, we introduce the energy-aware (eware) filter, which iteratively validates the ergodic trajectory to ensure that the robot has enough energy to return to the charging station when needed. The proposed eware filter is applicable to nonlinear robot models and is computationally lightweight. We demonstrate the working of the framework through a simulation case study. [Code]a[Video]b

Abstract Distributed architectures are used to improve performance and reliability of various systems. Examples include drone swarms and load-balancing servers. An important capability of a distributed architecture is the ability to reach consensus among all its nodes. Several consensus algorithms have been proposed, and many of these algorithms come with intricate proofs of correctness, that are not mechanically checked. In the controls community, algorithms often achieve consensusasymptotically, e.g., for problems such as the design of human control systems, or the analysis of natural systems like bird flocking. This is in contrast to exact consensus algorithm such as Paxos, which have received much more recent attention in the formal methods community. This paper presents the first formal proof of an asymptotic consensus algorithm, and addresses various challenges in its formalization. Using the Coq proof assistant, we verify the correctness of a widely used consensus algorithm in the distributed controls community, theWeighted-Mean Subsequence Reduced (W-MSR) algorithm. We formalize the necessary and sufficient conditions required to achieve resilient asymptotic consensus under the assumed attacker model. During the formalization, we clarify several imprecisions in the paper proof, including an imprecision on quantifiers in the main theorem.

This article presents thegatekeeperalgorithm, a real-time and computationally lightweight method that ensures that trajectories of a nonlinear system satisfy safety constraints despite sensing limitations.gatekeeperintegrates with existing path planners and feedback controllers by introducing an additional verification step to ensure that proposed trajectories can be executed safely, despite nonlinear dynamics subject to bounded disturbances, input constraints, and partial knowledge of the environment. Our key contribution is that 1) we propose an algorithm to recursively construct safe trajectories by numerically forward propagating the system over a (short) finite horizon, and 2) we prove that tracking such a trajectory ensures the system remains safe for all future time, i.e., beyond the finite horizon. We demonstrate the method in a simulation of a dynamic firefighting mission, and in physical experiments of a quadrotor navigating in an obstacle environment that is sensed online. We also provide comparisons against the state-of-the-art techniques for similar problems.

We propose a novel class of risk-aware control barrier functions (RA-CBFs) for the control of stochastic safety-critical systems. Leveraging a result from the stochastic level-crossing literature, we deviate from the martingale theory that is currently used in stochastic CBF techniques and prove that a RA-CBF based control synthesis confers a tighter upper bound on the probability of the system becoming unsafe within a finite time interval than existing approaches. We highlight the advantages of our proposed approach over the state-of-the-art via a comparative study on an mobile-robot example, and further demonstrate its viability on an autonomous vehicle highway merging problem in dense traffic.

This paper presents the gatekeeper algorithm, a real-time and computationally-lightweight method to ensure that nonlinear systems can operate safely in dynamic environments despite limited perception. gatekeeper integrates with existing path planners and feedback controllers by introducing an additional verification step that ensures that proposed trajectories can be executed safely, despite nonlinear dynamics subject to bounded disturbances, input constraints and partial knowledge of the environment. Our key contribution is that (A) we propose an algorithm to recursively construct committed trajectories, and (B) we prove that tracking the committed trajectory ensures the system is safe for all time into the future. The method is demonstrated on a complicated firefighting mission in a dynamic environment, and compares against the state-of-the-art techniques for similar problems.

This article presents a multimode solution to the problem of defending a circular protected area (target) from a wide range of attacks by swarms ofrisk-takingand/orrisk-averseattacking agents (attackers). The proposed multimode solution combines two defense strategies, namely: 1) an interception strategy for a team of defenders to intercept multiplerisk-takingattackers while ensuring that the defenders do not collide with each other; 2) a herding strategy to herd a swarm ofrisk-averseattackers to a safe area. In particular, we develop mixed integer programs (MIPs) and geometry-inspired heuristics to distribute and assign and/or reassign the defenders to interception and herding tasks under different spatiotemporal behaviors by the attackers such as splitting into smaller swarms to evade defenders easily or high-speed maneuvers by some risk-taking attackers to maximize damage to the protected area. We provide theoretical as well as numerical comparison of the computational costs of these MIPs and the heuristics, and demonstrate the overall approach in simulations.

Quadratic Program(QP) based state-feedback controllers, whose inequality constraints bound the rate of change of control barrier (CBFs) and lyapunov function with a class-$\mathcal{K}$function of their values, are sensitive to the parameters of these class-$\mathcal{K}$functions. The construction of valid CBFs, however, is not straightforward, and for arbitrarily chosen parameters of the QP, the system trajectories may enter states at which the QP either eventually becomes infeasible, or may not achieve desired performance. In this work, we pose the control synthesis problem as a differential policy whose parameters are optimized for performance over a time horizon at high level, thus resulting in a bi-level optimization routine. In the absence of knowledge of the set of feasible parameters, we develop a Recursive Feasibility Guided Gradient Descent approach for updating the parameters of QP so that the new solution performs at least as well as previous solution. By considering the dynamical system as a directed graph over time, this work presents a novel way of optimizing performance of a QP controller over a time horizon for multiple CBFs by (1) using the gradient of its solution with respect to its parameters by employing sensitivity analysis, and (2) backpropagating these as well as system dynamics gradients to update parameters while maintaining feasibility of QPs.

This article presents a novel method for a class of multirobot networks to resiliently propagate vector messages from a set of leaders to all followers within the network in the presence of faulty or adversarially behaving robots. It is shown that the proposed method can operate under heterogeneous communication rates between robots and perturbations of the leaders’ propagated information. As a case study, the proposed method is applied to the problem of time-varying trajectory tracking; more specifically, time-varying reference trajectories in the form of Bezier curves are encoded into vectors of static parameters, which, in turn, are resiliently propagated from the leaders to the followers.

This article presents a method for herding a swarm of adversarial agents toward a safe area in a 2-D obstacle environment. The team of defending agents (defenders) aims to block the path of a swarm of risk-averse, adversarial agents (attackers) and guide it to a safe area while navigating in an obstacle-populated environment. To achieve this, a closed formation (StringNet) of defenders is formed around the adversarial swarm. A combination of open-loop, near time-optimal controllers (that result in forming the defenders’ formation), and state-feedback controllers with finite-time convergence guarantees under bounded inputs (that guide the formation around attackers and toward the safe area) synthesize the herding strategy. For demonstration purpose, we consider that the attacking swarm moves under a flocking model, which however is unknown to the defenders. Collision-free trajectory generation for the defenders, as well as their convergence to the desired formations, is proved formally, and simulations are provided to demonstrate the efficacy of the proposed approach. An implementation of the proposed approach on quadrotor vehicles simulated in the Gazebo simulator is also provided.

This paper presents a novel method by which an assistive aerial robot can learn the relevant camera views within a task domain through tracking the head motions of a human collaborator. The human's visual field is modeled as an anisotropic spherical sensor, which decays in acuity towards the periphery, and is integrated in time throughout the domain. This data is resampled and fed into an expectation maximization solver in order to estimate the environment's visual interest as a mixture of Gaussians. A dynamic coverage control law directs the robot to capture camera views of the peaks of these Gaussians which is broadcast to an augmented reality display worn by the human operator. An experimental study is presented that assesses the influence of the assistive robot on reflex time, head motion, and task completion time.

This paper presents a novel method for generating the trajectory of a robot assisting a human in servicing a set of tasks embedded in a convex 2-D domain. This method makes use of Bayesian inference to predict human intent in task selection. Rather than following optimal trajectory towards a single task, the robot computes a set of potentially optimal tasks each weighted by the human's posterior probability and superimposes them into a cost function that is designed to minimize the weighted Euclidean distance relative to set. The effect is a flexible path human-robot collaborative network that is shown in simulation to complete all tasks in a given domain in less time than existing methods for a certain class of highly impulsive humans, i.e., humans that tend to randomly switch tasks at times generated by a Poisson counting process. The algorithm is also illustrated through an experimental demonstration.

This paper presents a novel method on the motion and path planning for unicycle robots in environments with static circular obstacles. The method employs a family of 2-dimensional analytic vector fields, which have singular points of high-order type and whose integral curves exhibit various patterns depending on the value of a parameter λ. More specifically, for a known value of λ the vector field has a unique singular point of dipole type and its integral curves are suitable for steering the unicycle to a goal configuration. Furthermore, for the value of λ that the vector field has a continuum of singular points, the integral curves can be used to define flows around circular obstacles. An almost global feedback motion plan is then constructed by suitably blending attractive and repulsive vector fields in a static obstacle environment. The proposed motion planning and control design is also extended to the multi-agent case, where each agent needs to converge to a desired configuration while avoiding collisions with other agents. The efficacy of the approach is demonstrated via simulation results.

This paper considers the problem of decentralized goal assignment and trajectory generation for multi-robot networks when only local communication is available, and proposes an approach based on methods related to switched systems and set invariance. A family of Lyapunov-like functions is employed to encode the (local) decision making among candidate goal assignments, under which the agents pick the assignment which results in the shortest total distance to the goals. An additional family of Lyapunov-like barrier functions is activated in the case when the optimal assignment may lead to colliding trajectories, thus maintaining system safety while preserving the convergence guarantees. The proposed switching strategies give rise to feedback control policies which are scalable as the number of agents increases, and therefore are suitable for applications including first-response deployment of robotic networks under limited information sharing. Simulations demonstrate the efficacy of the proposed method.

Vision-based formation control of multiple agents, such as mobile robots or fully autonomous cars, has recently received great interest due to its application in robotic networks and automated highways. This paper addresses the cooperative motion coordination of leader-follower formations of nonholonomic mobile robots, under visibility and communication constraints in known polygonal obstacle environments. We initially consider the case of N = 2 agents moving in L-F fashion and propose a feedback control strategy under which L ensures obstacle avoidance for both robots, while F ensures visibility maintenance with L and intervehicle collision avoidance. The derived algorithms are based on set-theoretic methods to guarantee visibility maintenance, dipolar vector fields to maintain the formation shape, and the consideration of the formation as a tractor-trailer system to ensure obstacle avoidance. We furthermore show how the coordination and control design extends to the case of N > 2 agents, and provide simulation results, which demonstrate the efficacy of the control solutions. The proposed algorithms do not require information exchange among robots, but are instead based on information locally available to each agent. In this way, the desired tasks are executed and achieved in a decentralized manner, with each robot taking care of converging to a desired configuration, while maintaining visibility with its target.

This paper presents a Leader-Follower formation control strategy for underactuated marine vehicles which move under sensing and communication constraints in the presence of bounded persistent environmental disturbances. We assume that the vehicles do not communicate for exchanging information regarding on their states (pose and velocities), and that their sensing capabilities are restricted, due to limited range and angle-of-view. Sensing constraints are thus realized as a set of inequality state constraints which should never be violated (viability constraints). The viability constraints define a closed subset K of the configuration space (viability set K). The control objective is thus reduced into to coordinating the motion of the vehicles in a Leader-Follower formation, while system trajectories starting in K always remain viable in K. The proposed control design employs dipolar vector fields and a viability-based switching control scheme, which guarantees that system viability is always maintained. The efficacy of the proposed algorithm, as well as its relevance with surveillance of (stationary) targets are demonstrated through simulations.

This paper addresses the problem of controlling a leader-follower (L - F) formation of two unicycle mobile robots moving under visibility constraints in a known obstacle environment. Visibility constraints are realized as inequality state constraints that determine a visibility set K. Maintaining visibility is translated into controlling the robots so that system trajectories starting in K always remain in K. We provide the conditions under which visibility is maintained, as well as a feedback control scheme that forces F to converge and remain into a set of desired configurations w.r.t. L while maintaining visibility. We also propose a cooperative control scheme for the motion of the formation in a known obstacle environment, so that both collision avoidance and maintaining visibility are ensured. The proposed control schemes are decentralized, in the sense that there is no direct communication between the robots. The efficacy of our algorithms is evaluated through simulations.

This paper presents a solution to the robust practical stabilization of a unicycle-like marine vehicle, under non vanishing current-induced perturbations. A hysteresis-based switching control strategy is proposed, rendering the system globally practically stable to a set G around the origin. The control scheme consists of three control laws; the first one is active out of G and drives the system trajectories into G, based on a dipole-like vector field. The other two control laws are active in G and alternately regulate the position and the orientation of the vehicle. The system is shown to be robust, in the sense that the vehicle enters and remains into G even if only a maximum bound of the perturbation is known. The efficacy of the solution is demonstrated through simulation results.

This paper introduces a framework that guides the design of stabilizing feedback control laws for systems with Pfaffian constraints. A new class of N-dimensional vector fields, the dipole-like vector fields is proposed, inspired by the form of the flow lines of the electric point dipole. A general connection between the dipole-like field and the Pfaffian constraints of catastatic nonholonomic systems is exploited, to establish systematic guidelines on the design of stabilizing control laws. The methodology is applied to the stabilization of the unicycle and of the nonholonomic double integrator. Based on these guidelines, switching control laws are constructed. The efficacy of the methodology is demonstrated through simulation results.