Recursive Least Squares with Fading Regularization for Finite-Time Convergence without Persistent Excitation

This paper extends recursive least squares (RLS) to include time-varying regularization. This extension provides flexibility for updating the least squares regularization term in real time. Existing results with constant regularization imply that the parameter-estimation error dynamics of RLS are globally attractive to zero if and only the regressor is weakly persistently exciting. This work shows that, by extending classical RLS to include a time-varying (fading) regularization term that converges to zero, the parameter-estimation error dynamics are globally attractive to zero without weakly persistent excitation. Moreover, if the fading regularization term converges to zero in finite time, then the parameter estimation error also converges to zero in finite time. Finally, we propose rank-1 fading regularization (R1FR) RLS, a time-varying regularization algorithm with fading regularization that converges to zero, and which runs in the same computational complexity as classical RLS. Numerical examples are presented to validate theoretical guarantees and to show how R1FR-RLS can protect against over-regularization.

Risk-aware MPPI for Stochastic Hybrid Systems

Path Planning for stochastic hybrid systems presents a unique challenge of predicting distributions of future states subject to a state-dependent dynamics switching function. In this work, we propose a variant of Model Predictive Path Integral Control (MPPI) to plan kinodynamic paths for such systems. Monte Carlo may be inaccurate when few samples are chosen to predict future states under state-dependent disturbances. We employ recently proposed Unscented Transform-based methods to capture stochasticity in the states as well as the state-dependent switching surfaces. This is in contrast to previous works that perform switching based only on the mean of predicted states. We focus our motion planning application on the navigation of a mobile robot in the presence of dynamically moving agents whose responses are based on sensor-constrained attention zones. We evaluate our framework on a simulated mobile robot and show faster convergence to a goal without collisions when the robot exploits the hybrid human dynamics versus when it does not.

Control Strategies for Pursuit-Evasion Under Occlusion Using Visibility and Safety Barrier Functions

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.

Learning to Refine Input Constrained Control Barrier Functions via Uncertainty-Aware Online Parameter Adaptation

Control Barrier Functions (CBFs) have become powerful tools for ensuring safety in nonlinear systems. However, 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-Renyi Divergence and distributionally-robust Conditional Value at Risk to identify valid parameters. This enables dynamic refinement 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.

Visibility-Aware RRT* for Safety-Critical Navigation of Perception-Limited Robots in Unknown Environments

Safe autonomous navigation in unknown environments remains a critical challenge for robots with limited sensing capabilities. While safety-critical control techniques, such as Control Barrier Functions (CBFs), have been proposed to ensure safety, their effectiveness relies on the assumption that the robot has complete knowledge of its surroundings. In reality, robots often operate with restricted field-of-view and finite sensing range, which can lead to collisions with unknown obstacles if the planning algorithm is agnostic to these limitations. To address this issue, we introduce the visibility-aware RRT* algorithm that combines sampling-based planning with CBFs to generate safe and efficient global reference paths in partially unknown environments. The algorithm incorporates a collision avoidance CBF and a novel visibility CBF, which guarantees that the robot remains within locally collision-free regions, enabling timely detection and avoidance of unknown obstacles. We conduct extensive experiments interfacing the path planners with two different safety-critical controllers, wherein our method outperforms all other compared baselines across both safety and efficiency aspects.

meSch: Multi-Agent Energy-Aware Scheduling for Task Persistence

This paper develops a scheduling protocol for a team of autonomous robots that operate in long-term persistent tasks. The proposed framework, called meSch, accounts for the robots' limited battery capacity and the presence of a single charging station, and achieves the following contributions: 1) First, it guarantees exclusive use of the charging station by one robot at a time; the approach is online, applicable to general nonlinear robot models, does not require robots to be deployed at different times, and can handle robots with different discharge rates. 2) Second, we consider the scenario when the charging station is mobile and subject to uncertainty. This approach ensures that the robots can rendezvous with the charging station while considering the uncertainty in its position. Finally, we provide the evaluation of the efficacy of meSch in simulation and experimental case studies.

Multi-Agent Clarity-Aware Dynamic Coverage with Gaussian Processes

This paper presents two algorithms for multi-agent dynamic coverage in spatiotemporal environments, where the coverage algorithms are informed by the method of data assimilation. In particular, we show that by considering the information assimilation algorithm, here a Numerical Gaussian Process Kalman Filter, the influence of measurements taken at one position on the uncertainty of the estimate at another location can be computed. We use this relationship to propose new coverage algorithms. Furthermore, we show that the controllers naturally extend to the multi-agent context, allowing for a distributed-control central-information paradigm for multi-agent coverage. Finally, we demonstrate the algorithms through a realistic simulation of a team of UAVs collecting wind data over a region in Austria.

A Constructive Method for Designing Safe Multirate Controllers for Differentially-Flat Systems

We present a multi-rate control architecture that leverages fundamental properties of differential flatness to synthesize controllers for safety-critical nonlinear dynamical systems. We propose a two-layer architecture, where the high-level generates reference trajectories using a linear Model Predictive Controller, and the low-level tracks this reference using a feedback controller. The novelty lies in how we couple these layers, to achieve formal guarantees on recursive feasibility of the MPC problem, and safety of the nonlinear system. Furthermore, using differential flatness, we provide a constructive means to synthesize the multi-rate controller, thereby removing the need to search for suitable Lyapunov or barrier functions, or to approximately linearize/discretize nonlinear dynamics. We show the synthesized controller is a convex optimization problem, making it amenable to real-time implementations. The method is demonstrated experimentally on a ground rover and a quadruped robotic system.

Online and Certifiably Correct Visual Odometry and Mapping

This paper proposes two new algorithms for certified perception in safety-critical robotic applications. The first is a Certified Visual Odometry algorithm, which uses a RGBD camera with bounded sensor noise to construct a visual odometry estimate with provable error bounds. The second is a Certified Mapping algorithm which, using the same RGBD images, constructs a Signed Distance Field of the obstacle environment, always safely underestimating the distance to the nearest obstacle. This is required to avoid errors due to VO drift. The algorithms are demonstrated in hardware experiments, where we demonstrate both running online at 30FPS. The methods are also compared to state-of-the-art techniques for odometry and mapping.

Feasible Space Monitoring for Multiple Control Barrier Functions with application to Large Scale Indoor Navigation

Quadratic programs (QP) subject to multiple time-dependent control barrier function (CBF) based constraints have been used to design safety-critical controllers. However, ensuring the existence of a solution at all times to the QP subject to multiple CBF constraints is non-trivial. We quantify the feasible solution space of the QP in terms of its volume. We introduce a novel feasible space volume monitoring control barrier function that promotes compatibility of barrier functions and, hence, existence of a solution at all times. We show empirically that our approach not only enhances feasibility but also exhibits reduced sensitivity to changes in the hyperparameters such as gains of nominal controller. Finally, paired with a global planner, we evaluate our controller for navigation among humans in the AWS Hospital gazebo environment. The proposed controller is demonstrated to outperform the standard CBF-QP controller in maintaining feasibility.