Safety-Critical Control with Uncertainty Quantification using Adaptive Conformal Prediction

Safety assurance is critical in the planning and control of robotic systems. For robots operating in the real world, the safety-critical design often needs to explicitly address uncertainties and the pre-computed guarantees often rely on the assumption of the particular distribution of the uncertainty. However, it is difficult to characterize the actual uncertainty distribution beforehand and thus the established safety guarantee may be violated due to possible distribution mismatch. In this paper, we propose a novel safe control framework that provides a high-probability safety guarantee for stochastic dynamical systems following unknown distributions of motion noise. Specifically, this framework adopts adaptive conformal prediction to dynamically quantify the prediction uncertainty from online observations and combines that with the probabilistic extension of the control barrier functions (CBFs) to characterize the uncertainty-aware control constraints. By integrating the constraints in the model predictive control scheme, it allows robots to adaptively capture the true prediction uncertainty online in a distribution-free setting and enjoys formally provable high-probability safety assurance. Simulation results on multi-robot systems with stochastic single-integrator dynamics and unicycle dynamics are provided to demonstrate the effectiveness of our framework.

Decentralized Multi-Robot Line-of-Sight Connectivity Maintenance under Uncertainty

In this paper, we propose a novel decentralized control method to maintain Line-of-Sight connectivity for multi-robot networks in the presence of Guassian-distributed localization uncertainty. In contrast to most existing work that assumes perfect positional information about robots or enforces overly restrictive rigid formation against uncertainty, our method enables robots to preserve Line-of-Sight connectivity with high probability under unbounded Gaussian-like positional noises while remaining minimally intrusive to the original robots' tasks. This is achieved by a motion coordination framework that jointly optimizes the set of existing Line-of-Sight edges to preserve and control revisions to the nominal task-related controllers, subject to the safety constraints and the corresponding composition of uncertainty-aware Line-of-Sight control constraints. Such compositional control constraints, expressed by our novel notion of probabilistic Line-of-Sight connectivity barrier certificates (PrLOS-CBC) for pairwise robots using control barrier functions, explicitly characterize the deterministic admissible control space for the two robots. The resulting motion ensures Line-of-Sight connectedness for the robot team with high probability. Furthermore, we propose a fully decentralized algorithm that decomposes the motion coordination framework by interleaving the composite constraint specification and solving for the resulting optimization-based controllers. The optimality of our approach is justified by the theoretical proofs. Simulation and real-world experiments results are given to demonstrate the effectiveness of our method.

Occlusion-Free Image Based Visual Servoing using Probabilistic Control Barrier Certificates

Image-based visual servoing (IBVS) is a widely-used approach in robotics that employs visual information to guide robots towards desired positions. However, occlusions in this approach can lead to visual servoing failure and degrade the control performance due to the obstructed vision feature points that are essential for providing visual feedback. In this paper, we propose a Control Barrier Function (CBF) based controller that enables occlusion-free IBVS tasks by automatically adjusting the robot's configuration to keep the feature points in the field of view and away from obstacles. In particular, to account for measurement noise of the feature points, we develop the Probabilistic Control Barrier Certificates (PrCBC) using control barrier functions that encode the chance-constrained occlusion avoidance constraints under uncertainty into deterministic admissible control space for the robot, from which the resulting configuration of robot ensures that the feature points stay occlusion free from obstacles with a satisfying predefined probability. By integrating such constraints with a Model Predictive Control (MPC) framework, the sequence of optimized control inputs can be derived to achieve the primary IBVS task while enforcing the occlusion avoidance during robot movements. Simulation results are provided to validate the performance of our proposed method.

A Depth-Adaptive Filtering Method for Effective GPR Tree Roots Detection in Tropical Area

This study presents a technique for processing Stepfrequency continuous wave (SFCW) ground penetrating radar (GPR) data to detect tree roots. SFCW GPR is portable and enables precise control of energy levels, balancing depth and resolution trade-offs. However, the high-frequency components of the transmission band suffers from poor penetrating capability and generates noise that interferes with root detection. The proposed time-frequency filtering technique uses a short-time Fourier transform (STFT) to track changes in frequency spectrum density over time. To obtain the filter window, a weighted linear regression (WLR) method is used. By adopting a conversion method that is a variant of the chirp Z-Transform (CZT), the timefrequency window filters out frequency samples that are not of interest when doing the frequency-to-time domain data conversion. The proposed depth-adaptive filter window can selfadjust to different scenarios, making it independent of soil information and effectively determines subsurface tree roots. The technique is successfully validated using SFCW GPR data from actual sites in a tropical area with different soil moisture levels, and the two-dimensional (2D) radar map of subsurface root systems is highly improved compared to existing methods.

Risk-aware Safe Control for Decentralized Multi-agent Systems via Dynamic Responsibility Allocation

Decentralized control schemes are increasingly favored in various domains that involve multi-agent systems due to the need for computational efficiency as well as general applicability to large-scale systems. However, in the absence of an explicit global coordinator, it is hard for distributed agents to determine how to efficiently interact with others. In this paper, we present a risk-aware decentralized control framework that provides guidance on how much relative responsibility share (a percentage) an individual agent should take to avoid collisions with others while moving efficiently without direct communications. We propose a novel Control Barrier Function (CBF)-inspired risk measurement to characterize the aggregate risk agents face from potential collisions under motion uncertainty. We use this measurement to allocate responsibility shares among agents dynamically and develop risk-aware decentralized safe controllers. In this way, we are able to leverage the flexibility of robots with lower risk to improve the motion flexibility for those with higher risk, thus achieving improved collective safety. We demonstrate the validity and efficiency of our proposed approach through two examples: ramp merging in autonomous driving and a multi-agent position-swapping game.

Minimally Constrained Multi-Robot Coordination with Line-of-sight Connectivity Maintenance

In this paper, we consider a team of mobile robots executing simultaneously multiple behaviors by different subgroups, while maintaining global and subgroup line-of-sight (LOS) network connectivity that minimally constrains the original multi-robot behaviors. The LOS connectivity between pairwise robots is preserved when two robots stay within the limited communication range and their LOS remains occlusion-free from static obstacles while moving. By using control barrier functions (CBF) and minimum volume enclosing ellipsoids (MVEE), we first introduce the LOS connectivity barrier certificate (LOS-CBC) to characterize the state-dependent admissible control space for pairwise robots, from which their resulting motion will keep the two robots LOS connected over time. We then propose the Minimum Line-of-Sight Connectivity Constraint Spanning Tree (MLCCST) as a step-wise bilevel optimization framework to jointly optimize (a) the minimum set of LOS edges to actively maintain, and (b) the control revision with respect to a nominal multi-robot controller due to LOS connectivity maintenance. As proved in the theoretical analysis, this allows the robots to improvise the optimal composition of LOS-CBC control constraints that are least constraining around the nominal controllers, and at the same time enforce the global and subgroup LOS connectivity through the resulting preserved set of pairwise LOS edges. The framework thus leads to robots staying as close to their nominal behaviors, while exhibiting dynamically changing LOS-connected network topology that provides the greatest flexibility for the existing multi-robot tasks in real time. We demonstrate the effectiveness of our approach through simulations with up to 64 robots.

Sample-efficient Safe Learning for Online Nonlinear Control with Control Barrier Functions

Reinforcement Learning (RL) and continuous nonlinear control have been successfully deployed in multiple domains of complicated sequential decision-making tasks. However, given the exploration nature of the learning process and the presence of model uncertainty, it is challenging to apply them to safety-critical control tasks due to the lack of safety guarantee. On the other hand, while combining control-theoretical approaches with learning algorithms has shown promise in safe RL applications, the sample efficiency of safe data collection process for control is not well addressed. In this paper, we propose a \emph{provably} sample efficient episodic safe learning framework for online control tasks that leverages safe exploration and exploitation in an unknown, nonlinear dynamical system. In particular, the framework 1) extends control barrier functions (CBFs) in a stochastic setting to achieve provable high-probability safety under uncertainty during model learning and 2) integrates an optimism-based exploration strategy to efficiently guide the safe exploration process with learned dynamics for \emph{near optimal} control performance. We provide formal analysis on the episodic regret bound against the optimal controller and probabilistic safety with theoretical guarantees. Simulation results are provided to demonstrate the effectiveness and efficiency of the proposed algorithm.

Responsibility-associated Multi-agent Collision Avoidance with Social Preferences

This paper introduces a novel social preference-aware decentralized safe control framework to address the responsibility allocation problem in multi-agent collision avoidance. Considering that agents do not necessarily cooperate in symmetric ways, this paper focuses on semi-cooperative behavior among heterogeneous agents with varying cooperation levels. Drawing upon the idea of Social Value Orientation (SVO) for quantifying the individual selfishness, we propose a novel concept of Responsibility-associated Social Value Orientation (R-SVO) to express the intended relative social implications between pairwise agents. This is used to redefine each agent's social preferences or personalities in terms of corresponding responsibility shares in contributing to the coordination scenario, such as semi-cooperative collision avoidance where all agents interact in an asymmetric way. By incorporating such relative social implications through proposed Local Pairwise Responsibility Weights, we develop a Responsibility-associated Control Barrier Function-based safe control framework for individual agents, and multi-agent collision avoidance is achieved with formally provable safety guarantees. Simulations are provided to demonstrate the effectiveness and efficiency of the proposed framework in several multi-agent navigation tasks, such as a position-swapping game, a self-driving car highway ramp merging scenario, and a circular position swapping game.

Accurate Tree Roots Positioning and Sizing over Undulated Ground Surfaces by Common Offset GPR Measurements

Tree roots detection is a popular application of the Ground-penetrating radar (GPR). Normally, the ground surface above the tree roots is assumed to be flat, and standard processing methods based on hyperbolic fitting are applied to the hyperbolae reflection patterns of tree roots for detection purposes. When the surface of the land is undulating (not flat), these typical hyperbolic fitting methods becomes inaccurate. This is because, the reflection patterns change with the uneven ground surfaces. When the soil surface is not flat, it is inaccurate to use the peak point of an asymmetric reflection pattern to identify the depth and horizontal position of the underground target. The reflection patterns of the complex shapes due to extreme surface variations results in analysis difficulties. Furthermore, when multiple objects are buried under an undulating ground, it is hard to judge their relative positions based on a B-scan that assumes a flat ground. In this paper, a roots fitting method based on electromagnetic waves (EM) travel time analysis is proposed to take into consideration the realistic undulating ground surface. A wheel-based (WB) GPR and an antenna-height-fixed (AHF) GPR System are presented, and their corresponding fitting models are proposed. The effectiveness of the proposed method is demonstrated and validated through numerical examples and field experiments.

Dual-Cross-Polarized GPR Measurement Method for Detection and Orientation Estimation of Shallowly Buried Elongated Object

Detecting a shallowly buried and elongated object and estimating its orientation using a commonly adopted co-polarized GPR system is challenging due to the presence of strong ground clutter that masks the target reflection. A cross-polarized configuration can be used to suppress ground clutter and reveal the object reflection, but it suffers from inconsistent detection capability which significantly varies with different object orientations. To address this issue, we propose a dual-cross-polarized detection (DCPD) method which utilizes two cross-polarized antennas with a special arrangement to detect the object. The signals reflected by the object and collected by the two antennas are combined in a rotationally invariant manner to ensure both effective ground clutter suppression and consistent detection irrespective of the object orientation. In addition, we present a dual-cross-polarized orientation estimation (DCPOE) algorithm to estimate the object orientation from the two cross-polarized data. The proposed DCPOE algorithm is less affected by environmental noise and performs robust and accurate azimuth angle estimation. The effectiveness of the proposed techniques in the detection and orientation estimation and their advantages over the existing method have been demonstrated using experimental data. Comparison results show that the maximum and average errors are 22.3{\deg} and 10.9{\deg} for the Alford rotation algorithm, while those are 4.9{\deg} and 1.8{\deg} for the proposed DCPOE algorithm in the demonstrated shallowly buried object cases. The proposed techniques can be unified in a framework to facilitate the investigation and mapping of shallowly buried and elongated targets.