Control Barrier Functions (CBFs) are a practical approach for designing safety-critical controllers, but constructing them for arbitrary nonlinear dynamical systems remains a challenge. Recent efforts have explored learning-based methods, such as neural CBFs (NCBFs), to address this issue. However, ensuring the validity of NCBFs is difficult due to potential learning errors. In this letter, we propose a novel framework that leverages split-conformal prediction to generate formally verified neural CBFs with probabilistic guarantees based on a user-defined error rate, referred to as CP-NCBF. Unlike existing methods that impose Lipschitz constraints on neural CBF-leading to scalability limitations and overly conservative safe sets--our approach is sample-efficient, scalable, and results in less restrictive safety regions. We validate our framework through case studies on obstacle avoidance in autonomous driving and geo-fencing of aerial vehicles, demonstrating its ability to generate larger and less conservative safe sets compared to conventional techniques.

Ensuring safe and generalizable control remains a fundamental challenge in robotics, particularly when deploying imitation learning in dynamic environments. Traditional behavior cloning (BC) struggles to generalize beyond its training distribution, as it lacks an understanding of the safety critical reasoning behind expert demonstrations. To address this limitation, we propose GenOSIL, a novel imitation learning framework that explicitly incorporates environment parameters into policy learning via a structured latent representation. Unlike conventional methods that treat the environment as a black box, GenOSIL employs a variational autoencoder (VAE) to encode measurable safety parameters such as obstacle position, velocity, and geometry into a latent space that captures intrinsic correlations between expert behavior and environmental constraints. This enables the policy to infer the rationale behind expert trajectories rather than merely replicating them. We validate our approach on two robotic platforms an autonomous ground vehicle and a Franka Emika Panda manipulator demonstrating superior safety and goal reaching performance compared to baseline methods. The simulation and hardware videos can be viewed on the project webpage: https://mumukshtayal.github.io/GenOSIL/.

As autonomous systems become more ubiquitous in daily life, ensuring high performance with guaranteed safety is crucial. However, safety and performance could be competing objectives, which makes their co-optimization difficult. Learning-based methods, such as Constrained Reinforcement Learning (CRL), achieve strong performance but lack formal safety guarantees due to safety being enforced as soft constraints, limiting their use in safety-critical settings. Conversely, formal methods such as Hamilton-Jacobi (HJ) Reachability Analysis and Control Barrier Functions (CBFs) provide rigorous safety assurances but often neglect performance, resulting in overly conservative controllers. To bridge this gap, we formulate the co-optimization of safety and performance as a state-constrained optimal control problem, where performance objectives are encoded via a cost function and safety requirements are imposed as state constraints. We demonstrate that the resultant value function satisfies a Hamilton-Jacobi-Bellman (HJB) equation, which we approximate efficiently using a novel physics-informed machine learning framework. In addition, we introduce a conformal prediction-based verification strategy to quantify the learning errors, recovering a high-confidence safety value function, along with a probabilistic error bound on performance degradation. Through several case studies, we demonstrate the efficacy of the proposed framework in enabling scalable learning of safe and performant controllers for complex, high-dimensional autonomous systems.

Locomotion on unknown terrains is essential for bipedal robots to handle novel real-world challenges, thus expanding their utility in disaster response and exploration. In this work, we introduce a lightweight framework that learns a single walking controller that yields locomotion on multiple terrains. We have designed a real-time robot controller based on diffusion models, which not only captures multiple behaviours with different velocities in a single policy but also generalizes well for unseen terrains. Our controller learns with offline data, which is better than online learning in aspects like scalability, simplicity in training scheme etc. We have designed and implemented a diffusion model-based policy controller in simulation on our custom-made Bipedal Robot model named Stoch BiRo. We have demonstrated its generalization capability and high frequency control step generation relative to typical generative models, which require huge onboarding compute.

Safety is a fundamental requirement of control systems. Control Barrier Functions (CBFs) are proposed to ensure the safety of the control system by constructing safety filters or synthesizing control inputs. However, the safety guarantee and performance of safe controllers rely on the construction of valid CBFs. Inspired by universal approximatability, CBFs are represented by neural networks, known as neural CBFs (NCBFs). This paper presents an algorithm for synthesizing formally verified continuous-time neural Control Barrier Functions in stochastic environments in a single step. The proposed training process ensures efficacy across the entire state space with only a finite number of data points by constructing a sample-based learning framework for Stochastic Neural CBFs (SNCBFs). Our methodology eliminates the need for post hoc verification by enforcing Lipschitz bounds on the neural network, its Jacobian, and Hessian terms. We demonstrate the effectiveness of our approach through case studies on the inverted pendulum system and obstacle avoidance in autonomous driving, showcasing larger safe regions compared to baseline methods.

This work presents a unified approach for collision avoidance using Collision-Cone Control Barrier Functions (CBFs) in both ground (UGV) and aerial (UAV) unmanned vehicles. We propose a novel CBF formulation inspired by collision cones, to ensure safety by constraining the relative velocity between the vehicle and the obstacle to always point away from each other. The efficacy of this approach is demonstrated through simulations and hardware implementations on the TurtleBot, Stoch-Jeep, and Crazyflie 2.1 quadrotor robot, showcasing its effectiveness in avoiding collisions with dynamic obstacles in both ground and aerial settings. The real-time controller is developed using CBF Quadratic Programs (CBF-QPs). Comparative analysis with the state-of-the-art CBFs highlights the less conservative nature of the proposed approach. Overall, this research contributes to a novel control formation that can give a guarantee for collision avoidance in unmanned vehicles by modifying the control inputs from existing path-planning controllers.

This paper introduces the Stoch BiRo, a cost-effective bipedal robot designed with a modular mechanical structure having point feet to navigate uneven and unfamiliar terrains. The robot employs proprioceptive actuation in abduction, hips, and knees, leveraging a Raspberry Pi4 for control. Overcoming computational limitations, a Learning-based Linear Policy controller manages balance and locomotion with only 3 degrees of freedom (DoF) per leg, distinct from the typical 5DoF in bipedal systems. Integrated within a modular control architecture, these controllers enable autonomous handling of unforeseen terrain disturbances without external sensors or prior environment knowledge. The robot's policies are trained and simulated using MuJoCo, transferring learned behaviors to the Stoch BiRo hardware for initial walking validations. This work highlights the Stoch BiRo's adaptability and cost-effectiveness in mechanical design, control strategies, and autonomous navigation, promising diverse applications in real-world robotics scenarios.

In fields such as mining, search and rescue, and archaeological exploration, ensuring real-time, collision-free navigation of robots in confined, cluttered environments is imperative. Despite the value of established path planning algorithms, they often face challenges in convergence rates and handling dynamic infeasibilities. Alternative techniques like collision cones struggle to accurately represent complex obstacle geometries. This paper introduces a novel category of control barrier functions, known as Polygonal Cone Control Barrier Function (PolyC2BF), which addresses overestimation and computational complexity issues. The proposed PolyC2BF, formulated as a Quadratic Programming (QP) problem, proves effective in facilitating collision-free movement of multiple robots in complex environments. The efficacy of this approach is further demonstrated through PyBullet simulations on quadruped (unicycle model), and crazyflie 2.1 (quadrotor model) in cluttered environments.

Autonomy advances have enabled robots in diverse environments and close human interaction, necessitating controllers with formal safety guarantees. This paper introduces an experimental platform designed for the validation and demonstration of a novel class of Control Barrier Functions (CBFs) tailored for Unmanned Ground Vehicles (UGVs) to proactively prevent collisions with kinematic obstacles by integrating the concept of collision cones. While existing CBF formulations excel with static obstacles, extensions to torque/acceleration-controlled unicycle and bicycle models have seen limited success. Conventional CBF applications in nonholonomic UGV models have demonstrated control conservatism, particularly in scenarios where steering/thrust control was deemed infeasible. Drawing inspiration from collision cones in path planning, we present a pioneering CBF formulation ensuring theoretical safety guarantees for both unicycle and bicycle models. The core premise revolves around aligning the obstacle's velocity away from the vehicle, establishing a constraint to perpetually avoid vectors directed towards it. This control methodology is rigorously validated through simulations and experimental verification on the Copernicus mobile robot (Unicycle Model) and FOCAS-Car (Bicycle Model).

In this paper, we propose a new class of Control Barrier Functions (CBFs) for Unmanned Ground Vehicles (UGVs) that help avoid collisions with kinematic (non-zero velocity) obstacles. While the current forms of CBFs have been successful in guaranteeing safety/collision avoidance with static obstacles, extensions for the dynamic case have seen limited success. Moreover, with the UGV models like the unicycle or the bicycle, applications of existing CBFs have been conservative in terms of control, i.e., steering/thrust control has not been possible under certain scenarios. Drawing inspiration from the classical use of collision cones for obstacle avoidance in trajectory planning, we introduce its novel CBF formulation with theoretical guarantees on safety for both the unicycle and bicycle models. The main idea is to ensure that the velocity of the obstacle w.r.t. the vehicle is always pointing away from the vehicle. Accordingly, we construct a constraint that ensures that the velocity vector always avoids a cone of vectors pointing at the vehicle. The efficacy of this new control methodology is later verified by Pybullet simulations on TurtleBot3 and F1Tenth.