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1. NMPC-LBF: Nonlinear MPC with Learned Barrier Function for Decentralized Safe Navigation of Multiple Robots in Unknown Environments

   https://doi.org/10.1109/IROS47612.2022.9981177  

   Lafmejani, Amir Salimi ; Berman, Spring ; Fainekos, Georgios ( October 2022 , 2022 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS))

   In this paper, we present a decentralized control approach based on a Nonlinear Model Predictive Control (NMPC) method that employs barrier certificates for safe navigation of multiple nonholonomic wheeled mobile robots in unknown environments with static and/or dynamic obstacles. This method incorporates a Learned Barrier Function (LBF) into the NMPC design in order to guarantee safe robot navigation, i.e., prevent robot collisions with other robots and the obstacles. We refer to our proposed control approach as NMPC-LBF. Since each robot does not have a priori knowledge about the obstacles and other robots, we use a Deep Neural Network (DeepNN) running in real-time on each robot to learn the Barrier Function (BF) only from the robot's LiDAR and odometry measurements. The DeepNN is trained to learn the BF that separates safe and unsafe regions. We implemented our proposed method on simulated and actual Turtlebot3 Burger robot(s) in different scenarios. The implementation results show the effectiveness of the NMPC-LBF method at ensuring safe navigation of the robots. 

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2. Reinforcement Learning for Safety-Critical Control under Model Uncertainty, using Control Lyapunov Functions and Control Barrier Functions

   Choi, Jason ; Castañeda, Fernando ; Tomlin, Claire J. ; Sreenath, Koushil ( July 2020 , Robotics: Science and Systems (RSS))

   In this paper, the issue of model uncertainty in safety-critical control is addressed with a data-driven approach. For this purpose, we utilize the structure of an input-output linearization controller based on a nominal model along with a Control Barrier Function and Control Lyapunov Function based Quadratic Program (CBF-CLF-QP). Specifically, we propose a novel reinforcement learning framework which learns the model uncertainty present in the CBF and CLF constraints, as well as other control-affine dynamic constraints in the quadratic program. The trained policy is combined with the nominal model based CBF-CLF-QP, resulting in the Reinforcement Learning based CBF-CLF-QP (RL-CBF-CLF-QP), which addresses the problem of model uncertainty in the safety constraints. The performance of the proposed method is validated by testing it on an underactuated nonlinear bipedal robot walking on randomly spaced stepping stones with one step preview, obtaining stable and safe walking under model uncertainty. 

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3. Control Barrier Functions for Complete and Incomplete Information Stochastic Systems

   https://doi.org/https://doi.org/10.23919/ACC.2019.8814901  

   Clark, A. ( January 2019 , American Control Conference (ACC))

   Real-time controllers must satisfy strict safety requirements. Recently, Control Barrier Functions (CBFs) have been proposed that guarantee safety by ensuring that a suitablydefined barrier function remains bounded for all time. The CBF method, however, has only been developed for deterministic systems and systems with worst-case disturbances and uncertainties. In this paper, we develop a CBF framework for safety of stochastic systems. We consider complete information systems, in which the controller has access to the exact system state, as well as incomplete information systems where the state must be reconstructed from noisy measurements. In the complete information case, we formulate a notion of barrier functions that leads to sufficient conditions for safety with probability 1. In the incomplete information case, we formulate barrier functions that take an estimate from an extended Kalman filter as input, and derive bounds on the probability of safety as a function of the asymptotic error in the filter. We show that, in both cases, the sufficient conditions for safety can be mapped to linear constraints on the control input at each time, enabling the development of tractable optimization-based controllers that guarantee safety, performance, and stability. Our approach is evaluated via simulation study on an adaptive cruise control case study. 

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4. Enhancing Safety in Learning from Demonstration Algorithms via Control Barrier Function Shielding

   https://doi.org/10.1145/3610977.3635002  

   Yang, Yue ; Chen, Letian ; Zaidi, Zulfiqar ; van Waveren, Sanne ; Krishna, Arjun ; Gombolay, Matthew ( March 2024 , Proceedings of the 2024 ACM/IEEE International Conference on Human-Robot Interaction)

   Learning from Demonstration (LfD) is a powerful method for nonroboticists end-users to teach robots new tasks, enabling them to customize the robot behavior. However, modern LfD techniques do not explicitly synthesize safe robot behavior, which limits the deployability of these approaches in the real world. To enforce safety in LfD without relying on experts, we propose a new framework, ShiElding with Control barrier fUnctions in inverse REinforcement learning (SECURE), which learns a customized Control Barrier Function (CBF) from end-users that prevents robots from taking unsafe actions while imposing little interference with the task completion. We evaluate SECURE in three sets of experiments. First, we empirically validate SECURE learns a high-quality CBF from demonstrations and outperforms conventional LfD methods on simulated robotic and autonomous driving tasks with improvements on safety by up to 100%. Second, we demonstrate that roboticists can leverage SECURE to outperform conventional LfD approaches on a real-world knife-cutting, meal-preparation task by 12.5% in task completion while driving the number of safety violations to zero. Finally, we demonstrate in a user study that non-roboticists can use SECURE to efectively teach the robot safe policies that avoid collisions with the person and prevent cofee from spilling. 

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5. Safe Bipedal Path Planning via Control Barrier Functions for Polynomial Shape Obstacles Estimated Using Logistic Regression

   https://doi.org/10.1109/ICRA48891.2023.10160671  

   Peng, Chengyang ; Donca, Octavian ; Castillo, Guillermo ; Hereid, Ayonga ( May 2023 , IEEE)

   Safe path planning is critical for bipedal robots to operate in safety-critical environments. Common path planning algorithms, such as RRT or RRT*, typically use geometric or kinematic collision check algorithms to ensure collision-free paths toward the target position. However, such approaches may generate non-smooth paths that do not comply with the dynamics constraints of walking robots. It has been shown that the control barrier function (CBF) can be integrated with RRT/RRT* to synthesize dynamically feasible collision-free paths. Yet, existing work has been limited to simple circular or elliptical shape obstacles due to the challenging nature of constructing appropriate barrier functions to represent irregularly shaped obstacles. In this paper, we present a CBF-based RRT* algorithm for bipedal robots to generate a collision-free path through space with multiple polynomial-shaped obstacles. In particular, we used logistic regression to construct polynomial barrier functions from a grid map of the environment to represent irregularly shaped obstacles. Moreover, we developed a multi-step CBF steering controller to ensure the efficiency of free space exploration. The proposed approach was first validated in simulation for a differential drive model, and then experimentally evaluated with a 3D humanoid robot, Digit, in a lab setting with randomly placed obstacles. 

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