Barrier Functions and Model Free Safety With Applications to Fixed Wing Collision Avoidance

Robotics is now being applied to a diversity of real-world applications and in many areas such as industrial, medical, and mobile robotics, safety is a critical consideration for continued adoption. In this thesis we therefore investigate how to develop algorithms that improve the safety of autonomous systems using both a model-based and model-free framework. To begin, we make a variety of assumptions (e.g., that a model is known, there is a single safety constraint, there are no communication limits, and that the state can be sensed everywhere), and show how to guarantee the safety of the system. The contribution of the initial approach is a generalization of an existing method for creating a barrier function, which is a function similar to a Lyapunov function that can be used to make safety guarantees. We then investigate relaxing these initial assumptions. In some cases, new additional assumptions are required, performance may be reduced, or safety guarantees may no longer be available. We motivate the thesis with collision avoidance for fixed wing aircraft which can be viewed as a pairwise constraint on each pair of aircraft. This introduces the need for considering multiple safety factors simultaneously, and we show that an additional assumption is needed in this case. We then relax the assumption that the vehicles have unlimited communication and find that safety can still be guaranteed. However, it is possible in this case that the overriding safety controller may be more invasive than if more communication is allowed. When we then further relax the assumption that the state can be sensed at all times, safety can still be guaranteed in some specified situations but the system may be more permissive in approaching safety boundaries. We finally remove the assumption of a known model for dynamics. Although removing this assumption means the system is no longer guaranteed to be safe, the benefit is that it allows a safety designer to build a far less invasive override to get more performance out of the system.Ph.D

Outdoor operations of multiple quadrotors in windy environment

Coordinated multiple small unmanned aerial vehicles (sUAVs) offer several advantages over a single sUAV platform. These advantages include improved task efficiency, reduced task completion time, improved fault tolerance, and higher task flexibility. However, their deployment in an outdoor environment is challenging due to the presence of wind gusts. The coordinated motion of a multi-sUAV system in the presence of wind disturbances is a challenging problem when considering collision avoidance (safety), scalability, and communication connectivity. Performing wind-agnostic motion planning for sUAVs may produce a sizeable cross-track error if the wind on the planned route leads to actuator saturation. In a multi-sUAV system, each sUAV has to locally counter the wind disturbance while maintaining the safety of the system. Such continuous manipulation of the control effort for multiple sUAVs under uncertain environmental conditions is computationally taxing and can lead to reduced efficiency and safety concerns. Additionally, modern day sUAV systems are susceptible to cyberattacks due to their use of commercial wireless communication infrastructure. This dissertation aims to address these multi-faceted challenges related to the operation of outdoor rotor-based multi-sUAV systems. A comprehensive review of four representative techniques to measure and estimate wind speed and direction using rotor-based sUAVs is discussed. After developing a clear understanding of the role wind gusts play in quadrotor motion, two decentralized motion planners for a multi-quadrotor system are implemented and experimentally evaluated in the presence of wind disturbances. The first planner is rooted in the reinforcement learning (RL) technique of state-action-reward-state-action (SARSA) to provide generalized path plans in the presence of wind disturbances. While this planner provides feasible trajectories for the quadrotors, it does not provide guarantees of collision avoidance. The second planner implements a receding horizon (RH) mixed-integer nonlinear programming (MINLP) model that is integrated with control barrier functions (CBFs) to guarantee collision-free transit of the multiple quadrotors in the presence of wind disturbances. Finally, a novel communication protocol using Ethereum blockchain-based smart contracts is presented to address the challenge of secure wireless communication. The U.S. sUAV market is expected to be worth $92 Billion by 2030. The Association for Unmanned Vehicle Systems International (AUVSI) noted in its seminal economic report that UAVs would be responsible for creating 100,000 jobs by 2025 in the U.S. The rapid proliferation of drone technology in various applications has led to an increasing need for professionals skilled in sUAV piloting, designing, fabricating, repairing, and programming. Engineering educators have recognized this demand for certified sUAV professionals. This dissertation aims to address this growing sUAV-market need by evaluating two active learning-based instructional approaches designed for undergraduate sUAV education. The two approaches leverages the interactive-constructive-active-passive (ICAP) framework of engagement and explores the use of Competition based Learning (CBL) and Project based Learning (PBL). The CBL approach is implemented through a drone building and piloting competition that featured 97 students from undergraduate and graduate programs at NJIT. The competition focused on 1) drone assembly, testing, and validation using commercial off-the-shelf (COTS) parts, 2) simulation of drone flight missions, and 3) manual and semi-autonomous drone piloting were implemented. The effective student learning experience from this competition served as the basis of a new undergraduate course on drone science fundamentals at NJIT. This undergraduate course focused on the three foundational pillars of drone careers: 1) drone programming using Python, 2) designing and fabricating drones using Computer-Aided Design (CAD) and rapid prototyping, and 3) the US Federal Aviation Administration (FAA) Part 107 Commercial small Unmanned Aerial Vehicles (sUAVs) pilot test. Multiple assessment methods are applied to examine the students’ gains in sUAV skills and knowledge and student attitudes towards an active learning-based approach for sUAV education. The use of active learning techniques to address these challenges lead to meaningful student engagement and positive gains in the learning outcomes as indicated by quantitative and qualitative assessments

Control Barrier Functions: Theory and Applications

This paper provides an introduction and overview of recent work on control barrier functions and their use to verify and enforce safety properties in the context of (optimization based) safety-critical controllers. We survey the main technical results and discuss applications to several domains including robotic systems

Control Barrier Functions: Theory and Applications

This paper provides an introduction and overview of recent work on control barrier functions and their use to verify and enforce safety properties in the context of (optimization based) safety-critical controllers. We survey the main technical results and discuss applications to several domains including robotic systems

Robust Control Barrier Functions under High Relative Degree and Input Constraints for Satellite Trajectories

This paper presents methodologies for constructing Control Barrier Functions (CBFs) for nonlinear, control-affine systems, in the presence of input constraints and bounded disturbances. More specifically, given a constraint function with high-relative-degree with respect to the system dynamics, the paper considers three methodologies, two for relative-degree 2 and one for higher relative-degrees, for converting the constraint function into a CBF. Three special forms of Robust CBFs (RCBFs) are developed as functions of the input constraints, system dynamics, and disturbance bounds, and are applied to provably safe satellite control for asteroid exploration missions. The resultant RCBF conditions on the control input are enforced in a switched fashion, which expands the set of allowable trajectories and simplifies control input computation in the presence of multiple constraints. The proposed methods are verified in simulations demonstrating the developed RCBFs in an asteroid flyby scenario for a satellite with low-thrust actuators, and in asteroid proximity operations for a satellite with high-thrust actuators.Comment: 19 pages. Submitted to Automatic

Auxiliary-Variable Adaptive Control Barrier Functions for Safety Critical Systems

This paper studies safety guarantees for systems with time-varying control bounds. It has been shown that optimizing quadratic costs subject to state and control constraints can be reduced to a sequence of Quadratic Programs (QPs) using Control Barrier Functions (CBFs). One of the main challenges in this method is that the CBF-based QP could easily become infeasible under tight control bounds, especially when the control bounds are time-varying. The recently proposed adaptive CBFs have addressed such infeasibility issues, but require extensive and non-trivial hyperparameter tuning for the CBF-based QP and may introduce overshooting control near the boundaries of safe sets. To address these issues, we propose a new type of adaptive CBFs called Auxiliary-Variable Adaptive CBFs (AVCBFs). Specifically, we introduce an auxiliary variable that multiplies each CBF itself, and define dynamics for the auxiliary variable to adapt it in constructing the corresponding CBF constraint. In this way, we can improve the feasibility of the CBF-based QP while avoiding extensive parameter tuning with non-overshooting control since the formulation is identical to classical CBF methods. We demonstrate the advantages of using AVCBFs and compare them with existing techniques on an Adaptive Cruise Control (ACC) problem with time-varying control bounds.Comment: 8 pages, 4 figure