Control Barrier Functions (CBF) have been recently utilized in the design of provably safe feedback control laws for nonlinear systems. These feedback control methods typically compute the next control input by solving an online Quadratic Program (QP). Solving QP in real-time can be a computationally expensive process for resource constraint systems. In this work, we propose to use imitation learning to learn Neural Network-based feedback controllers which will satisfy the CBF constraints. In the process, we also develop a new class of High Order CBF for systems under external disturbances. We demonstrate the framework on a unicycle model subject to external disturbances, e.g., wind or currents.

Training Neural Network Controllers Using Control Barrier Functions in the Presence of Disturbances

Control Barrier Functions (CBF) have been recently utilized in the design of provably safe feedback control laws for nonlinear systems. These feedback control methods typically compute the next control input by solving an online Quadratic Program (QP). Solving QPs in real-time can be a computationally expensive process for resource-constrained systems. In the presence of disturbances, finding CBF-based safe control inputs can get even more time consuming as finding the worst-case of the disturbance requires solving a nonlinear program in general. In this work, we propose to use imitation learning to learn Neural Network based feedback controllers which will satisfy the CBF constraints. In the process, we also develop a new class of High Order CBF for systems under external disturbances. We demonstrate the framework on a unicycle model subject to external disturbances, e.g., wind or currents.

Control Barrier Functions (CBF) are widely used to enforce the safety-critical constraints on nonlinear systems. Recently, these functions are being incorporated into a path planning framework to design safety-critical path planners. However, these methods fall short of providing a realistic path considering both the algorithm's run-time complexity and enforcement of the safety-critical constraints. This paper proposes a novel motion planning approach using the well-known Rapidly Exploring Random Trees (RRT) algorithm that enforces both CBF and the robot Kinodynamic constraints to generate a safety-critical path. The proposed algorithm also outputs the corresponding control signals that resulted in the obstacle-free path. The approach also allows considering model uncertainties by incorporating the robust CBF constraints into the proposed framework. Thus, the resulting path is free of any obstacles and accounts for the model uncertainty from robot dynamics and perception. Result analysis indicates that the proposed method outperforms various conventional RRT-based path planners, guaranteeing a safety-critical path with minimal computational overhead. We present numerical validation of the algorithm on the Hamster V7 robot car, a micro autonomous Unmanned Ground Vehicle that performs dynamic navigation on an obstacle-ridden path with various uncertainties in perception noises and robot dynamics.

Safe and Robust Motion Planning for Dynamic Robotics via Control Barrier Functions.

Sampling-based methods such as Rapidly-exploring Random Trees (RRTs) have been widely used for generating motion paths for autonomous mobile systems. In this work, we extend time-based RRTs with Control Barrier Functions (CBFs) to generate, safe motion plans in dynamic environments with many pedestrians. Our framework is based upon a human motion prediction model which is well suited for indoor narrow environments. We demonstrate our approach on a high-fidelity model of the Toyota Human Support Robot navigating in narrow corridors. We show in three scenarios that our proposed online method can navigate safely in the presence of moving agents with unknown dynamics.

Safe Navigation in Human Occupied Environments Using Sampling and Control Barrier Functions.

In this paper, we propose an abstraction that captures high-level formation and location-based swarm behaviors, and an automated control synthesis framework to generate correct-by-construction behaviors. Our abstraction includes symbols representing both possible formations and physical locations in the workspace. We allow users to write linear temporal logic (LTL) specifications over the symbols to specify high-level tasks for the swarm. To satisfy a specification, we automatically synthesize a centralized symbolic plan, and environment and swarm-size-dependent motion controllers that are guaranteed to implement the symbolic transitions. In addition, using integer programming (IP), we assign robots to different sub-swarms to execute the synthesized symbolic plan. Our framework gives insights into controlling a large fleet of autonomous robots to achieve complex tasks which require composition of behaviors at different locations and coordination among different groups of robots in a correct-by-construction way. We demonstrate the proposed framework in simulation with 16 UAVs and 8 ground vehicles, and on a physical platform with 20 ground robots, showcasing the generality of the approach and discussing the implications of controlling constrained physical hardware.

Automatic Control Synthesis for Swarm Robots from Formation and Location-based High-level Specifications

Robot motion planning is central to real-world autonomous applications, such as self-driving cars, persistence surveillance, and robotic arm manipulation. One challenge in motion planning is generating control signals for nonlinear systems that result in obstacle free paths through dynamic environments. In this paper, we propose Control Barrier Function guided Rapidly-exploring Random Trees (CBF-RRT), a sampling-based motion planning algorithm for continuoustime nonlinear systems in dynamic environments. The algorithm focuses on two objectives: efficiently generating feasible controls that steer the system toward a goal region, and handling environments with dynamical obstacles in continuous time. We formulate the control synthesis problem as a Quadratic Program (QP) that enforces Control Barrier Function (CBF) constraints to achieve obstacle avoidance. Additionally, CBF-RRT does not require nearest neighbor or explicit collision checks during sampling.

https://dl.acm.org/doi/pdf/10.1145/3365265.3365282

Sampling-based Motion Planning via Control Barrier Functions

In this paper, we present a simple geometric attitude controller that is globally, exponentially stable. To overcome the topological restriction, the controller is designed to follow a reference trajectory that in turn converges to the desired equilibrium (making it discontinuous in the initial conditions, but continuous in time). The system and reference dynamics are studied as a single augmented system that can be analyzed and tuned simultaneously. The controller’s stability is proved using contraction analysis (on the manifold), and the bounds on the convergence rate can be found via a semi-definite program with linear matrix inequalities. Additionally, our approach allows the use of the Nelder-Mead algorithm to automatically select controller gains and reference trajectory parameters by optimizing the aforementioned bounds. The resulting controller is verified through simulations.

Global Attitude Control via Contraction on Manifolds with Reference Trajectory and Optimization

In this paper we propose a new analysis of a simple geometric attitude controller, showing that it is locally exponentially stable and almost globally asymptotically stable; the exponential convergence region is much larger than existing non-hybrid geometric controllers (and covers almost the entire rotation space). The controller’s stability is proved using contraction analysis combined with optimization. The key in this combination is that the contraction metric is a linear matrix inequality with a special structure stemming from the configuration manifold SO(3).As an additional contribution, we propose a general framework to automatically select controller gains by optimizing bounds on the system’s convergence rate; while this principle is quite general, its application is particularly straightforward with our contraction-based analysis.We demonstrate our results through simulations.

Geometric Attitude Control via Contraction on Manifolds with Automatic Gain Selection

Natural metrics provide a way to induce a metric on the tangent bundle from the metric on its base manifold. The most studied type is the Sasaki metric, which applies the base metric separately to the vertical and horizontal components. We study a more general class of metrics which introduces interactions between the vertical and horizontal components, with scalar weights. Additionally, we explicitly clarify how to apply our and other induced metrics on the tangent bundle to vector fields where the vertical component is not constant along the fibers. We give application to the Special Orthogonal Group SO(3) as an example.

Non-natural metrics on the tangent bundle

We present a framework to automatically tune the gains of a geometric attitude controller based on operating conditions (distance from equilibrium). We propose a two-thread architecture: on the one hand, a computationally simple geometric control law provides real-time control inputs to globally stabilize the system; on the other hand, an optimization procedure continuously varies the gains of the control law to improve the convergence rate guarantees when possible. In particular, we use Control Barrier and Lyapunov functions to find rates of change for the gains that improve bounds on the convergence rate while guaranteeing exponential stability for all subsequent times. The advantage of our architecture is that the gain updates can be computed at a rate possibly much slower than the control law; thanks to the constraints used, even if the gain updates were to stop, exponential stability would still be guaranteed for all future times.The resulting controller is compared via simulations against a static feedback controller and a version based on traditional discontinuous gain scheduling. While we focus on attitude control, our framework could be generalized to any static feedback controller equipped with explicit convergence conditions.

Bee Vang

Papers

Sampling-based Motion Planning via Control Barrier Functions

Global Attitude Control via Contraction on Manifolds with Reference Trajectory and Optimization

Geometric Attitude Control via Contraction on Manifolds with Automatic Gain Selection

Non-natural metrics on the tangent bundle

Online Automatic Gain Tuning for Geometric Attitude Control