Input-to-State Safety with Input Delay in Longitudinal Vehicle Control

Safe longitudinal control is discussed for a connected automated truck traveling behind a preceding connected vehicle. A controller is proposed based on control barrier function theory and predictor feedback for provably safe, collision-free behavior by taking into account the significant response time of the truck as input delay and the uncertainty of its dynamical model as input disturbance. The benefits of the proposed controller compared to control designs that neglect the delay or treat the delay as disturbance are shown by numerical simulations.

Safety-Critical Manipulation for Collision-Free Food Preparation

Recent advances allow for the automation of food preparation in high-throughput environments, yet the successful deployment of these robots requires the planning and execution of quick, robust, and ultimately collision-free behaviors. In this work, we showcase a novel framework for modifying previously generated trajectories of robotic manipulators in highly detailed and dynamic collision environments using Control Barrier Functions (CBFs). This method dynamically re-plans previously validated behaviors in the presence of changing environments -- and does so in a computationally efficient manner. Moreover, the approach provides rigorous safety guarantees of the resulting trajectories, factoring in the true underlying dynamics of the manipulator. This methodology is extensively validated on a full-scale robotic manipulator in a real-world cooking environment, and has resulted in substantial improvements in computation time and robustness over re-planning.

Sample-Based Bounds for Coherent Risk Measures: Applications to Policy Synthesis and Verification

The dramatic increase of autonomous systems subject to variable environments has given rise to the pressing need to consider risk in both the synthesis and verification of policies for these systems. This paper aims to address a few problems regarding risk-aware verification and policy synthesis, by first developing a sample-based method to bound the risk measure evaluation of a random variable whose distribution is unknown. These bounds permit us to generate high-confidence verification statements for a large class of robotic systems. Second, we develop a sample-based method to determine solutions to non-convex optimization problems that outperform a large fraction of the decision space of possible solutions. Both sample-based approaches then permit us to rapidly synthesize risk-aware policies that are guaranteed to achieve a minimum level of system performance. To showcase our approach in simulation, we verify a cooperative multi-agent system and develop a risk-aware controller that outperforms the system's baseline controller. We also mention how our approach can be extended to account for any $g$-entropic risk measure - the subset of coherent risk measures on which we focus.

Neural Gaits: Learning Bipedal Locomotion via Control Barrier Functions and Zero Dynamics Policies

This work presents Neural Gaits, a method for learning dynamic walking gaits through the enforcement of set invariance that can be refined episodically using experimental data from the robot. We frame walking as a set invariance problem enforceable via control barrier functions (CBFs) defined on the reduced-order dynamics quantifying the underactuated component of the robot: the zero dynamics. Our approach contains two learning modules: one for learning a policy that satisfies the CBF condition, and another for learning a residual dynamics model to refine imperfections of the nominal model. Importantly, learning only over the zero dynamics significantly reduces the dimensionality of the learning problem while using CBFs allows us to still make guarantees for the full-order system. The method is demonstrated experimentally on an underactuated bipedal robot, where we are able to show agile and dynamic locomotion, even with partially unknown dynamics.

Safety of Sampled-Data Systems with Control Barrier Functions via Approximate Discrete Time Models

Control Barrier Functions (CBFs) have been demonstrated to be a powerful tool for safety-critical controller design for nonlinear systems. Existing design paradigms do not address the gap between theory (controller design with continuous time models) and practice (the discrete time sampled implementation of the resulting controllers); this can lead to poor performance and violations of safety for hardware instantiations. We propose an approach to close this gap by synthesizing sampled-data counterparts to these CBF-based controllers using approximate discrete time models and Sampled-Data Control Barrier Functions (SD-CBFs). Using properties of a system's continuous time model, we establish a relationship between SD-CBFs and a notion of practical safety for sampled-data systems. Furthermore, we construct convex optimization-based controllers that formally endow nonlinear systems with safety guarantees in practice. We demonstrate the efficacy of these controllers in simulation.

Bipedal Locomotion with Nonlinear Model Predictive Control: Online Gait Generation using Whole-Body Dynamics

The ability to generate dynamic walking in real-time for bipedal robots with compliance and underactuation has the potential to enable locomotion in complex and unstructured environments. Yet, the high-dimensional nature of bipedal robots has limited the use of full-order rigid body dynamics to gaits which are synthesized offline and then tracked online, e.g., via whole-body controllers. In this work we develop an online nonlinear model predictive control approach that leverages the full-order dynamics to realize diverse walking behaviors. Additionally, this approach can be coupled with gaits synthesized offline via a terminal cost that enables a shorter prediction horizon; this makes rapid online re-planning feasible and bridges the gap between online reactive control and offline gait planning. We demonstrate the proposed method on the planar robot AMBER-3M, both in simulation and on hardware.

Self-Supervised Online Learning for Safety-Critical Control using Stereo Vision

With the increasing prevalence of complex vision-based sensing methods for use in obstacle identification and state estimation, characterizing environment-dependent measurement errors has become a difficult and essential part of modern robotics. This paper presents a self-supervised learning approach to safety-critical control. In particular, the uncertainty associated with stereo vision is estimated, and adapted online to new visual environments, wherein this estimate is leveraged in a safety-critical controller in a robust fashion. To this end, we propose an algorithm that exploits the structure of stereo-vision to learn an uncertainty estimate without the need for ground-truth data. We then robustify existing Control Barrier Function-based controllers to provide safety in the presence of this uncertainty estimate. We demonstrate the efficacy of our method on a quadrupedal robot in a variety of environments. When not using our method safety is violated. With offline training alone we observe the robot is safe, but overly-conservative. With our online method the quadruped remains safe and conservatism is reduced.

LyaNet: A Lyapunov Framework for Training Neural ODEs

We propose a method for training ordinary differential equations by using a control-theoretic Lyapunov condition for stability. Our approach, called LyaNet, is based on a novel Lyapunov loss formulation that encourages the inference dynamics to converge quickly to the correct prediction. Theoretically, we show that minimizing Lyapunov loss guarantees exponential convergence to the correct solution and enables a novel robustness guarantee. We also provide practical algorithms, including one that avoids the cost of backpropagating through a solver or using the adjoint method. Relative to standard Neural ODE training, we empirically find that LyaNet can offer improved prediction performance, faster convergence of inference dynamics, and improved adversarial robustness. Our code available at https://github.com/ivandariojr/LyapunovLearning .

Onboard Safety Guarantees for Racing Drones: High-speed Geofencing with Control Barrier Functions

This paper details the theory and implementation behind practically ensuring safety of remotely piloted racing drones. We demonstrate robust and practical safety guarantees on a 7" racing drone at speeds exceeding 100 km/h, utilizing only online computations on a 10 gram micro-controller. To achieve this goal, we utilize the framework of control barrier functions (CBFs) which give guaranteed safety encoded as forward set invariance. To make this methodology practically applicable, we present an implicitly defined CBF which leverages backup controllers to enable gradient-free evaluations that ensure safety. The method applied to hardware results in smooth, minimally conservative alterations of the pilots' desired inputs, enabling them to push the limits of their drone without fear of crashing. Moreover, the method works in conjunction with the preexisting flight controller, resulting in unaltered flight when there are no nearby safety risks. Additional benefits include safety and stability of the drone when losing line-of-sight or in the event of radio failure.

Test and Evaluation of Quadrupedal Walking Gaits through Sim2Real Gap Quantification

In this letter, the authors propose a two-step approach to evaluate and verify a true system's capacity to satisfy its operational objective. Specifically, whenever the system objective has a quantifiable measure of satisfaction, i.e. a signal temporal logic specification, a barrier function, etc - the authors develop two separate optimization problems solvable via a Bayesian Optimization procedure detailed within. This dual approach has the added benefit of quantifying the Sim2Real Gap between a system simulator and its hardware counterpart. Our contributions are twofold. First, we show repeatability with respect to our outlined optimization procedure in solving these optimization problems. Second, we show that the same procedure can discriminate between different environments by identifying the Sim2Real Gap between a simulator and its hardware counterpart operating in different environments.