Learning Disturbances Online for Risk-Aware Control: Risk-Aware Flight with Less Than One Minute of Data

Recent advances in safety-critical risk-aware control are predicated on apriori knowledge of the disturbances a system might face. This paper proposes a method to efficiently learn these disturbances online, in a risk-aware context. First, we introduce the concept of a Surface-at-Risk, a risk measure for stochastic processes that extends Value-at-Risk -- a commonly utilized risk measure in the risk-aware controls community. Second, we model the norm of the state discrepancy between the model and the true system evolution as a scalar-valued stochastic process and determine an upper bound to its Surface-at-Risk via Gaussian Process Regression. Third, we provide theoretical results on the accuracy of our fitted surface subject to mild assumptions that are verifiable with respect to the data sets collected during system operation. Finally, we experimentally verify our procedure by augmenting a drone's controller and highlight performance increases achieved via our risk-aware approach after collecting less than a minute of operating data.

Synthesizing Reactive Test Environments for Autonomous Systems: Testing Reach-Avoid Specifications with Multi-Commodity Flows

We study automated test generation for verifying discrete decision-making modules in autonomous systems. We utilize linear temporal logic to encode the requirements on the system under test in the system specification and the behavior that we want to observe during the test is given as the test specification which is unknown to the system. First, we use the specifications and their corresponding non-deterministic B\"uchi automata to generate the specification product automaton. Second, a virtual product graph representing the high-level interaction between the system and the test environment is constructed modeling the product automaton encoding the system, the test environment, and specifications. The main result of this paper is an optimization problem, framed as a multi-commodity network flow problem, that solves for constraints on the virtual product graph which can then be projected to the test environment. Therefore, the result of the optimization problem is reactive test synthesis that ensures that the system meets the test specifications along with satisfying the system specifications. This framework is illustrated in simulation on grid world examples, and demonstrated on hardware with the Unitree A1 quadruped, wherein dynamic locomotion behaviors are verified in the context of reactive test environments.

Emulating Human Kinematic Behavior on Lower-Limb Prostheses via Multi-Contact Models and Force-Based Nonlinear Control

Ankle push-off largely contributes to limb energy generation in human walking, leading to smoother and more efficient locomotion. Providing this net positive work to an amputee requires an active prosthesis, but has the potential to enable more natural assisted locomotion. To this end, this paper uses multi-contact models of locomotion together with force-based nonlinear optimization-based controllers to achieve human-like kinematic behavior, including ankle push-off, on a powered transfemoral prosthesis for 2 subjects. In particular, we leverage model-based control approaches for dynamic bipedal robotic walking to develop a systematic method to realize human-like walking on a powered prosthesis that does not require subject-specific tuning. We begin by synthesizing an optimization problem that yields gaits that resemble human joint trajectories at a kinematic level, and realize these gaits on a prosthesis through a control Lyapunov function based nonlinear controller that responds to real-time ground reaction forces and interaction forces with the human. The proposed controller is implemented on a prosthesis for two subjects without tuning between subjects, emulating subject-specific human kinematic trends on the prosthesis joints. These experimental results demonstrate that our force-based nonlinear control approach achieves better tracking of human kinematic trajectories than traditional methods.

Nonlinear Model Predictive Control of a 3D Hopping Robot: Leveraging Lie Group Integrators for Dynamically Stable Behaviors

Achieving stable hopping has been a hallmark challenge in the field of dynamic legged locomotion. Controlled hopping is notably difficult due to extended periods of underactuation, combined with very short ground phases wherein ground interactions must be modulated to regulate global state. In this work, we explore the use of hybrid nonlinear model predictive control, paired with a low-level feedback controller in a multi-rate hierarchy, to achieve dynamically stable motions on a novel 3D hopping robot. In order to demonstrate richer behaviors on the manifold of rotations, both the planning and feedback layers must be done in a geometrically consistent fashion; therefore, we develop the necessary tools to employ Lie group integrators and an appropriate feedback controller. We experimentally demonstrate stable 3D hopping on a novel robot, as well as trajectory tracking and flipping in simulation.

Robust Bipedal Locomotion: Leveraging Saltation Matrices for Gait Optimization

The ability to generate robust walking gaits on bipedal robots is key to their successful realization on hardware. To this end, this work extends the method of Hybrid Zero Dynamics (HZD) -- which traditionally only accounts for locomotive stability via periodicity constraints under perfect impact events -- through the inclusion of the saltation matrix with a view toward synthesizing robust walking gaits. By jointly minimizing the norm of the extended saltation matrix and the torque of the robot directly in the gait generation process, we show that the synthesized gaits are more robust than gaits generated with either term alone; these results are shown in simulation and on hardware for both the AMBER-3M planar biped and the Atalante lower-body exoskeleton (both with and without a human subject). The end result is experimental validation that combining saltation matrices with HZD methods produces more robust bipedal walking in practice.

Data-driven Step-to-step Dynamics based Adaptive Control for Robust and Versatile Underactuated Bipedal Robotic Walking

This paper presents a framework for synthesizing bipedal robotic walking that adapts to unknown environment and dynamics error via a data-driven step-to-step (S2S) dynamics model. We begin by synthesizing an S2S controller that stabilizes the walking using foot placement through nominal S2S dynamics from the hybrid linear inverted pendulum (H-LIP) model. Next, a data-driven representation of the S2S dynamics of the robot is learned online via classical adaptive control methods. The desired discrete foot placement on the robot is thereby realized by proper continuous output synthesis capturing the data-driven S2S controller coupled with a low-level tracking controller. The proposed approach is implemented in simulation on an underactuated 3D bipedal robot, Cassie, and improved reference velocity tracking is demonstrated. The proposed approach is also able to realize walking behavior that is robustly adaptive to unknown loads, inaccurate robot models, external disturbance forces, biased velocity estimation, and unknown slopes.

POLAR: Preference Optimization and Learning Algorithms for Robotics

Parameter tuning for robotic systems is a time-consuming and challenging task that often relies on domain expertise of the human operator. Moreover, existing learning methods are not well suited for parameter tuning for many reasons including: the absence of a clear numerical metric for `good robotic behavior'; limited data due to the reliance on real-world experimental data; and the large search space of parameter combinations. In this work, we present an open-source MATLAB Preference Optimization and Learning Algorithms for Robotics toolbox (POLAR) for systematically exploring high-dimensional parameter spaces using human-in-the-loop preference-based learning. This aim of this toolbox is to systematically and efficiently accomplish one of two objectives: 1) to optimize robotic behaviors for human operator preference; 2) to learn the operator's underlying preference landscape to better understand the relationship between adjustable parameters and operator preference. The POLAR toolbox achieves these objectives using only subjective feedback mechanisms (pairwise preferences, coactive feedback, and ordinal labels) to infer a Bayesian posterior over the underlying reward function dictating the user's preferences. We demonstrate the performance of the toolbox in simulation and present various applications of human-in-the-loop preference-based learning.

Safe Drone Flight with Time-Varying Backup Controllers

The weight, space, and power limitations of small aerial vehicles often prevent the application of modern control techniques without significant model simplifications. Moreover, high-speed agile behavior, such as that exhibited in drone racing, make these simplified models too unreliable for safety-critical control. In this work, we introduce the concept of time-varying backup controllers (TBCs): user-specified maneuvers combined with backup controllers that generate reference trajectories which guarantee the safety of nonlinear systems. TBCs reduce conservatism when compared to traditional backup controllers and can be directly applied to multi-agent coordination to guarantee safety. Theoretically, we provide conditions under which TBCs strictly reduce conservatism, describe how to switch between several TBC's and show how to embed TBCs in a multi-agent setting. Experimentally, we verify that TBCs safely increase operational freedom when filtering a pilot's actions and demonstrate robustness and computational efficiency when applied to decentralized safety filtering of two quadrotors.

Control Barrier Functionals: Safety-critical Control for Time Delay Systems

This work presents a theoretical framework for the safety-critical control of time delay systems. The theory of control barrier functions, that provides formal safety guarantees for delay-free systems, is extended to systems with state delay. The notion of control barrier functionals is introduced to attain formal safety guarantees, by enforcing the forward invariance of safe sets defined in the infinite dimensional state space. The proposed framework is able to handle multiple delays and distributed delays both in the dynamics and in the safety condition, and provides an affine constraint on the control input that yields provable safety. This constraint can be incorporated into optimization problems to synthesize pointwise optimal and provable safe controllers. The applicability of the proposed method is demonstrated by numerical simulation examples.

Control Barrier Functions and Input-to-State Safety with Application to Automated Vehicles

Balancing safety and performance is one of the predominant challenges in modern control system design. Moreover, it is crucial to robustly ensure safety without inducing unnecessary conservativeness that degrades performance. In this work we present a constructive approach for safety-critical control synthesis via Control Barrier Functions (CBF). By filtering a hand-designed controller via a CBF, we are able to attain performant behavior while providing rigorous guarantees of safety. In the face of disturbances, robust safety and performance are simultaneously achieved through the notion of Input-to-State Safety (ISSf). We take a tutorial approach by developing the CBF-design methodology in parallel with an inverted pendulum example, making the challenges and sensitivities in the design process concrete. To establish the capability of the proposed approach, we consider the practical setting of safety-critical design via CBFs for a connected automated vehicle (CAV) in the form of a class-8 truck without a trailer. Through experimentation we see the impact of unmodeled disturbances in the truck's actuation system on the safety guarantees provided by CBFs. We characterize these disturbances and using ISSf, produce a robust controller that achieves safety without conceding performance. We evaluate our design both in simulation, and for the first time on an automotive system, experimentally.