Data-Driven Safety-Critical Autonomy in Unknown, Unstructured, and Dynamic Environments

Citation

Wei, Skylar X. (2024) Data-Driven Safety-Critical Autonomy in Unknown, Unstructured, and Dynamic Environments. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/qpbp-0x81. https://resolver.caltech.edu/CaltechTHESIS:03042024-201031352

Abstract

This thesis addresses the critical challenge of ensuring safety in autonomous exploration within unknown, unstructured, dynamic environments, a domain filled with various types of uncertainties. These include model uncertainties in system dynamics, localization uncertainties stemming from measurement noises, and the risks of collision in environments with dynamic obstacles. Traditional models for vehicle planning and control are often simplified for computational feasibility, but this simplification without careful analysis can compromise safety and system stability. My research introduces a novel, comprehensive framework to provide probabilistically safe planning and control for robot autonomy, structured around three components:

(1) Probabilistic Uncertainty Quantification for Model Mismatches:

This segment focuses on identifying model discrepancies given closed-loop tracking data in an unstructured environment where a reduced-order robot model is used for planning and control. The disturbance is modeled as a scalar-valued stochastic process of a norm on the difference between the reduce-order robot model and actual system evolution. In an online and risk-aware framework, Gaussian Process Regression is employed to extract the probabilistic upper bound to such stochastic process, referred to as the Surface-at-Risk. Theoretical guarantees on the accuracy of the fitted discrepancy surface are analyzed and verified to the data sets collected during system operation.

In an offline setting, conformal prediction, a statistical inference tool, is employed to obtain probabilistic upper bounds of matched and unmatched model disturbance in the system from data, without any assumption of the latent probability distribution governing these discrepancies. Building on these bounds, the robot's nominal ancillary controller is augmented for extending robustness and stability guarantees of the closed-loop system in the face of such discrepancies. Additionally, a maximum tracking error tube is constructed along the planned trajectory using the reduced-order model. Such error tubes describe the maximum permissible deviation in actual trajectory tracking under the augmented ancillary controller and the worst-case matched and unmatched model uncertainties, thereby delineating safe operational boundaries for the system.

(2) Data-Driven Unsafe Set Prediction for Dynamic Obstacles:

This thesis topic develops an online, data-driven predictive model for dynamic obstacles, accounting for measurement noise and low-frequency data rates. First inspired by singular spectrum analysis (SSA), a time-series forecast technique, obstacle models characterized by linear recurrence relationships are extracted from real-time position observables. Using the statistical bootstrap technique, a set of predicted obstacle trajectories are constructed, which in turn are reformulated into deterministic distributionally robust obstacle avoidance constraints, reflecting a user-defined risk tolerance.

Further refining the obstacle predictor for intention-unknown obstacles, a linear, time-varying model is learned from data using time-delay embedding of obstacle position observables. Additive process and measurement noises are anticipated in the learned model, where their intensities are estimated from data. For inferring prediction uncertainties, a companion data-driven Kalman Filter (DDKF) is constructed to forecast obstacle positions and uncertainties. This "heuristic unsafe set" from DDKF is then dynamically calibrated using adaptive conformal prediction, ensuring safety without relying on any distribution assumptions regarding the uncertainties or model accuracy. The calibrated sets, called conformal prediction sets, are then reformulated into convex state constraints.

(3) Safety-Critical Planning:

The thesis proposes two methods for ensuring safety in planning and navigation: Probabilistic-Safe Model Predictive Control (MPC) and Probabilistic-Safe Model Predictive Path Integral (MPPI) given uncertainties arising from operating in unknown, unstructured, and dynamic environments. The MPC approach integrates the quantified obstacle avoidance constraints into a convex program to balance computational tractability while providing probabilistic safety guarantees. In contrast, the MPPI method, a sampling-based strategy, incorporating unsafe sets into a cost map derived from sensory data, optimizes reference tracking trajectory while guaranteeing collision avoidance up to a user-defined risk tolerance.

In unknown and cluttered environments automatically, the proposed framework learns an upper bound on model residuals from data and systematically calculates the safety buffers needed to provide the desired probabilistic safe navigation of robotics systems. Additionally, in the presence of dynamic obstacles, the proposed data-driven predictor systematically extracts an obstacle model and makes obstacle-occupied unsafe set forecasts. These features largely eliminate the "hand tuning" of the underlying planner and controller that is normally required in heuristic-based algorithms. The efficacy of these proposed frameworks is empirically validated through Monte Carlo Simulations, alongside hardware validations on both ground and aerial vehicles, demonstrating their robustness, versatility, and applicability in real-world scenarios.

Thesis Files