Robust STL Control Synthesis under Maximal Disturbance Sets

This work addresses maximally robust control synthesis under unknown disturbances. We consider a general nonlinear system, subject to a Signal Temporal Logic (STL) specification, and wish to jointly synthesize the maximal possible disturbance bounds and the corresponding controllers that ensure the STL specification is satisfied under these bounds. Many works have considered STL satisfaction under given bounded disturbances. Yet, to the authors' best knowledge, this is the first work that aims to maximize the permissible disturbance set and find the corresponding controllers that ensure satisfying the STL specification with maximum disturbance robustness. We extend the notion of disturbance-robust semantics for STL, which is a property of a specification, dynamical system, and controller, and provide an algorithm to get the maximal disturbance robust controllers satisfying an STL specification using Hamilton-Jacobi reachability. We show its soundness and provide a simulation example with an Autonomous Underwater Vehicle (AUV).

Risk-Aware Robotics: Tail Risk Measures in Planning, Control, and Verification

The need for a systematic approach to risk assessment has increased in recent years due to the ubiquity of autonomous systems that alter our day-to-day experiences and their need for safety, e.g., for self-driving vehicles, mobile service robots, and bipedal robots. These systems are expected to function safely in unpredictable environments and interact seamlessly with humans, whose behavior is notably challenging to forecast. We present a survey of risk-aware methodologies for autonomous systems. We adopt a contemporary risk-aware approach to mitigate rare and detrimental outcomes by advocating the use of tail risk measures, a concept borrowed from financial literature. This survey will introduce these measures and explain their relevance in the context of robotic systems for planning, control, and verification applications.

Conformalized Adaptive Forecasting of Heterogeneous Trajectories

This paper presents a new conformal method for generating simultaneous forecasting bands guaranteed to cover the entire path of a new random trajectory with sufficiently high probability. Prompted by the need for dependable uncertainty estimates in motion planning applications where the behavior of diverse objects may be more or less unpredictable, we blend different techniques from online conformal prediction of single and multiple time series, as well as ideas for addressing heteroscedasticity in regression. This solution is both principled, providing precise finite-sample guarantees, and effective, often leading to more informative predictions than prior methods.

Conformal Predictive Programming for Chance Constrained Optimization

Motivated by the advances in conformal prediction (CP), we propose conformal predictive programming (CPP), an approach to solve chance constrained optimization (CCO) problems, i.e., optimization problems with nonlinear constraint functions affected by arbitrary random parameters. CPP utilizes samples from these random parameters along with the quantile lemma -- which is central to CP -- to transform the CCO problem into a deterministic optimization problem. We then present two tractable reformulations of CPP by: (1) writing the quantile as a linear program along with its KKT conditions (CPP-KKT), and (2) using mixed integer programming (CPP-MIP). CPP comes with marginal probabilistic feasibility guarantees for the CCO problem that are conceptually different from existing approaches, e.g., the sample approximation and the scenario approach. While we explore algorithmic similarities with the sample approximation approach, we emphasize that the strength of CPP is that it can easily be extended to incorporate different variants of CP. To illustrate this, we present robust conformal predictive programming to deal with distribution shifts in the uncertain parameters of the CCO problem.

Multi-Modal Conformal Prediction Regions by Optimizing Convex Shape Templates

Conformal prediction is a statistical tool for producing prediction regions for machine learning models that are valid with high probability. A key component of conformal prediction algorithms is a non-conformity score function that quantifies how different a model's prediction is from the unknown ground truth value. Essentially, these functions determine the shape and the size of the conformal prediction regions. However, little work has gone into finding non-conformity score functions that produce prediction regions that are multi-modal and practical, i.e., that can efficiently be used in engineering applications. We propose a method that optimizes parameterized shape template functions over calibration data, which results in non-conformity score functions that produce prediction regions with minimum volume. Our approach results in prediction regions that are multi-modal, so they can properly capture residuals of distributions that have multiple modes, and practical, so each region is convex and can be easily incorporated into downstream tasks, such as a motion planner using conformal prediction regions. Our method applies to general supervised learning tasks, while we illustrate its use in time-series prediction. We provide a toolbox and present illustrative case studies of F16 fighter jets and autonomous vehicles, showing an up to $68\%$ reduction in prediction region area.

Robust Conformal Prediction for STL Runtime Verification under Distribution Shift

Cyber-physical systems (CPS) designed in simulators behave differently in the real-world. Once they are deployed in the real-world, we would hence like to predict system failures during runtime. We propose robust predictive runtime verification (RPRV) algorithms under signal temporal logic (STL) tasks for general stochastic CPS. The RPRV problem faces several challenges: (1) there may not be sufficient data of the behavior of the deployed CPS, (2) predictive models are based on a distribution over system trajectories encountered during the design phase, i.e., there may be a distribution shift during deployment. To address these challenges, we assume to know an upper bound on the statistical distance (in terms of an f-divergence) between the distributions at deployment and design time, and we utilize techniques based on robust conformal prediction. Motivated by our results in [1], we construct an accurate and an interpretable RPRV algorithm. We use a trajectory prediction model to estimate the system behavior at runtime and robust conformal prediction to obtain probabilistic guarantees by accounting for distribution shifts. We precisely quantify the relationship between calibration data, desired confidence, and permissible distribution shift. To the best of our knowledge, these are the first statistically valid algorithms under distribution shift in this setting. We empirically validate our algorithms on a Franka manipulator within the NVIDIA Isaac sim environment.

Temporally Robust Multi-Agent STL Motion Planning in Continuous Time

Signal Temporal Logic (STL) is a formal language over continuous-time signals (such as trajectories of a multi-agent system) that allows for the specification of complex spatial and temporal system requirements (such as staying sufficiently close to each other within certain time intervals). To promote robustness in multi-agent motion planning with such complex requirements, we consider motion planning with the goal of maximizing the temporal robustness of their joint STL specification, i.e. maximizing the permissible time shifts of each agent's trajectory while still satisfying the STL specification. Previous methods presented temporally robust motion planning and control in a discrete-time Mixed Integer Linear Programming (MILP) optimization scheme. In contrast, we parameterize the trajectory by continuous B\'ezier curves, where the curvature and the time-traversal of the trajectory are parameterized individually. We show an algorithm generating continuous-time temporally robust trajectories and prove soundness of our approach. Moreover, we empirically show that our parametrization realizes this with a considerable speed-up compared to state-of-the-art methods based on constant interval time discretization.

Data-Driven Reachability Analysis of Stochastic Dynamical Systems with Conformal Inference

We consider data-driven reachability analysis of discrete-time stochastic dynamical systems using conformal inference. We assume that we are not provided with a symbolic representation of the stochastic system, but instead have access to a dataset of $K$-step trajectories. The reachability problem is to construct a probabilistic flowpipe such that the probability that a $K$-step trajectory can violate the bounds of the flowpipe does not exceed a user-specified failure probability threshold. The key ideas in this paper are: (1) to learn a surrogate predictor model from data, (2) to perform reachability analysis using the surrogate model, and (3) to quantify the surrogate model's incurred error using conformal inference in order to give probabilistic reachability guarantees. We focus on learning-enabled control systems with complex closed-loop dynamics that are difficult to model symbolically, but where state transition pairs can be queried, e.g., using a simulator. We demonstrate the applicability of our method on examples from the domain of learning-enabled cyber-physical systems.

Conformal Predictive Safety Filter for RL Controllers in Dynamic Environments

The interest in using reinforcement learning (RL) controllers in safety-critical applications such as robot navigation around pedestrians motivates the development of additional safety mechanisms. Running RL-enabled systems among uncertain dynamic agents may result in high counts of collisions and failures to reach the goal. The system could be safer if the pre-trained RL policy was uncertainty-informed. For that reason, we propose conformal predictive safety filters that: 1) predict the other agents' trajectories, 2) use statistical techniques to provide uncertainty intervals around these predictions, and 3) learn an additional safety filter that closely follows the RL controller but avoids the uncertainty intervals. We use conformal prediction to learn uncertainty-informed predictive safety filters, which make no assumptions about the agents' distribution. The framework is modular and outperforms the existing controllers in simulation. We demonstrate our approach with multiple experiments in a collision avoidance gym environment and show that our approach minimizes the number of collisions without making overly-conservative predictions.

Conformal Prediction Regions for Time Series using Linear Complementarity Programming

Conformal prediction is a statistical tool for producing prediction regions of machine learning models that are valid with high probability. However, applying conformal prediction to time series data leads to conservative prediction regions. In fact, to obtain prediction regions over $T$ time steps with confidence $1-\delta$, {previous works require that each individual prediction region is valid} with confidence $1-\delta/T$. We propose an optimization-based method for reducing this conservatism to enable long horizon planning and verification when using learning-enabled time series predictors. Instead of considering prediction errors individually at each time step, we consider a parameterized prediction error over multiple time steps. By optimizing the parameters over an additional dataset, we find prediction regions that are not conservative. We show that this problem can be cast as a mixed integer linear complementarity program (MILCP), which we then relax into a linear complementarity program (LCP). Additionally, we prove that the relaxed LP has the same optimal cost as the original MILCP. Finally, we demonstrate the efficacy of our method on a case study using pedestrian trajectory predictors.