arXiv subjects

Marco Pavone

Publications and source records attributed to Marco Pavone.

At least 253 records · Page 14Linked to original sources

arXiv2022

Sequential Convex Programming For Non-Linear Stochastic Optimal Control

This work introduces a sequential convex programming framework for non-linear, finite-dimensional stochastic optimal control, where uncertainties are modeled by a multidimensional Wiener process. We prove that any accumulation point of the sequence of iterates generated by sequential convex programming is a candidate locally-optimal solution for the original problem in the sense of the stochastic Pontryagin Maximum Principle. Moreover, we provide sufficient conditions for the existence of at least one such accumulation point. We then leverage these properties to design a practical numerical method for solving non-linear stochastic optimal control problems based on a deterministic transcription of stochastic sequential convex programming.

math.OC↗

arXiv2022

Data Lifecycle Management in Evolving Input Distributions for Learning-based Aerospace Applications

As input distributions evolve over a mission lifetime, maintaining performance of learning-based models becomes challenging. This paper presents a framework to incrementally retrain a model by selecting a subset of test inputs to label, which allows the model to adapt to changing input distributions. Algorithms within this framework are evaluated based on (1) model performance throughout mission lifetime and (2) cumulative costs associated with labeling and model retraining. We provide an open-source benchmark of a satellite pose estimation model trained on images of a satellite in space and deployed in novel scenarios (e.g., different backgrounds or misbehaving pixels), where algorithms are evaluated on their ability to maintain high performance by retraining on a subset of inputs. We also propose a novel algorithm to select a diverse subset of inputs for labeling, by characterizing the information gain from an input using Bayesian uncertainty quantification and choosing a subset that maximizes collective information gain using concepts from batch active learning. We show that our algorithm outperforms others on the benchmark, e.g., achieves comparable performance to an algorithm that labels 100% of inputs, while only labeling 50% of inputs, resulting in low costs and high performance over the mission lifetime.

cs.CV↗

arXiv2022

Motion Planning for a Climbing Robot with Stochastic Grasps

Motion planning for a multi-limbed climbing robot must consider the robot's posture, joint torques, and how it uses contact forces to interact with its environment. This paper focuses on motion planning for a robot that uses nontraditional locomotion to explore unpredictable environments such as martian caves. Our robotic concept, ReachBot, uses extendable and retractable booms as limbs to achieve a large reachable workspace while climbing. Each extendable boom is capped by a microspine gripper designed for grasping rocky surfaces. ReachBot leverages its large workspace to navigate around obstacles, over crevasses, and through challenging terrain. Our planning approach must be versatile to accommodate variable terrain features and robust to mitigate risks from the stochastic nature of grasping with spines. In this paper, we introduce a graph traversal algorithm to select a discrete sequence of grasps based on available terrain features suitable for grasping. This discrete plan is complemented by a decoupled motion planner that considers the alternating phases of body movement and end-effector movement, using a combination of sampling-based planning and sequential convex programming to optimize individual phases. We use our motion planner to plan a trajectory across a simulated 2D cave environment with at least 95% probability of success and demonstrate improved robustness over a baseline trajectory. Finally, we verify our motion planning algorithm through experimentation on a 2D planar prototype.

cs.RO↗

arXiv2022

Data-Driven Spectral Submanifold Reduction for Nonlinear Optimal Control of High-Dimensional Robots

Modeling and control of high-dimensional, nonlinear robotic systems remains a challenging task. While various model- and learning-based approaches have been proposed to address these challenges, they broadly lack generalizability to different control tasks and rarely preserve the structure of the dynamics. In this work, we propose a new, data-driven approach for extracting low-dimensional models from data using Spectral Submanifold Reduction (SSMR). In contrast to other data-driven methods which fit dynamical models to training trajectories, we identify the dynamics on generic, low-dimensional attractors embedded in the full phase space of the robotic system. This allows us to obtain computationally-tractable models for control which preserve the system's dominant dynamics and better track trajectories radically different from the training data. We demonstrate the superior performance and generalizability of SSMR in dynamic trajectory tracking tasks vis-a-vis the state of the art, including Koopman operator-based approaches.

cs.RO↗

arXiv2022

AdvDO: Realistic Adversarial Attacks for Trajectory Prediction

Trajectory prediction is essential for autonomous vehicles (AVs) to plan correct and safe driving behaviors. While many prior works aim to achieve higher prediction accuracy, few study the adversarial robustness of their methods. To bridge this gap, we propose to study the adversarial robustness of data-driven trajectory prediction systems. We devise an optimization-based adversarial attack framework that leverages a carefully-designed differentiable dynamic model to generate realistic adversarial trajectories. Empirically, we benchmark the adversarial robustness of state-of-the-art prediction models and show that our attack increases the prediction error for both general metrics and planning-aware metrics by more than 50% and 37%. We also show that our attack can lead an AV to drive off road or collide into other vehicles in simulation. Finally, we demonstrate how to mitigate the adversarial attacks using an adversarial training scheme.

cs.LG↗

arXiv2022

Using Spectral Submanifolds for Nonlinear Periodic Control

Very high dimensional nonlinear systems arise in many engineering problems due to semi-discretization of the governing partial differential equations, e.g. through finite element methods. The complexity of these systems present computational challenges for direct application to automatic control. While model reduction has seen ubiquitous applications in control, the use of nonlinear model reduction methods in this setting remains difficult. The problem lies in preserving the structure of the nonlinear dynamics in the reduced order model for high-fidelity control. In this work, we leverage recent advances in Spectral Submanifold (SSM) theory to enable model reduction under well-defined assumptions for the purpose of efficiently synthesizing feedback controllers.

math.OC↗

arXiv2022

Analysis of Theoretical and Numerical Properties of Sequential Convex Programming for Continuous-Time Optimal Control

Sequential Convex Programming (SCP) has recently gained significant popularity as an effective method for solving optimal control problems and has been successfully applied in several different domains. However, the theoretical analysis of SCP has received comparatively limited attention, and it is often restricted to discrete-time formulations. In this paper, we present a unifying theoretical analysis of a fairly general class of SCP procedures for continuous-time optimal control problems. In addition to the derivation of convergence guarantees in a continuous-time setting, our analysis reveals two new numerical and practical insights. First, we show how one can more easily account for manifold-type constraints, which are a defining feature of optimal control of mechanical systems. Second, we show how our theoretical analysis can be leveraged to accelerate SCP-based optimal control methods by infusing techniques from indirect optimal control.

math.OC↗

arXiv2022

BITS: Bi-level Imitation for Traffic Simulation

Simulation is the key to scaling up validation and verification for robotic systems such as autonomous vehicles. Despite advances in high-fidelity physics and sensor simulation, a critical gap remains in simulating realistic behaviors of road users. This is because, unlike simulating physics and graphics, devising first principle models for human-like behaviors is generally infeasible. In this work, we take a data-driven approach and propose a method that can learn to generate traffic behaviors from real-world driving logs. The method achieves high sample efficiency and behavior diversity by exploiting the bi-level hierarchy of driving behaviors by decoupling the traffic simulation problem into high-level intent inference and low-level driving behavior imitation. The method also incorporates a planning module to obtain stable long-horizon behaviors. We empirically validate our method, named Bi-level Imitation for Traffic Simulation (BITS), with scenarios from two large-scale driving datasets and show that BITS achieves balanced traffic simulation performance in realism, diversity, and long-horizon stability. We also explore ways to evaluate behavior realism and introduce a suite of evaluation metrics for traffic simulation. Finally, as part of our core contributions, we develop and open source a software tool that unifies data formats across different driving datasets and converts scenes from existing datasets into interactive simulation environments. For additional information and videos, see https://sites.google.com/view/nvr-bits2022/home

cs.RO↗

arXiv2022

Local Calibration: Metrics and Recalibration

Probabilistic classifiers output confidence scores along with their predictions, and these confidence scores should be calibrated, i.e., they should reflect the reliability of the prediction. Confidence scores that minimize standard metrics such as the expected calibration error (ECE) accurately measure the reliability on average across the entire population. However, it is in general impossible to measure the reliability of an individual prediction. In this work, we propose the local calibration error (LCE) to span the gap between average and individual reliability. For each individual prediction, the LCE measures the average reliability of a set of similar predictions, where similarity is quantified by a kernel function on a pretrained feature space and by a binning scheme over predicted model confidences. We show theoretically that the LCE can be estimated sample-efficiently from data, and empirically find that it reveals miscalibration modes that are more fine-grained than the ECE can detect. Our key result is a novel local recalibration method LoRe, to improve confidence scores for individual predictions and decrease the LCE. Experimentally, we show that our recalibration method produces more accurate confidence scores, which improves downstream fairness and decision making on classification tasks with both image and tabular data.

cs.LG↗

arXiv2022

Learning Deep SDF Maps Online for Robot Navigation and Exploration

We propose an algorithm to (i) learn online a deep signed distance function (SDF) with a LiDAR-equipped robot to represent the 3D environment geometry, and (ii) plan collision-free trajectories given this deep learned map. Our algorithm takes a stream of incoming LiDAR scans and continually optimizes a neural network to represent the SDF of the environment around its current vicinity. When the SDF network quality saturates, we cache a copy of the network, along with a learned confidence metric, and initialize a new SDF network to continue mapping new regions of the environment. We then concatenate all the cached local SDFs through a confidence-weighted scheme to give a global SDF for planning. For planning, we make use of a sequential convex model predictive control (MPC) algorithm. The MPC planner optimizes a dynamically feasible trajectory for the robot while enforcing no collisions with obstacles mapped in the global SDF. We show that our online mapping algorithm produces higher-quality maps than existing methods for online SDF training. In the WeBots simulator, we further showcase the combined mapper and planner running online -- navigating autonomously and without collisions in an unknown environment.

cs.RO↗

arXiv2022

Robust Trajectory Prediction against Adversarial Attacks

Trajectory prediction using deep neural networks (DNNs) is an essential component of autonomous driving (AD) systems. However, these methods are vulnerable to adversarial attacks, leading to serious consequences such as collisions. In this work, we identify two key ingredients to defend trajectory prediction models against adversarial attacks including (1) designing effective adversarial training methods and (2) adding domain-specific data augmentation to mitigate the performance degradation on clean data. We demonstrate that our method is able to improve the performance by 46% on adversarial data and at the cost of only 3% performance degradation on clean data, compared to the model trained with clean data. Additionally, compared to existing robust methods, our method can improve performance by 21% on adversarial examples and 9% on clean data. Our robust model is evaluated with a planner to study its downstream impacts. We demonstrate that our model can significantly reduce the severe accident rates (e.g., collisions and off-road driving).

cs.LG↗

arXiv2022

Propagating State Uncertainty Through Trajectory Forecasting

Uncertainty pervades through the modern robotic autonomy stack, with nearly every component (e.g., sensors, detection, classification, tracking, behavior prediction) producing continuous or discrete probabilistic distributions. Trajectory forecasting, in particular, is surrounded by uncertainty as its inputs are produced by (noisy) upstream perception and its outputs are predictions that are often probabilistic for use in downstream planning. However, most trajectory forecasting methods do not account for upstream uncertainty, instead taking only the most-likely values. As a result, perceptual uncertainties are not propagated through forecasting and predictions are frequently overconfident. To address this, we present a novel method for incorporating perceptual state uncertainty in trajectory forecasting, a key component of which is a new statistical distance-based loss function which encourages predicting uncertainties that better match upstream perception. We evaluate our approach both in illustrative simulations and on large-scale, real-world data, demonstrating its efficacy in propagating perceptual state uncertainty through prediction and producing more calibrated predictions.

cs.RO↗

arXiv2022

Risk-sensitive safety analysis using Conditional Value-at-Risk

This paper develops a safety analysis method for stochastic systems that is sensitive to the possibility and severity of rare harmful outcomes. We define risk-sensitive safe sets as sub-level sets of the solution to a non-standard optimal control problem, where a random maximum cost is assessed via Conditional Value-at-Risk (CVaR). The objective function represents the maximum extent of constraint violation of the state trajectory, averaged over a given percentage of worst cases. This problem is well-motivated but difficult to solve tractably because the temporal decomposition for CVaR is history-dependent. Our primary theoretical contribution is to derive computationally tractable under-approximations to risk-sensitive safe sets. Our method provides a novel, theoretically guaranteed, parameter-dependent upper bound to the CVaR of a maximum cost without the need to augment the state space. For a fixed parameter value, the solution to only one Markov decision process problem is required to obtain the under-approximations for any family of risk-sensitivity levels. In addition, we propose a second definition for risk-sensitive safe sets and provide a tractable method for their estimation without using a parameter-dependent upper bound. The second definition is expressed in terms of a new coherent risk functional, which is inspired by CVaR. We demonstrate our primary theoretical contribution via numerical examples.

eess.SY↗

arXiv2022

Interaction-Dynamics-Aware Perception Zones for Obstacle Detection Safety Evaluation

To enable safe autonomous vehicle (AV) operations, it is critical that an AV's obstacle detection module can reliably detect obstacles that pose a safety threat (i.e., are safety-critical). It is therefore desirable that the evaluation metric for the perception system captures the safety-criticality of objects. Unfortunately, existing perception evaluation metrics tend to make strong assumptions about the objects and ignore the dynamic interactions between agents, and thus do not accurately capture the safety risks in reality. To address these shortcomings, we introduce an interaction-dynamics-aware obstacle detection evaluation metric by accounting for closed-loop dynamic interactions between an ego vehicle and obstacles in the scene. By borrowing existing theory from optimal control theory, namely Hamilton-Jacobi reachability, we present a computationally tractable method for constructing a ``safety zone'': a region in state space that defines where safety-critical obstacles lie for the purpose of defining safety metrics. Our proposed safety zone is mathematically complete, and can be easily computed to reflect a variety of safety requirements. Using an off-the-shelf detection algorithm from the nuScenes detection challenge leaderboard, we demonstrate that our approach is computationally lightweight, and can better capture safety-critical perception errors than a baseline approach.

cs.RO↗

arXiv2022

Towards Data-Driven Synthesis of Autonomous Vehicle Safety Concepts

As safety-critical autonomous vehicles (AVs) will soon become pervasive in our society, a number of safety concepts for trusted AV deployment have recently been proposed throughout industry and academia. Yet, achieving consensus on an appropriate safety concept is still an elusive task. In this paper, we advocate for the use of Hamilton-Jacobi (HJ) reachability as a unifying mathematical framework for comparing existing safety concepts, and through elements of this framework propose ways to tailor safety concepts (and thus expand their applicability) to scenarios with implicit expectations on agent behavior in a data-driven fashion. Specifically, we show that (i) existing predominant safety concepts can be embedded in the HJ reachability framework, thereby enabling a common language for comparing and contrasting modeling assumptions, and (ii) HJ reachability can serve as an inductive bias to effectively reason, in a learning context, about two critical, yet often overlooked aspects of safety: responsibility and context-dependency.

cs.RO↗

arXiv2022

ScePT: Scene-consistent, Policy-based Trajectory Predictions for Planning

Trajectory prediction is a critical functionality of autonomous systems that share environments with uncontrolled agents, one prominent example being self-driving vehicles. Currently, most prediction methods do not enforce scene consistency, i.e., there are a substantial amount of self-collisions between predicted trajectories of different agents in the scene. Moreover, many approaches generate individual trajectory predictions per agent instead of joint trajectory predictions of the whole scene, which makes downstream planning difficult. In this work, we present ScePT, a policy planning-based trajectory prediction model that generates accurate, scene-consistent trajectory predictions suitable for autonomous system motion planning. It explicitly enforces scene consistency and learns an agent interaction policy that can be used for conditional prediction. Experiments on multiple real-world pedestrians and autonomous vehicle datasets show that ScePT} matches current state-of-the-art prediction accuracy with significantly improved scene consistency. We also demonstrate ScePT's ability to work with a downstream contingency planner.

cs.AI↗

arXiv2022

Linear Reduced Order Model Predictive Control

Model predictive controllers use dynamics models to solve constrained optimal control problems. However, computational requirements for real-time control have limited their use to systems with low-dimensional models. Nevertheless, high-dimensional models arise in many settings, for example discretization methods for generating finite-dimensional approximations to partial differential equations can result in models with thousands to millions of dimensions. In such cases, reduced order models (ROMs) can significantly reduce computational requirements, but model approximation error must be considered to guarantee controller performance. In this work, a reduced order model predictive control (ROMPC) scheme is proposed to solve robust, output feedback, constrained optimal control problems for high-dimensional linear systems. Computational efficiency is obtained by using projection-based ROMs, and guarantees on robust constraint satisfaction and stability are provided. Performance of the approach is demonstrated in simulation for several examples, including an aircraft control problem leveraging an inviscid computational fluid dynamics model with dimension 998,930.

eess.SY↗

arXiv2022

Second-Order Sensitivity Analysis for Bilevel Optimization

In this work we derive a second-order approach to bilevel optimization, a type of mathematical programming in which the solution to a parameterized optimization problem (the "lower" problem) is itself to be optimized (in the "upper" problem) as a function of the parameters. Many existing approaches to bilevel optimization employ first-order sensitivity analysis, based on the implicit function theorem (IFT), for the lower problem to derive a gradient of the lower problem solution with respect to its parameters; this IFT gradient is then used in a first-order optimization method for the upper problem. This paper extends this sensitivity analysis to provide second-order derivative information of the lower problem (which we call the IFT Hessian), enabling the usage of faster-converging second-order optimization methods at the upper level. Our analysis shows that (i) much of the computation already used to produce the IFT gradient can be reused for the IFT Hessian, (ii) errors bounds derived for the IFT gradient readily apply to the IFT Hessian, (iii) computing IFT Hessians can significantly reduce overall computation by extracting more information from each lower level solve. We corroborate our findings and demonstrate the broad range of applications of our method by applying it to problem instances of least squares hyperparameter auto-tuning, multi-class SVM auto-tuning, and inverse optimal control.

math.OC↗