arXiv subjects

Matthias Althoff

Publications and source records attributed to Matthias Althoff.

90 records · Page 5Linked to original sources

arXiv2023

Geometric Deep Learning for Autonomous Driving: Unlocking the Power of Graph Neural Networks With CommonRoad-Geometric

Heterogeneous graphs offer powerful data representations for traffic, given their ability to model the complex interaction effects among a varying number of traffic participants and the underlying road infrastructure. With the recent advent of graph neural networks (GNNs) as the accompanying deep learning framework, the graph structure can be efficiently leveraged for various machine learning applications such as trajectory prediction. As a first of its kind, our proposed Python framework offers an easy-to-use and fully customizable data processing pipeline to extract standardized graph datasets from traffic scenarios. Providing a platform for GNN-based autonomous driving research, it improves comparability between approaches and allows researchers to focus on model implementation instead of dataset curation.

cs.LG↗

arXiv2023

Open- and Closed-Loop Neural Network Verification using Polynomial Zonotopes

We present a novel approach to efficiently compute tight non-convex enclosures of the image through neural networks with ReLU, sigmoid, or hyperbolic tangent activation functions. In particular, we abstract the input-output relation of each neuron by a polynomial approximation, which is evaluated in a set-based manner using polynomial zonotopes. While our approach can also can be beneficial for open-loop neural network verification, our main application is reachability analysis of neural network controlled systems, where polynomial zonotopes are able to capture the non-convexity caused by the neural network as well as the system dynamics. This results in a superior performance compared to other methods, as we demonstrate on various benchmarks.

cs.CV↗

arXiv2023

Constrained Polynomial Zonotopes

We introduce constrained polynomial zonotopes, a novel non-convex set representation that is closed under linear map, Minkowski sum, Cartesian product, convex hull, intersection, union, and quadratic as well as higher-order maps. We show that the computational complexity of the above-mentioned set operations for constrained polynomial zonotopes is at most polynomial in the representation size. The fact that constrained polynomial zonotopes are generalizations of zonotopes, polytopes, polynomial zonotopes, Taylor models, and ellipsoids, further substantiates the relevance of this new set representation. The conversion from other set representations to constrained polynomial zonotopes is at most polynomial with respect to the dimension.

math.CO↗

arXiv2023

Falsification-Based Robust Adversarial Reinforcement Learning

Reinforcement learning (RL) has achieved enormous progress in solving various sequential decision-making problems, such as control tasks in robotics. Since policies are overfitted to training environments, RL methods have often failed to be generalized to safety-critical test scenarios. Robust adversarial RL (RARL) was previously proposed to train an adversarial network that applies disturbances to a system, which improves the robustness in test scenarios. However, an issue of neural network-based adversaries is that integrating system requirements without handcrafting sophisticated reward signals are difficult. Safety falsification methods allow one to find a set of initial conditions and an input sequence, such that the system violates a given property formulated in temporal logic. In this paper, we propose falsification-based RARL (FRARL): this is the first generic framework for integrating temporal logic falsification in adversarial learning to improve policy robustness. By applying our falsification method, we do not need to construct an extra reward function for the adversary. Moreover, we evaluate our approach on a braking assistance system and an adaptive cruise control system of autonomous vehicles. Our experimental results demonstrate that policies trained with a falsification-based adversary generalize better and show less violation of the safety specification in test scenarios than those trained without an adversary or with an adversarial network.

cs.RO↗

arXiv2023

Provably Safe Reinforcement Learning via Action Projection using Reachability Analysis and Polynomial Zonotopes

While reinforcement learning produces very promising results for many applications, its main disadvantage is the lack of safety guarantees, which prevents its use in safety-critical systems. In this work, we address this issue by a safety shield for nonlinear continuous systems that solve reach-avoid tasks. Our safety shield prevents applying potentially unsafe actions from a reinforcement learning agent by projecting the proposed action to the closest safe action. This approach is called action projection and is implemented via mixed-integer optimization. The safety constraints for action projection are obtained by applying parameterized reachability analysis using polynomial zonotopes, which enables to accurately capture the nonlinear effects of the actions on the system. In contrast to other state-of-the-art approaches for action projection, our safety shield can efficiently handle input constraints and dynamic obstacles, eases incorporation of the spatial robot dimensions into the safety constraints, guarantees robust safety despite process noise and measurement errors, and is well suited for high-dimensional systems, as we demonstrate on several challenging benchmark systems.

cs.RO↗

arXiv2023

M-Representation of Polytopes

We introduce the M-representation of polytopes, which makes it possible to compute linear transformations, convex hulls, and Minkowski sums with linear complexity in the dimension of the polytopes. When the polytope is a convex hull of a zonotope and a polytope, the representation size can be smaller than any of the known representations (V-representation, H-representation, and Z-representation). We also provide a variant of the M-representation: The chain representation is more compact and we can directly use it to compute linear transformations and convex hulls -- for all other operations on the chain representation, one requires a conversion to the M-representation.

math.CO↗

arXiv2023

Deep Occupancy-Predictive Representations for Autonomous Driving

Manually specifying features that capture the diversity in traffic environments is impractical. Consequently, learning-based agents cannot realize their full potential as neural motion planners for autonomous vehicles. Instead, this work proposes to learn which features are task-relevant. Given its immediate relevance to motion planning, our proposed architecture encodes the probabilistic occupancy map as a proxy for obtaining pre-trained state representations. By leveraging a map-aware graph formulation of the environment, our agent-centric encoder generalizes to arbitrary road networks and traffic situations. We show that our approach significantly improves the downstream performance of a reinforcement learning agent operating in urban traffic environments.

cs.LG↗

arXiv2023

Privacy Preserving Set-Based Estimation Using Partially Homomorphic Encryption

The set-based estimation has gained a lot of attention due to its ability to guarantee state enclosures for safety-critical systems. However, collecting measurements from distributed sensors often requires outsourcing the set-based operations to an aggregator node, raising many privacy concerns. To address this problem, we present set-based estimation protocols using partially homomorphic encryption that preserve the privacy of the measurements and sets bounding the estimates. We consider a linear discrete-time dynamical system with bounded modeling and measurement uncertainties. Sets are represented by zonotopes and constrained zonotopes as they can compactly represent high-dimensional sets and are closed under linear maps and Minkowski addition. By selectively encrypting parameters of the set representations, we establish the notion of encrypted sets and intersect sets in the encrypted domain, which enables guaranteed state estimation while ensuring privacy. In particular, we show that our protocols achieve computational privacy using the cryptographic notion of computational indistinguishability. We demonstrate the efficiency of our approach by localizing a real mobile quadcopter using ultra-wideband wireless devices.

cs.CR↗

arXiv2022

On Computing the Minkowski Difference of Zonotopes

Zonotopes are becoming an increasingly popular set representation for formal verification techniques. This is mainly due to their efficient representation and their favorable computational complexity of important operations in high-dimensional spaces. In particular, zonotopes are closed under Minkowski addition and linear maps, which can be very efficiently implemented. Unfortunately, zonotopes are not closed under Minkowski difference for dimensions greater than two. However, we present an algorithm that efficiently computes a halfspace representation of the Minkowski difference of two zonotopes. In addition, we present an efficient algorithm that computes an approximation of the Minkowski difference in generator representation. The efficiency of the proposed solution is demonstrated by numerical experiments. These experiments show a reduced computation time in comparison to that when first the halfspace representation of zonotopes is obtained and the Minkowski difference is performed subsequently.

cs.CG↗

arXiv2022

Provably Safe Deep Reinforcement Learning for Robotic Manipulation in Human Environments

Deep reinforcement learning (RL) has shown promising results in the motion planning of manipulators. However, no method guarantees the safety of highly dynamic obstacles, such as humans, in RL-based manipulator control. This lack of formal safety assurances prevents the application of RL for manipulators in real-world human environments. Therefore, we propose a shielding mechanism that ensures ISO-verified human safety while training and deploying RL algorithms on manipulators. We utilize a fast reachability analysis of humans and manipulators to guarantee that the manipulator comes to a complete stop before a human is within its range. Our proposed method guarantees safety and significantly improves the RL performance by preventing episode-ending collisions. We demonstrate the performance of our proposed method in simulation using human motion capture data.

cs.RO↗

arXiv2021

Formal synthesis of closed-form sampled-data controllers for nonlinear continuous-time systems under STL specifications

We propose a counterexample-guided inductive synthesis framework for the formal synthesis of closed-form sampled-data controllers for nonlinear systems to meet STL specifications over finite-time trajectories. Rather than stating the STL specification for a single initial condition, we consider an (infinite and bounded) set of initial conditions. Candidate solutions are proposed using genetic programming, which evolves controllers based on a finite number of simulations. Subsequently, the best candidate is verified using reachability analysis; if the candidate solution does not satisfy the specification, an initial condition violating the specification is extracted as a counterexample. Based on this counterexample, candidate solutions are refined until eventually a solution is found (or a user-specified number of iterations is met). The resulting sampled-data controller is expressed as a closed-form expression, enabling both interpretability and the implementation in embedded hardware with limited memory and computation power. The effectiveness of our approach is demonstrated for multiple systems.

eess.SY↗

arXiv2020

Sparse Polynomial Zonotopes: A Novel Set Representation for Reachability Analysis

We introduce sparse polynomial zonotopes, a new set representation for formal verification of hybrid systems. Sparse polynomial zonotopes can represent non-convex sets and are generalizations of zonotopes, polytopes, and Taylor models. Operations like Minkowski sum, quadratic mapping, and reduction of the representation size can be computed with polynomial complexity w.r.t. the dimension of the system. In particular, for reachability analysis of nonlinear systems, the wrapping effect is substantially reduced using sparse polynomial zonotopes, as demonstrated by numerical examples. In addition, we can significantly reduce the computation time compared to zonotopes when dealing with nonlinear dynamics.

eess.SY↗

arXiv2020

Utilizing Dependencies to Obtain Subsets of Reachable Sets

Reachability analysis, in general, is a fundamental method that supports formally-correct synthesis, robust model predictive control, set-based observers, fault detection, invariant computation, and conformance checking, to name but a few. In many of these applications, one requires to compute a reachable set starting within a previously computed reachable set. While it was previously required to re-compute the entire reachable set, we demonstrate that one can leverage the dependencies of states within the previously computed set. As a result, we almost instantly obtain an over-approximative subset of a previously computed reachable set by evaluating analytical maps. The advantages of our novel method are demonstrated for falsification of systems, optimization over reachable sets, and synthesizing safe maneuver automata. In all of these applications, the computation time is reduced significantly.

eess.SY↗

arXiv2020

Reachability Analysis of Large Linear Systems with Uncertain Inputs in the Krylov Subspace

One often wishes for the ability to formally analyze large-scale systems---typically, however, one can either formally analyze a rather small system or informally analyze a large-scale system. This work tries to further close this performance gap for reachability analysis of linear systems. Reachability analysis can capture the whole set of possible solutions of a dynamic system and is thus used to prove that unsafe states are never reached; this requires full consideration of arbitrarily varying uncertain inputs, since sensor noise or disturbances usually do not follow any patterns. We use Krylov methods in this work to compute reachable sets for large-scale linear systems. While Krylov methods have been used before in reachability analysis, we overcome the previous limitation that inputs must be (piecewise) constant. As a result, we can compute reachable sets of systems with several thousand state variables for bounded, but arbitrarily varying inputs.

math.NA↗

arXiv2020

Pedestrian Models for Autonomous Driving Part II: High-Level Models of Human Behavior

Autonomous vehicles (AVs) must share space with pedestrians, both in carriageway cases such as cars at pedestrian crossings and off-carriageway cases such as delivery vehicles navigating through crowds on pedestrianized high-streets. Unlike static obstacles, pedestrians are active agents with complex, interactive motions. Planning AV actions in the presence of pedestrians thus requires modelling of their probable future behaviour as well as detecting and tracking them. This narrative review article is Part II of a pair, together surveying the current technology stack involved in this process, organising recent research into a hierarchical taxonomy ranging from low-level image detection to high-level psychological models, from the perspective of an AV designer. This self-contained Part II covers the higher levels of this stack, consisting of models of pedestrian behaviour, from prediction of individual pedestrians' likely destinations and paths, to game-theoretic models of interactions between pedestrians and autonomous vehicles. This survey clearly shows that, although there are good models for optimal walking behaviour, high-level psychological and social modelling of pedestrian behaviour still remains an open research question that requires many conceptual issues to be clarified. Early work has been done on descriptive and qualitative models of behaviour, but much work is still needed to translate them into quantitative algorithms for practical AV control.

cs.RO↗

arXiv2020

Pedestrian Models for Autonomous Driving Part I: Low-Level Models, from Sensing to Tracking

Autonomous vehicles (AVs) must share space with pedestrians, both in carriageway cases such as cars at pedestrian crossings and off-carriageway cases such as delivery vehicles navigating through crowds on pedestrianized high-streets. Unlike static obstacles, pedestrians are active agents with complex, interactive motions. Planning AV actions in the presence of pedestrians thus requires modelling of their probable future behaviour as well as detecting and tracking them. This narrative review article is Part I of a pair, together surveying the current technology stack involved in this process, organising recent research into a hierarchical taxonomy ranging from low-level image detection to high-level psychology models, from the perspective of an AV designer. This self-contained Part I covers the lower levels of this stack, from sensing, through detection and recognition, up to tracking of pedestrians. Technologies at these levels are found to be mature and available as foundations for use in high-level systems, such as behaviour modelling, prediction and interaction control.

cs.CV↗

arXiv2020

Event-Triggered Diffusion Kalman Filters

Distributed state estimation strongly depends on collaborative signal processing, which often requires excessive communication and computation to be executed on resource-constrained sensor nodes. To address this problem, we propose an event-triggered diffusion Kalman filter, which collects measurements and exchanges messages between nodes based on a local signal indicating the estimation error. On this basis, we develop an energy-aware state estimation algorithm that regulates the resource consumption in wireless networks and ensures the effectiveness of every consumed resource. The proposed algorithm does not require the nodes to share its local covariance matrices, and thereby allows considerably reducing the number of transmission messages. To confirm its efficiency, we apply the proposed algorithm to the distributed simultaneous localization and time synchronization problem and evaluate it on a physical testbed of a mobile quadrotor node and stationary custom ultra-wideband wireless devices. The obtained experimental results indicate that the proposed algorithm allows saving 86% of the communication overhead associated with the original diffusion Kalman filter while causing deterioration of performance by 16% only. We make the Matlab code and the real testing data available online.

eess.SY↗

arXiv2019

Representation of Polytopes as Polynomial Zonotopes

We prove that each bounded polytope can be represented as a polynomial zonotope, which we refer to as the Z-representation of polytopes. Previous representations are the vertex representation (V-representation) and the halfspace representation (H-representation). Depending on the polytope, the Z-representation can be more compact than the V-representation and the H-representation. In addition, the Z-representation enables the computation of linear maps, Minkowski addition, and convex hull with a computational complexity that is polynomial in the representation size. The usefulness of the new representation is demonstrated by range bounding within polytopes.

math.CO↗