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Marc Heinrich

Publications and source records attributed to Marc Heinrich.

At least 19 recordsLinked to original sources

The ATLAS of Traffic Lights: A Reliable Perception Framework for Autonomous Driving

Traffic light perception is an essential component of the camera-based perception system for autonomous vehicles, enabling accurate detection and interpretation of traffic lights to ensure safe navigation through complex urban environments. In this work, we propose a modularized perception framework that integrates state-of-the-art detection models with a novel real-time association and decision framework, enabling seamless deployment into an autonomous driving stack. To address the limitations of existing public datasets, we introduce the ATLAS dataset, which provides comprehensive annotations of traffic light states and pictograms across diverse environmental conditions and camera setups. This dataset is publicly available at https://url.fzi.de/ATLAS. We train and evaluate several state-of-the-art traffic light detection architectures on ATLAS, demonstrating significant performance improvements in both accuracy and robustness. Finally, we evaluate the framework in real-world scenarios by deploying it in an autonomous vehicle to make decisions at traffic light-controlled intersections, highlighting its reliability and effectiveness for real-time operation.

cs.CV

A Chefs KISS -- Utilizing semantic information in both ICP and SLAM framework

For utilizing autonomous vehicle in urban areas a reliable localization is needed. Especially when HD maps are used, a precise and repeatable method has to be chosen. Therefore accurate map generation but also re-localization against these maps is necessary. Due to best 3D reconstruction of the surrounding, LiDAR has become a reliable modality for localization. The latest LiDAR odometry estimation are based on iterative closest point (ICP) approaches, namely KISS-ICP and SAGE-ICP. We extend the capabilities of KISS-ICP by incorporating semantic information into the point alignment process using a generalizable approach with minimal parameter tuning. This enhancement allows us to surpass KISS-ICP in terms of absolute trajectory error (ATE), the primary metric for map accuracy. Additionally, we improve the Cartographer mapping framework to handle semantic information. Cartographer facilitates loop closure detection over larger areas, mitigating odometry drift and further enhancing ATE accuracy. By integrating semantic information into the mapping process, we enable the filtering of specific classes, such as parked vehicles, from the resulting map. This filtering improves relocalization quality by addressing temporal changes, such as vehicles being moved.

cs.RO

Modular Fault Diagnosis Framework for Complex Autonomous Driving Systems

Fault diagnosis is crucial for complex autonomous mobile systems, especially for modern-day autonomous driving (AD). Different actors, numerous use cases, and complex heterogeneous components motivate a fault diagnosis of the system and overall system integrity. AD systems are composed of many heterogeneous components, each with different functionality and possibly using a different algorithm (e.g., rule-based vs. AI components). In addition, these components are subject to the vehicle's driving state and are highly dependent. This paper, therefore, faces this problem by presenting the concept of a modular fault diagnosis framework for AD systems. The concept suggests modular state monitoring and diagnosis elements, together with a state- and dependency-aware aggregation method. Our proposed classification scheme allows for the categorization of the fault diagnosis modules. The concept is implemented on AD shuttle buses and evaluated to demonstrate its capabilities.

cs.RO

CoCar NextGen: a Multi-Purpose Platform for Connected Autonomous Driving Research

Real world testing is of vital importance to the success of automated driving. While many players in the business design purpose build testing vehicles, we designed and build a modular platform that offers high flexibility for any kind of scenario. CoCar NextGen is equipped with next generation hardware that addresses all future use cases. Its extensive, redundant sensor setup allows to develop cross-domain data driven approaches that manage the transfer to other sensor setups. Together with the possibility of being deployed on public roads, this creates a unique research platform that supports the road to automated driving on SAE Level 5.

cs.RO

Leveraging Swarm Intelligence to Drive Autonomously: A Particle Swarm Optimization based Approach to Motion Planning

Motion planning is an essential part of autonomous mobile platforms. A good pipeline should be modular enough to handle different vehicles, environments, and perception modules. The planning process has to cope with all the different modalities and has to have a modular and flexible design. But most importantly, it has to be safe and robust. In this paper, we want to present our motion planning pipeline with particle swarm optimization (PSO) at its core. This solution is independent of the vehicle type and has a clear and simple-to-implement interface for perception modules. Moreover, the approach stands out for being easily adaptable to new scenarios. Parallel calculation allows for fast planning cycles. Following the principles of PSO, the trajectory planer first generates a swarm of initial trajectories that are optimized afterward. We present the underlying control space and inner workings. Finally, the application to real-world automated driving is shown in the evaluation with a deeper look at the modeling of the cost function. The approach is used in our automated shuttles that have already driven more than 3.500 km safely and entirely autonomously in sub-urban everyday traffic.

cs.RO

One Stack to Rule them All: To Drive Automated Vehicles, and Reach for the 4th level

Most automated driving functions are designed for a specific task or vehicle. Most often, the underlying architecture is fixed to specific algorithms to increase performance. Therefore, it is not possible to deploy new modules and algorithms easily. In this paper, we present our automated driving stack which combines both scalability and adaptability. Due to the modular design, our stack allows for a fast integration and testing of novel and state-of-the-art research approaches. Furthermore, it is flexible to be used for our different testing vehicles, including modified EasyMile EZ10 shuttles and different passenger cars. These vehicles differ in multiple ways, e.g. sensor setups, control systems, maximum speed, or steering angle limitations. Finally, our stack is deployed in real world environments, including passenger transport in urban areas. Our stack includes all components needed for operating an autonomous vehicle, including localization, perception, planning, controller, and additional safety modules. Our stack is developed, tested, and evaluated in real world traffic in multiple test sites, including the Test Area Autonomous Driving Baden-W\"urttemberg.

cs.RO

Short and local transformations between ($Δ+1$)-colorings

Recoloring a graph is about finding a sequence of proper colorings of this graph from an initial coloring $σ$ to a target coloring $η$. Adding the constraint that each pair of consecutive colorings must differ on exactly one vertex, one asks: Is there a sequence of colorings from $σ$ to $η$? If yes, how short can it be? In this paper, we focus on $(Δ+1)$-colorings of graphs of maximum degree $Δ$. Feghali, Johnson and Paulusma proved that, if both colorings are non-frozen (i.e. we can change the color of a least one vertex), then a quadratic recoloring sequence always exists. We improve their result by proving that there actually exists a linear transformation (assuming that $Δ$ is a constant). In addition, we prove that the core of our algorithm can be performed locally. Informally, this means that after some preprocessing, the color changes that a given node has to perform only depend on the colors of the vertices in a constant size neighborhood. We make this precise by designing of an efficient recoloring algorithm in the LOCAL model of distributed computing.

cs.DM

An Application of Scenario Exploration to Find New Scenarios for the Development and Testing of Automated Driving Systems in Urban Scenarios

Verification and validation are major challenges for developing automated driving systems. A concept that gets more and more recognized for testing in automated driving is scenario-based testing. However, it introduces the problem of what scenarios are relevant for testing and which are not. This work aims to find relevant, interesting, or critical parameter sets within logical scenarios by utilizing Bayes optimization and Gaussian processes. The parameter optimization is done by comparing and evaluating six different metrics in two urban intersection scenarios. Finally, a list of ideas this work leads to and should be investigated further is presented.

cs.SE

Recolouring planar graphs of girth at least five

For a positive integer $k$, the $k$-recolouring graph of a graph $G$ has as vertex set all proper $k$-colourings of $G$ with two $k$-colourings being adjacent if they differ by the colour of exactly one vertex. A result of Dyer et al. regarding graphs of bounded degeneracy implies that the $7$-recolouring graphs of planar graphs, the $5$-recolouring graphs of triangle-free planar graphs and the $4$-recolouring graphs planar graphs of girth at least six are connected. On the other hand, there are planar graphs whose $6$-recolouring graph is disconnected, triangle-free planar graphs whose $4$-recolouring graph is disconnected and planar graphs of any given girth whose $3$-recolouring graph is disconnected. The main result of this paper consists in showing, via a novel application of the discharging method, that the $4$-recolouring graph of every planar graph of girth five is connected. This completes the classification of the connectedness of the recolouring graph for planar graphs of given girth. We also prove some theorems regarding the diameter of the recolouring graph of planar graphs.

math.CO

Distributed recoloring of interval and chordal graphs

One of the fundamental and most-studied algorithmic problems in distributed computing on networks is graph coloring, both in bounded-degree and in general graphs. Recently, the study of this problem has been extended in two directions. First, the problem of recoloring, that is computing an efficient transformation between two given colorings (instead of computing a new coloring), has been considered, both to model radio network updates, and as a useful subroutine for coloring. Second, as it appears that general graphs and bounded-degree graphs do not model real networks very well (with, respectively, pathological worst-case topologies and too strong assumptions), coloring has been studied in more specific graph classes. In this paper, we study the intersection of these two directions: distributed recoloring in two relevant graph classes, interval and chordal graphs.

cs.DC

On a recolouring version of Hadwiger's conjecture

We prove that for any $\varepsilon>0$, for any large enough $t$, there is a graph $G$ that admits no $K_t$-minor but admits a $(\frac32-\varepsilon)t$-colouring that is "frozen" with respect to Kempe changes, i.e. any two colour classes induce a connected component. This disproves three conjectures of Las Vergnas and Meyniel from 1981.

math.CO

Polynomial-time approximation algorithms for the antiferromagnetic Ising model on line graphs

We present a polynomial-time Markov chain Monte Carlo algorithm for estimating the partition function of the antiferromagnetic Ising model on any line graph. The analysis of the algorithm exploits the "winding" technology devised by McQuillan [CoRR abs/1301.2880 (2013)] and developed by Huang, Lu and Zhang [Proc. 27th Symp. on Disc. Algorithms (SODA16), 514-527]. We show that exact computation of the partition function is #P-hard, even for line graphs, indicating that an approximation algorithm is the best that can be expected. We also show that Glauber dynamics for the Ising model is rapidly mixing on line graphs, an example being the kagome lattice.

cs.DS

Counting independent sets in strongly orderable graphs

We consider the problem of devising algorithms to count exactly the number of independent sets of a graph G . We show that there is a polynomial time algorithm for this problem when G is restricted to the class of strongly orderable graphs, a superclass of chordal bipartite graphs. We also show that such an algorithm exists for graphs of bounded clique-width. Our results extends to a more general setting of counting independent sets in a weighted graph and can be used to count the number of independent sets of any given size k .

cs.DM

Partizan Subtraction Games

Partizan subtraction games are combinatorial games where two players, say Left and Right, alternately remove a number n of tokens from a heap of tokens, with $n \in S_L$ (resp. $n \in S_R$) when it is Left's (resp. Right's) turn. The first player unable to move loses. These games were introduced by Fraenkel and Kotzig in 1987, where they introduced the notion of dominance, i.e. an asymptotic behavior of the outcome sequence where Left always wins if the heap is sufficiently large. In the current paper, we investigate the other kinds of behaviors for the outcome sequence. In addition to dominance, three other disjoint behaviors are defined, namely weak dominance, fairness and ultimate impartiality. We consider the problem of computing this behavior with respect to $S_L$ and $S_R$, which is connected to the well-known Frobenius coin problem. General results are given, together with arithmetic and geometric characterizations when the sets $S_L$ and $S_R$ have size at most 2.

math.CO

Recoloring graphs of treewidth 2

Two (proper) colorings of a graph are adjacent if they differ on exactly one vertex. Jerrum proved that any $(d + 2)$-coloring of any d-degenerate graph can be transformed into any other via a sequence of adjacent colorings. A result of Bonamy et al. ensures that a shortest transformation can have a quadratic length even for $d = 1$. Bousquet and Perarnau proved that a linear transformation exists for between $(2d + 2)$-colorings. It is open to determine if this bound can be reduced. In this note, we prove that it can be reduced for graphs of treewidth 2, which are 2-degenerate. There exists a linear transformation between 5-colorings. It completes the picture for graphs of treewidth 2 since there exist graphs of treewidth 2 such a linear transformation between 4-colorings does not exist.

cs.DM

Glauber dynamics for colourings of chordal graphs and graphs of bounded treewidth

The Glauber dynamics on the colourings of a graph is a random process which consists in recolouring at each step a random vertex of a graph with a new colour chosen uniformly at random among the colours not already present in its neighbourhood. It is known that when the total number of colours available is at least $Δ+2$, where $Δ$ is the maximum degree of the graph, this process converges to a uniform distribution on the set of all the colourings. Moreover, a well known conjecture is that the time it takes for the convergence to happen, called the mixing time, is polynomial in the size of the graph. Many weaker variants of this conjecture have been studied in the literature by allowing either more colours, or restricting the graphs to particular classes, or both. This paper follows this line of research by studying the mixing time of the Glauber dynamics on chordal graphs, as well as graphs of bounded treewidth. We show that the mixing time is polynomial in the size of the graph in the two following cases: - on graphs with bounded treewidth, and at least $Δ+2$ colours, - on chordal graphs if the number of colours is at least $(1+\varepsilon) (Δ+1)$, for any fixed constant $\varepsilon$.

math.CO

The Glauber dynamics for edge-colourings of trees

Let $T$ be a tree on $n$ vertices and with maximum degree $Δ$. We show that for $k\geq Δ+1$ the Glauber dynamics for $k$-edge-colourings of $T$ mixes in polynomial time in $n$. The bound on the number of colours is best possible as the chain is not even ergodic for $k \leq Δ$. Our proof uses a recursive decomposition of the tree into subtrees; we bound the relaxation time of the original tree in terms of the relaxation time of its subtrees using block dynamics and chain comparison techniques. Of independent interest, we also introduce a monotonicity result for Glauber dynamics that simplifies our proof.

cs.DS

Enumerating minimal dominating sets in $K_t$-free graphs and variants

It is a long-standing open problem whether the minimal dominating sets of a graph can be enumerated in output-polynomial time. In this paper we investigate this problem in graph classes defined by forbidding an induced subgraph. In particular, we provide output-polynomial time algorithms for $K_t$-free graphs and variants. This answers a question of Kanté et al. about enumeration in bipartite graphs.

cs.DM