Models, code, and papers for "Alexander Liniger":

A Non-Cooperative Game Approach to Autonomous Racing

Jan 10, 2019
Alexander Liniger, John Lygeros

We consider autonomous racing of two cars and present an approach to formulate racing decisions as a non-cooperative non-zero-sum game. We design three different games where the players aim to fulfill static track constraints as well as avoid collision with each other; the latter constraint depends on the combined actions of the two players. The difference between the games are the collision constraints and the payoff. In the first game collision avoidance is only considered by the follower, and each player maximizes their own progress towards the finish line. We show that, thanks to the sequential structure of this game, equilibria can be computed through an efficient sequential maximization approach. Further, we show these actions, if feasible, are also a Stackelberg and Nash equilibrium in pure strategies of our second game where both players consider the collision constraints. The payoff of our third game is designed to promote blocking, by additionally rewarding the cars for staying ahead at the end of the horizon. We show that this changes the Stackelberg equilibrium, but has a minor influence on the Nash equilibria. For online implementation, we propose to play the games in a moving horizon fashion, and discuss two methods for guaranteeing feasibility of the resulting coupled repeated games. Finally, we study the performance of the proposed approaches in simulation for a set-up that replicates the miniature race car tested at the Automatic Control Laboratory of ETH Zurich. The simulation study shows that the presented games can successfully model different racing behaviors and generate interesting racing situations.

* 14 pages, 5 figuers 

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Real-Time Control for Autonomous Racing Based on Viability Theory

Nov 06, 2017
Alexander Liniger, John Lygeros

In this paper we consider autonomous driving of miniature race cars. The viability kernel is used to efficiently generate finite look-ahead trajectories that maximize progress while remaining recursively feasible with respect to static obstacles (e.g., stay inside the track). Together with a low-level model predictive controller, this method makes real-time autonomous racing possible. The viability kernel computation is based on space discretization. To make the calculation robust against discretization errors, we propose a novel numerical scheme based on game theoretical methods, in particular the discriminating kernel. We show that the resulting algorithm provides an inner approximation of the viability kernel and guarantees that, for all states in the cell surrounding a viable grid point, there exists a control that keeps the system within the kernel. The performance of the proposed control method is studied in simulation where we determine the effects of various design choices and parameters and in experiments on an autonomous racing set-up maintained at the Automatic Control Laboratory of ETH Zurich. Both simulation and experimental results suggest that the more conservative approximation using the discriminating kernel results in safer driving style at the cost of a small increase in lap time.

* 26 pages, 11 figures 

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Optimization-Based Autonomous Racing of 1:43 Scale RC Cars

Nov 20, 2017
Alexander Liniger, Alexander Domahidi, Manfred Morari

This paper describes autonomous racing of RC race cars based on mathematical optimization. Using a dynamical model of the vehicle, control inputs are computed by receding horizon based controllers, where the objective is to maximize progress on the track subject to the requirement of staying on the track and avoiding opponents. Two different control formulations are presented. The first controller employs a two-level structure, consisting of a path planner and a nonlinear model predictive controller (NMPC) for tracking. The second controller combines both tasks in one nonlinear optimization problem (NLP) following the ideas of contouring control. Linear time varying models obtained by linearization are used to build local approximations of the control NLPs in the form of convex quadratic programs (QPs) at each sampling time. The resulting QPs have a typical MPC structure and can be solved in the range of milliseconds by recent structure exploiting solvers, which is key to the real-time feasibility of the overall control scheme. Obstacle avoidance is incorporated by means of a high-level corridor planner based on dynamic programming, which generates convex constraints for the controllers according to the current position of opponents and the track layout. The control performance is investigated experimentally using 1:43 scale RC race cars, driven at speeds of more than 3 m/s and in operating regions with saturated rear tire forces (drifting). The algorithms run at 50 Hz sampling rate on embedded computing platforms, demonstrating the real-time feasibility and high performance of optimization-based approaches for autonomous racing.

* Optimal Control Applications and Methods, 36(5), 2015, pp.628-647 

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Optimization-Based Collision Avoidance

Jun 10, 2018
Xiaojing Zhang, Alexander Liniger, Francesco Borrelli

This paper presents a novel method for reformulating non-differentiable collision avoidance constraints into smooth nonlinear constraints using strong duality of convex optimization. We focus on a controlled object whose goal is to avoid obstacles while moving in an n-dimensional space. The proposed reformulation does not introduce approximations, and applies to general obstacles and controlled objects that can be represented in an n-dimensional space as the finite union of convex sets. Furthermore, we connect our results with the notion of signed distance, which is widely used in traditional trajectory generation algorithms. Our method can be used in generic navigation and trajectory planning tasks, and the smoothness property allows the use of general-purpose gradient- and Hessian-based optimization algorithms. Finally, in case a collision cannot be avoided, our framework allows us to find "least-intrusive" trajectories, measured in terms of penetration. We demonstrate the efficacy of our framework on a quadcopter navigation and automated parking problem, and our numerical experiments suggest that the proposed methods enable real-time optimization-based trajectory planning problems in tight environments. Source code of our implementation is provided at

* 27 pages, 9 figures, 2 tables 

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Cautious NMPC with Gaussian Process Dynamics for Miniature Race Cars

Nov 17, 2017
Lukas Hewing, Alexander Liniger, Melanie N. Zeilinger

This paper presents an adaptive high performance control method for autonomous miniature race cars. Racing dynamics are notoriously hard to model from first principles, which is addressed by means of a cautious nonlinear model predictive control (NMPC) approach that learns to improve its dynamics model from data and safely increases racing performance. The approach makes use of a Gaussian Process (GP) and takes residual model uncertainty into account through a chance constrained formulation. We present a sparse GP approximation with dynamically adjusting inducing inputs, enabling a real-time implementable controller. The formulation is demonstrated in simulations, which show significant improvement with respect to both lap time and constraint satisfaction compared to an NMPC without model learning.

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Learning a Curve Guardian for Motorcycles

Jul 12, 2019
Simon Hecker, Alexander Liniger, Henrik Maurenbrecher, Dengxin Dai, Luc Van Gool

Up to 17% of all motorcycle accidents occur when the rider is maneuvering through a curve and the main cause of curve accidents can be attributed to inappropriate speed and wrong intra-lane position of the motorcycle. Existing curve warning systems lack crucial state estimation components and do not scale well. We propose a new type of road curvature warning system for motorcycles, combining the latest advances in computer vision, optimal control and mapping technologies to alleviate these shortcomings. Our contributes are fourfold: 1) we predict the motorcycle's intra-lane position using a convolutional neural network (CNN), 2) we predict the motorcycle roll angle using a CNN, 3) we use an upgraded controller model that incorporates road incline for a more realistic model and prediction, 4) we design a scale-able system by utilizing HERE Technologies map database to obtain the accurate road geometry of the future path. In addition, we present two datasets that are used for training and evaluating of our system respectively, both datasets will be made publicly available. We test our system on a diverse set of real world scenarios and present a detailed case-study. We show that our system is able to predict more accurate and safer curve trajectories, and consequently warn and improve the safety for motorcyclists.

* 8 pages, to be presented at IEEE-ITSC 2019 

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AMZ Driverless: The Full Autonomous Racing System

May 13, 2019
Juraj Kabzan, Miguel de la Iglesia Valls, Victor Reijgwart, Hubertus Franciscus Cornelis Hendrikx, Claas Ehmke, Manish Prajapat, Andreas Bühler, Nikhil Gosala, Mehak Gupta, Ramya Sivanesan, Ankit Dhall, Eugenio Chisari, Napat Karnchanachari, Sonja Brits, Manuel Dangel, Inkyu Sa, Renaud Dubé, Abel Gawel, Mark Pfeiffer, Alexander Liniger, John Lygeros, Roland Siegwart

This paper presents the algorithms and system architecture of an autonomous racecar. The introduced vehicle is powered by a software stack designed for robustness, reliability, and extensibility. In order to autonomously race around a previously unknown track, the proposed solution combines state of the art techniques from different fields of robotics. Specifically, perception, estimation, and control are incorporated into one high-performance autonomous racecar. This complex robotic system, developed by AMZ Driverless and ETH Zurich, finished 1st overall at each competition we attended: Formula Student Germany 2017, Formula Student Italy 2018 and Formula Student Germany 2018. We discuss the findings and learnings from these competitions and present an experimental evaluation of each module of our solution.

* 40 pages, 32 figures, submitted to Journal of Field Robotics 

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