/pdf/convex-analysisnoer-san-nojin-zhan-nituite-5dl2rbmoyr.pdf

Convex Analysisの二,三の進展について

“Multivalued Analysis” is the theory of set-valued maps (called multifonctions) and has important applications in many different areas. Multivalued analysis is a remarkable mixture of many different parts of mathematics such as point-set topology, measure theory and nonlinear functional analysis. It is also closely related to “Nonsmooth Analysis” (Chapter 5) and in fact one of the main motivations behind the development of the theory, was in order to provide necessary analytical tools for the study of problems in nonsmooth analysis. It is not a coincidence that the development of the two fields coincide chronologically and follow parallel paths. Today multivalued analysis is a mature mathematical field with its own methods, techniques and applications that range from social and economic sciences to biological sciences and engineering. There is no doubt that a modern treatise on “Nonlinear Functional Analysis” can not afford the luxury of ignoring multivalued analysis. The omission of the theory of multifunctions will drastically limit the possible applications.

SET-Valued Analysis

In this review, we provide an overview of emerging trends and challenges in the field of intelligent and autonomous, or self-driving, vehicles. Recent advances in the field of perception, planning,...

Planning and Decision-Making for Autonomous Vehicles

Gaussian process (GP) regression has been widely used in supervised machine learning due to its flexibility and inherent ability to describe uncertainty in function estimation. In the context of control, it is seeing increasing use for modeling of nonlinear dynamical systems from data, as it allows the direct assessment of residual model uncertainty. We present a model predictive control (MPC) approach that integrates a nominal system with an additive nonlinear part of the dynamics modeled as a GP. We describe a principled way of formulating the chance-constrained MPC problem, which takes into account residual uncertainties provided by the GP model to enable cautious control. Using additional approximations for efficient computation, we finally demonstrate the approach in a simulation example, as well as in a hardware implementation for autonomous racing of remote-controlled race cars with fast sampling times of 20 ms, highlighting improvements with regard to both performance and safety over a nominal controller.

/pdf/cautious-model-predictive-control-using-gaussian-process-22h61bh9m4.pdf

Cautious Model Predictive Control Using Gaussian Process Regression

Control of connected and automated vehicles: State of the art and future challenges

Summary

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. Copyright © 2014 John Wiley & Sons, Ltd.

Optimization‐based autonomous racing of 1:43 scale RC cars

In this letter, we present a learning-based control approach for autonomous racing with an application to the AMZ Driverless race car gotthard 
. One major issue in autonomous racing is that accurate vehicle models that cover the entire performance envelope of a race car are highly nonlinear, complex, and complicated to identify, rendering them impractical for control. To address this issue, we employ a relatively simple nominal vehicle model, which is improved based on measurement data and tools from machine learning.The resulting formulation is an online learning data-driven model predictive controller, which uses Gaussian processes regression to take residual model uncertainty into account and achieve safe driving behavior. To improve the vehicle model online, we select from a constant in-flow of data points according to a criterion reflecting the information gain, and maintain a small dictionary of 300 data points. The framework is tested on the full-size AMZ Driverless race car, where it is able to improve the vehicle model and reduce lap times by $ {\mathbf{10}{\%}}$ while maintaining safety of the vehicle.

/pdf/learning-based-model-predictive-control-for-autonomous-hel0mymyfc.pdf

Learning-Based Model Predictive Control for Autonomous Racing

This article presents a novel method for exactly reformulating nondifferentiable collision avoidance constraints into smooth, differentiable 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 is exact, does not introduce any approximations, and applies to general obstacles and controlled objects that can be represented as the union of convex sets. We connect our results with the notion of signed distance, which is widely used in traditional trajectory generation algorithms. Our method can be applied to 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 an automated parking problem, where our numerical experiments suggest that the proposed method is robust and enables real-time optimization-based trajectory planning in tight environments. Sample code of our example is provided at https://github.com/XiaojingGeorgeZhang/OBCA .

Optimization-Based Collision Avoidance

We present an optimization-based approach for autonomous parking. Building on recent advances in the area of optimization-based collision avoidance (OBCA), we show that the autonomous parking problem can be formulated as a smooth non-convex optimization problem. Unfortunately, such problems are numerically challenging to solve in general and require appropriate warm-starting. To address this limitation, we propose a novel algorithm called Hierarchical OBCA (H-OBCA). The main idea is to first use a generic path planner, such as Hybrid A*, to compute a coarse trajectory using a simplified vehicle model and by discretizing the state-input space. This path is subsequently used to warm-start the OBCA algorithm, which optimizes and smoothens the coarse path using a full vehicle model and continuous optimization. Our studies indicate that the proposed H-OBCA parking algorithm combines Hybrid A*'s global path planning capability with OBCA's ability to generate smooth, collision-free, and dynamically feasible paths. Extensive simulations suggest that the proposed H-OBCA algorithm is robust and admits realtime parking for autonomous vehicles. Sample code is provided at https://github.com/XiaojingGeorgeZhang/H-OBCA.

Autonomous Parking Using Optimization-Based Collision Avoidance

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.

Alexander Liniger

Papers

Optimization‐based autonomous racing of 1:43 scale RC cars

Learning-Based Model Predictive Control for Autonomous Racing

Optimization-Based Collision Avoidance

Autonomous Parking Using Optimization-Based Collision Avoidance

AMZ Driverless: The full autonomous racing system