Models for Human Navigation and Optimal Path Planning Using Level Set Methods and Hamilton-Jacobi Equations

We present several models for different physical scenarios which are centered around human movement or optimal path planning, and use partial differential equations and concepts from control theory. The first model is a game-theoretic model for environmental crime which tracks criminals' movement using the level set method, and improves upon previous continuous models by removing overly restrictive assumptions of symmetry. Next, we design a method for determining optimal hiking paths in mountainous regions using an anisotropic level set equation. After this, we present a model for optimal human navigation with uncertainty which is rooted in dynamic programming and stochastic optimal control theory. Lastly, we consider optimal path planning for simple, self-driving cars in the Hamilton-Jacobi formulation. We improve upon previous models which simplify the car to a point mass, and present a reasonably general upwind, sweeping scheme to solve the relevant Hamilton-Jacobi equation

A motion planner for nonholonomic mobile robots

This paper considers the problem of motion planning for a car-like robot (i.e., a mobile robot with a nonholonomic constraint whose turning radius is lower-bounded). We present a fast and exact planner for our mobile robot model, based upon recursive subdivision of a collision-free path generated by a lower-level geometric planner that ignores the motion constraints. The resultant trajectory is optimized to give a path that is of near-minimal length in its homotopy class. Our claims of high speed are supported by experimental results for implementations that assume a robot moving amid polygonal obstacles. The completeness and the complexity of the algorithm are proven using an appropriate metric in the configuration space R^2 x S^1 of the robot. This metric is defined by using the length of the shortest paths in the absence of obstacles as the distance between two configurations. We prove that the new induced topology and the classical one are the same. Although we concentrate upon the car-like robot, the generalization of these techniques leads to new theoretical issues involving sub-Riemannian geometry and to practical results for nonholonomic motion planning

A Novel Obstacle Avoidance Approach For Nonholonomic Ground Vehicle Autonomy

Tez (Doktora) -- İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 2012Thesis (PhD) -- İstanbul Technical University, Institute of Science and Technology, 2012Bu çalışmada, holonom olmayan bir kara taşıtı için, “Boşluğu Takip Et” (BTE) isimli yeni bir engelden kaçma ve çarpışma önleme metodu geliştirilmiştir. Bu metod, probleme yeni bir çözüm getirmektedir ve diğer metodlara göre çeşitli avantajlara sahiptir. Geliştirilen metodun, benzer metodlarla yapılan karşılaştırılmalar sonucunda, daha güvenli güzergahlarla sonuçlandığı gösterilmiştir. Ayrıca BTE, yapay potansiyel alanlar (YPA) metodu ve bu tabanda çalışan diğer tüm metodların ortak problemi olan lokal minimum probleminden bağımsızdır. BTE’nin bir diğer özelliği, aracın holonom olmayan kısıtlarını ve sensörlerin görüş açısı kısıtlarını da göz önünde bulundurabilmesidir. BTE’nin tamamen reaktif yapısı sayesinde, yalnızca durağan engellerden değil, hareketli engellerden de rahatlıkla sıyrıldığı da tez içerisinde gösterilmiştir. Son olarak, sadece bir ayar parametresine sahip olduğu için, kullanımı da oldukça kolaydır. Engelden kaçınmak için, yalnızca aracın yönelim açısının belirlenmesinin yetmeyeceği düşüncesinden hareketle, aracın engelli bir ortamda hız planlaması için de yeni bir metod geliştirilmiştir. İki adet bulanık çıkarım sisteminin (BÇS) tasarlanmasıyla oluşturulan bu yeni yapı, engellerin oluşturduğu risk durumuna ve aracın yönelim açısına bağlı olarak çalışır. Planlanan hızın takip edilmesi için de yine bulanık mantık kullanılarak yeni bir alt seviye hız kontrolörü tasarlanmıştır. Tasarlanan tüm metodlar, literatürdeki bezerleriyle simülasyon ortamında karşılaştırılmış ve sonuçları gösterilmiştir. Geliştirilen her üç yeni metod, tam otonom kara taşıtı (OKT) üzerinde deneysel olarak da test edilerek sonuçların başarılı olduğu gösterilmiştir. Simülasyonlarda kullanılan araç modelleri ve deneysel düzeneğin tasarımı da tez içerisinde ayrı bölümler halinde anlatılmıştır.In this study, a new obstacle avoidance algorithm “Follow the Gap Method” (FGM) is designed for nonholonomic ground vehicle autonomy. The proposed method brings a new solution to the problem and has several advantages compared to previous methods. Fisrstly, the FGM results in safer trajectories than other compared approaches. This new method is free from local minima which is a big problem for Artificial Potential Fields (APF) and similar methods. Taking into consideration the field of view and the nonholonomic constraints of the vehicle is another advantage of the FGM. Through the purely reactive nature of the FGM, it is shown that not only the static but also the dynamic obstacles are avoided. Besides these, it is easy to tune the algorithm with only one tuning parameter. Vehicle speed is as important as the appropriate steering angle for obstacle avoidance. From this view point, a new speed planning method is designed for the vehicle. Two fuzzy inference systems operate depending on the danger level of the obstacles and the steering angle. In order to track the speed commands from the speed planner, a new low level speed controller is designed based on fuzzy rules. All designed methods are simulated and compared with other methods in literature. The designed methods are also tested experimentally using the real unmanned ground vehicle (UGV) platform and it is shown that experimental results are successful too. The used models for the simulations and designed experimental platform are illustrated in separated sections throughout the thesis.DoktoraPh

A motion planner for nonholonomic mobile robots

This paper considers the problem of motion planning for a car-like robot (i.e., a mobile robot with a nonholonomic constraint whose turning radius is lower-bounded). We present a fast and exact planner for our mobile robot model, based upon recursive subdivision of a collision-free path generated by a lower-level geometric planner that ignores the motion constraints. The resultant trajectory is optimized to give a path that is of near-minimal length in its homotopy class. Our claims of high speed are supported by experimental results for implementations that assume a robot moving amid polygonal obstacles. The completeness and the complexity of the algorithm are proven using an appropriate metric in the configuration space R^2 x S^1 of the robot. This metric is defined by using the length of the shortest paths in the absence of obstacles as the distance between two configurations. We prove that the new induced topology and the classical one are the same. Although we concentrate upon the car-like robot, the generalization of these techniques leads to new theoretical issues involving sub-Riemannian geometry and to practical results for nonholonomic motion planning

Sliding mode control applied in trajectory-tracking of WMRs and autonomous vehicles

Tese de doutoramento apresentada à Fac. de Ciências e Tecnologia da Universidade de CoimbraThe thesis is structured as follows: • Chapter 2: Trajectory tracking problems are summarized. • Chapter 3: Kinematic and dynamic modeling of theWMRs and car-like robots are presented. • Chapter 4: The concept of sliding mode are first introduced. Then the fundamentals of SMC are summarized, including basic definitions, methods of sliding surface and control law design, robustness properties and the methods on handling chattering problems. New sliding-mode trajectory-tracking and slidingmode path-following controllers for WMRs and car-like vehicles, are also proposed in this chapter. • Chapter 5: The trajectory/path planning are developed, including the velocity profile. • Chapter 6: A model with two freedom degrees is considered for the HNC model. The user comfort is examined not only in the time domain, but also in the frequency domain. • Chapter 7: Experimental results obtained with the implementation of the proposed controllers in RobChair are summarized and discussed. • Chapter 8: Finally, conclusions are drawn and some suggestions for future work are provided

Research on a semiautonomous mobile robot for loosely structured environments focused on transporting mail trolleys

In this thesis is presented a novel approach to model, control, and planning the motion of a nonholonomic wheeled mobile robot that applies stable pushes and pulls to a nonholonomic cart (York mail trolley) in a loosely structured environment. The method is based on grasping and ungrasping the nonholonomic cart, as a result, the robot changes its kinematics properties. In consequence, two robot configurations are produced by the task of grasping and ungrasping the load, they are: the single-robot configuration and the robot-trolley configuration. Furthermore, in order to comply with the general planar motion law of rigid bodies and the kinematic constraints imposed by the robot wheels for each configuration, the robot has been provided with two motorized steerable wheels in order to have a flexible platform able to adapt to these restrictions. [Continues.