48 research outputs found
On Time-optimal Trajectories for a Car-like Robot with One Trailer
In addition to the theoretical value of challenging optimal control problmes,
recent progress in autonomous vehicles mandates further research in optimal
motion planning for wheeled vehicles. Since current numerical optimal control
techniques suffer from either the curse of dimens ionality, e.g. the
Hamilton-Jacobi-Bellman equation, or the curse of complexity, e.g.
pseudospectral optimal control and max-plus methods, analytical
characterization of geodesics for wheeled vehicles becomes important not only
from a theoretical point of view but also from a prac tical one. Such an
analytical characterization provides a fast motion planning algorithm that can
be used in robust feedback loops. In this work, we use the Pontryagin Maximum
Principle to characterize extremal trajectories, i.e. candidate geodesics, for
a car-like robot with one trailer. We use time as the distance function. In
spite of partial progress, this problem has remained open in the past two
decades. Besides straight motion and turn with maximum allowed curvature, we
identify planar elastica as the third piece of motion that occurs along our
extr emals. We give a detailed characterization of such curves, a special case
of which, called \emph{merging curve}, connects maximum curvature turns to
straight line segments. The structure of extremals in our case is revealed
through analytical integration of the system and adjoint equations
Path Planning of Airplane with Obstacles
CĂlem tĂ©to diplomovĂ© práce je implementace plánovánĂ optimálnĂ trajektorie letadla letĂcĂho v nižšĂch výškách, kterĂ© se musĂ vyhĂ˝bat pĹ™ekážkám. Pro metodu plánovánĂ se pĹ™edpokládá statickĂ© a pĹ™edem známĂ© prostĹ™edĂ. V tĂ©to práci jsou popsány principy, optimálnost a sloĹľitost vybranĂ˝ch metod plánovánĂ. Na základÄ› vlastnostĂ metod je vybrána metoda nejvhodnÄ›jšà k implementaci.The aim of this master's thesis is the implementation of optimal trajectory planning for an airplane flying in lower altitudes, which has to avoid collision with obstacles. For the planning we assume static and fully known environment. There are described principals, optimality and complexity for some chosen methods of planning in this thesis. And based on the methods' characteristics it's chosen the best method for implementation.
PATH PLANNING OF UNMANNED AERIAL VEHICLE USING DUBINS GEOMETRY WITH AN OBSTACLE
Motivation: Unmanned Aerial Vehicles (UAV) is an aircraft that is controlled without the use of human beings crew. One of main problem of Unmanned Aerial Vehicle’s (UAV) flight is guide. UAV need a guide who can direct the movement of aircraft to arrive at the destination, so it takes planning trajectory (path planning) appropriate to the aircraft can be controlled in accordance with the objectives and can pass the desired trajectory. Given two points on a 2-dimensional plane, the two points are coordinates the initial and final coordinates to be taken by UAV. And between the two points is given a obstacle in the form circle. Planning algorithm trajectory using Dubins geometry. Results obtained from this paper are path planning to produce path between two points with the shortest distance and shortest time. The first track is the track without a obstacle and the second path is the path to the obstacle. Differences in distance on the second track is provided
Inverse Optimal Planning for Air Traffic Control
We envision a system that concisely describes the rules of air traffic
control, assists human operators and supports dense autonomous air traffic
around commercial airports. We develop a method to learn the rules of air
traffic control from real data as a cost function via maximum entropy inverse
reinforcement learning. This cost function is used as a penalty for a
search-based motion planning method that discretizes both the control and the
state space. We illustrate the methodology by showing that our approach can
learn to imitate the airport arrival routes and separation rules of dense
commercial air traffic. The resulting trajectories are shown to be safe,
feasible, and efficient
Navigasi dan Kendali pada Pesawat Udara Nir Awak (Puna) untuk Menghindari Halangan
Pesawat udara nir awak(PUNA) adalah pesawat udara multifungsi yang dikendalikan tanpa menggunakan awak manusia. PUNA dapat bergerak sampai ke tempat tujuan jika diterapkan sebuah navigasi dan kendali. Masalah yang muncul pada pernerbangan PUNA diantaranya masalah jalur tempuh dan halangan pada lintasan. Navigasi penerbangan adalah proses mengarahkan posisi pesawat dari satu titik ke titik yang lain dengan selamat dan lancar untuk menghindari rintangan penerbangan. Navigasi yang digunakan adalah dengan merancang Algoritma perencanaan lintasan menggunakan geometri Dubins. Agar PUNA tetap pada lintasan yang dibangun maka diperlukan suau kendali optimal. Kendali yang digunakan adalah Prin- sip Minimum Pontryagin(PMP) yang berguna untuk meminimumkan atau memaksimumkan fungsi tujuan. Kasus yang diteliti dalam paper ini, yaitu PUNA bergerak mengikuti lintasan yang dibangun dengan metode geometri dubins. Hasil yang diperoleh dalam paper ini adalah mendapatkan suatu lintasan optimal untuk menghindari halangan berupa lingkaran
Navigasi dan Kendali pada Pesawat Udara Nir Awak (Puna) untuk Menghindari Halangan
Pesawat udara nir awak(PUNA) adalah pesawat udara multifungsi yang dikendalikan tanpa menggunakan awak manusia. PUNA dapat bergerak sampai ke tempat tujuan jika diterapkan sebuah navigasi dan kendali. Masalah yang muncul pada pernerbangan PUNA diantaranya masalah jalur tempuh dan halangan pada lintasan. Navigasi penerbangan adalah proses mengarahkan posisi pesawat dari satu titik ke titik yang lain dengan selamat dan lancar untuk menghindari rintangan penerbangan. Navigasi yang digunakan adalah dengan merancang Algoritma perencanaan lintasan menggunakan geometri Dubins. Agar PUNA tetap pada lintasan yang dibangun maka diperlukan suau kendali optimal. Kendali yang digunakan adalah Prin- sip Minimum Pontryagin(PMP) yang berguna untuk meminimumkan atau memaksimumkan fungsi tujuan. Kasus yang diteliti dalam paper ini, yaitu PUNA bergerak mengikuti lintasan yang dibangun dengan metode geometri dubins. Hasil yang diperoleh dalam paper ini adalah mendapatkan suatu lintasan optimal untuk menghindari halangan berupa lingkaran
A New Algorithm for Optimizing Dubins Paths to Intercept a Moving Target
This paper is concerned with determining the shortest path for a pursuer
aiming to intercept a moving target travelling at a constant speed. We
introduce an intuitive and efficient mathematical model outlined as an optimal
control problem to address this challenge. The proposed model is based on
Dubins path where we concatenate two possible paths: a left-circular curve or a
right-circular curve followed by a straight line. We develop and explore this
model, providing a comprehensive geometric interpretation, and design an
algorithm tailored to implement the proposed mathematical approach efficiently.
Extensive numerical experiments involving diverse target positions highlight
the strength of the model. The method exhibits a remarkably high convergence
rate in finding solutions. For experiment purposes, we utilized the modelling
software AMPL, employing a range of solvers to solve the problem. Subsequently,
we simulated the obtained solutions using MATLAB, demonstrating the efficiency
of the model in intercepting a moving target. The proposed model distinguishes
itself by employing fewer parameters and making fewer assumptions, setting the
model simplifies the complexities, and thus, makes it easier for experts to
design optimal path plans