Robotics and Human Machine Interaction Lab Prof. Dr.-Ing. Ulrike Thomas Motion Planning - Trajectory calculation, PRM, RRT 1. Trajectory planning a) Lin and ptp are the two most common methods for trajectory planning, de- scribe them briefly. b) The simplest way to calculate a trajectory (ptp) is a 3rd order polynomial. Why shouldn’t this be applied? c) Calculate the progression of a two-axis mani

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/MotionPlanning2019/exercise_RRT_Monday.pdf - 2025-02-23

A Course in Optimal Control and Optimal Transport Dongjun Wu dongjun.wu@control.lth.se August, 2023 i CONTENTS Contents 1 1 Dynamic Programming 5 1.1 Discrete time systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.1.1 Shortest path problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.1.2 Optimal control on finite horizon .

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/Optimal_Control/2023/A_course_in_optimal_control_and_optimal_transport.pdf - 2025-02-23

Lecture 3. The maximum principle In the last lecture, we learned calculus of variation (CoV). The key idea of CoV for the minimization problem min u∈U J(u) can be summarized as follows. 1) Assume u∗ is a minimizer, and choose a one-parameter variation uϵ s.t. u0 = u∗ and uϵ ∈ U for ϵ small. 2) The function ϵ 7→ J(uϵ) has a minimizer at ϵ = 0. Thus it satisfies the first and second order necessary

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/Optimal_Control/2023/Lecture3.pdf - 2025-02-23

Exercise for Optimal control – Week 1 Choose two problems to solve. Disclaimer This is not a complete solution manual. For some of the exercises, we provide only partial answers, especially those involving numerical problems. If one is willing to use the solution manual, one should judge whether the solutions are correct or wrong him/herself. Exercise 1 (Fundamental lemma of CoV). Let f be a real

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/Optimal_Control/2023/ex1-sol.pdf - 2025-02-23

Exercise for Optimal control – Week 2 Choose one problem to solve. Exercise 1 (Insect control). Let w(t) and r(t) denote, respectively, the worker and reproductive population levels in a colony of insects, e.g. wasps. At any time t, 0 ≤ t ≤ T in the season the colony can devote a fraction u(t) of its effort to enlarging the worker force and the remaining fraction u(t) to producing reproductives. T

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/Optimal_Control/2023/ex2.pdf - 2025-02-23

Exercise for Optimal control – Week 3 Choose 1.5 problems to solve. Disclaimer This is not a complete solution manual. For some of the exercises, we provide only partial answers, especially those involving numerical problems. If one is willing to use the solution manual, one should judge whether the solutions are correct or wrong by him/herself. Exercise 1. Consider a harmonic oscillator ẍ + x =

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/Optimal_Control/2023/ex3-sol.pdf - 2025-02-23

Exercise for Optimal control – Week 5 Choose one problem to solve. Exercise 1. Use tent method to derive the KKT condition (google it if you don’t know) for the nonlinear optimization problem: min f(x) subject to gi(x) ≤ 0, i = 1, · · · ,m hj(x) = 0, j = 1, · · · , l where f , gi, hj are continuously differentiable real-valued functions on Rn. Exercise 2. Find a variation of inputs uϵ near u∗ that

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/Optimal_Control/2023/ex4.pdf - 2025-02-23

Exercise for Optimal control – Week 6 Choose 1.5 problems to solve. Exercise 1. Derive the policy iteration scheme for the LQR problem min u(·) ∞∑ k=1 x⊤ k Qxk + u⊤ k Ruk with Q = Q⊤ ≥ 0 and R = R⊤ > 0 subject to: xk+1 = Axk +Buk. Assume the system is stabilizable. Start the iteration with a stabilizing policy. Run the policy iteration and value iteration on a computer for the following matrices:

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/Optimal_Control/2023/ex6.pdf - 2025-02-23

5 Lecture 5. Proof of the maximum principle 5.1 The tent method We continue with the static nonlinear optimization problem: min g0(x) subject to gi(x) ≤ 0, i = 1, · · · ,m (LM) in which {gi}mi=0 ∈ C1(Rn;R). Suppose that the problem is feasible, i.e., there exists an admissible x∗ which minimizes g0(x). Recall that we defined the following sets: Ωi = {x ∈ Rn : gi(x) ≤ 0}, i = 1, · · · ,m and for x1

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/Optimal_Control/2023/lec5.pdf - 2025-02-23

7 Lecture 7. Dynamic programming II 7.1 Policy iteration In previous lecture, we studied dynamic programming for discrete time systems based on Bellman’s principle of optimality. We studied both finite horizon cost J = φ(xN ) + N−1∑ k=1 Lk(xk, uk), uk ∈ Uk and infinite horizon cost J = ∞∑ k=1 L(xk, uk), uk ∈ U(xk). The key ingredients we obtained were the Bellman equations. For finite horizon, J∗

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/Optimal_Control/2023/lec7.pdf - 2025-02-23

PowerPoint Presentation Optimal Control and Planning CS 285: Deep Reinforcement Learning, Decision Making, and Control Sergey Levine Class Notes 1. Homework 3 is out! • Start early, this one will take a bit longer! Today’s Lecture 1. Introduction to model-based reinforcement learning 2. What if we know the dynamics? How can we make decisions? 3. Stochastic optimization methods 4. Monte Carlo tree

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/StudyCircleDeepReinforcementLearning/CS285-Lecture10-ModelBasedPlanning_Control.pdf - 2025-02-23

PowerPoint Presentation Model-Based Reinforcement Learning CS 285: Deep Reinforcement Learning, Decision Making, and Control Sergey Levine Class Notes 1. Homework 3 is out! Due next week • Start early, this one will take a bit longer! 1. Basics of model-based RL: learn a model, use model for control • Why does naïve approach not work? • The effect of distributional shift in model-based RL 2. Uncer

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/StudyCircleDeepReinforcementLearning/CS285-Lecture11-ModelBasedRL.pdf - 2025-02-23

PowerPoint Presentation Deep RL with Q-Functions CS 285: Deep Reinforcement Learning, Decision Making, and Control Sergey Levine Class Notes 1. Homework 2 is due next Monday 2. Project proposal due 9/25, that’s today! • Remember to upload to both Gradescope and CMT (see Piazza post) Today’s Lecture 1. How we can make Q-learning work with deep networks 2. A generalized view of Q-learning algorithms

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/StudyCircleDeepReinforcementLearning/CS285-Lecture8-DeepRLwithQfunctions.pdf - 2025-02-23

PowerPoint Presentation Advanced Policy Gradients CS 285: Deep Reinforcement Learning, Decision Making, and Control Sergey Levine Class Notes 1. Homework 2 due today (11:59 pm)! • Don’t be late! 2. Homework 3 comes out this week • Start early! Q-learning takes a while to run Today’s Lecture 1. Why does policy gradient work? 2. Policy gradient is a type of policy iteration 3. Policy gradient as a c

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/StudyCircleDeepReinforcementLearning/CS285-Lecture9-AdvancedPolicyGradients.pdf - 2025-02-23

CS285 Deep Reinforcement Learning HW4: Model-Based RL Due November 4th, 11:59 pm 1 Introduction The goal of this assignment is to get experience with model-based reinforcement learning. In general, model-based reinforcement learning consists of two main parts: learning a dynamics function to model observed state transitions, and then using predictions from that model in some way to decide what to

https://www.control.lth.se/fileadmin/control/Education/DoctorateProgram/StudyCircleDeepReinforcementLearning/hw4.pdf - 2025-02-23

02 - Virtualisation and Networking Slide title 70 pt CAPITALS Slide subtitle Cloud Computing #2a - Virtualisation and Networking Ericsson Internal | 2018-02-21 A p p Operating System A p p A p p A p p Virtualisation layer A p p Operating System A p p A p p A p p A p p Operating System A p p A p p A p p Hardware Virtual machine #1 Virtual machine #2 Virtual machine #3 Network virtualisation Storage

https://www.control.lth.se/fileadmin/control/staff/JohanEker/02_-_Virtualisation_and_Networking.pdf - 2025-02-23

05 - Hello k8s! Slide title 70 pt CAPITALS Slide subtitle Cloud Native #5 - Hello K8s! Ericsson Internal | 2018-02-21 git clone http://github.com/kubernetes-up-and-running/examples Hands-on with Kubernetes This Session http://github.com/kubernetes-up-and-running/examples http://github.com/kubernetes-up-and-running/examples Ericsson Internal | 2018-02-21 Containers at scale Containers is great tech

https://www.control.lth.se/fileadmin/control/staff/JohanEker/05_-_Hello_k8s_.pdf - 2025-02-23

06 - Distributed Computing Slide title 70 pt CAPITALS Slide subtitle Cloud Computing #6 - Distributed computing topics & cloud Ericsson Internal | 2018-02-21 Homework #1 Ericsson Internal | 2018-02-21 Ericsson Internal | 2018-02-21 Last week: k8 architecture Ericsson Internal | 2018-02-21 Distributed Computing Distributed computations are concurrent programs in which processes communicate by messa

https://www.control.lth.se/fileadmin/control/staff/JohanEker/07_-_Distributed_Computing.pdf - 2025-02-23

Microsoft Word - Assignment 2.docx Assignment 2 - A simple service the Docker way The task is to extend the simple web service from assignment one. This time you are going to use containers instead of virtual machine images for deploying your applications to the cloud (the containers, however, will still run in virtual machines.). Instead of configuring your image by snapshotting it or installing

https://www.control.lth.se/fileadmin/control/staff/JohanEker/Assignment_2.pdf - 2025-02-23

Warning_17 | Department of Biomedical Engineering Skip to main content This site uses cookies to enhance the user experience. By continuing to use the site you agree that cookies are used according to our Cookie Policy (on the website of LTH) . Essential cookies These cookies are necessary for the website to function and cannot be turned off in our systems. These cookies do not store any personall

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