September 11, Deliberative Algorithms II
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This document discusses exact and approximate algorithms for multi-robot systems. Exact algorithms always find the optimal solution but can be computationally expensive for problems like the traveling salesman problem (TSP) that are NP-hard. Approximate algorithms trade off optimality for speed. Market-based algorithms provide a distributed solution for task allocation problems where robots bid on tasks. Centralized systems require communication but have single points of failure, while distributed algorithms allow for robust self-organization but may produce ambiguous solutions.
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This document discusses processing natural language commands in robotics applications. It outlines goals of implementing sentence recognition from text to pick up objects. It reviews existing tools for text processing, speech processing, and robot actions. It also covers parsing orders by mapping verbs to targets and using parts-of-speech tagging to determine word categories. Further work includes generating robot actions from mapped commands and controlling a robot's movement.
Indoor Localization Systems
The document discusses designing an indoor positioning system as an alternative to the existing costly and power-hungry StarGazer localization system. It surveys different wireless technologies like Wi-Fi, Zigbee, and ultrasonic options before proposing an RSSI-based triangulation solution using TI's low-power CC2431 SoC. Some implementation issues discussed include the non-linear relationship between RSSI and distance, needing additional algorithms and an RSSI map survey, and methods for orientation and multi-level positioning detection.
Lecture 10: Summary
This document provides a summary of the key topics covered in an introduction to robotics course over 15 weeks, including:
- Locomotion and kinematics concepts like dynamic and static stability, forward and inverse kinematics, and differential drive constraints.
- Sensors like laser range scanners, their properties and how to model uncertainty. Visual sensors, odometry, and localization using Bayes' rule and Kalman filters.
- Midterm and final exam preparation advice focusing on understanding core concepts rather than derivations, and practicing examples like kinematics and localization problems.
- The final exam is scheduled for Wednesday, December 15 from 7:30-10:00 pm in the CAETE classroom.
Lecture 09: SLAM
1) Probabilistic state estimation techniques like the Kalman filter, extended Kalman filter, unscented Kalman filter, and particle filters allow estimating the state of a system using probabilistic models and sensor measurements with uncertainty.
2) The Kalman filter provides a recursive solution to the linear filtering problem by estimating the current state as a weighted average of the prior state and new measurements, with the weights based on their uncertainties.
3) Extensions to the Kalman filter like the extended and unscented Kalman filters allow handling nonlinear systems by linearizing around the current estimate, while particle filters represent the state distribution with random samples and are more flexible for nonlinear and non-Gaussian problems like SLAM.
Lecture 08: Localization and Mapping II
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive functioning. Exercise causes chemical changes in the brain that may help protect against mental illness and improve symptoms.
Lecture 07: Localization and Mapping I
The document discusses a midterm exam for a robotics localization and mapping course that will be harder than the final exam but require less time. It provides an overview of the last two weeks' exercises including tasks related to vision, mapping, navigation, and planning. The document then summarizes the previous lecture on the Gaussian distribution and error propagation before covering today's topics of sensors for localization, error propagation for localization, position representation, and planning. Localization, differential drive robot odometry, belief representation, environment representation, and reactive versus deliberative planning are all discussed. Students will work in groups on an exercise involving navigation algorithms.
Lecture 06: Features and Uncertainty
1. The document discusses various topics related to robotics including vision, midterm exams, locomotion, control, mapping, and homework.
2. Key concepts that are reviewed include line detection, calculating uncertainty from sensor measurements, propagating uncertainty in features, and different algorithms for mapping like watershed segmentation.
3. Exercises are assigned related to writing controllers for different robots, dealing with obstacles, and improving control parameters. Students are divided into groups to work on a final project to implement a controller.
Lecture 04
This document discusses robot sensors and perception. It begins with a review of robot kinematics and control concepts like forward and inverse kinematics, feedback control, and proportional control. It then covers specific sensors like laser rangefinders, infrared sensors, and cameras. Examples of sensors on robots like Roomba, PrairieDog, Nao, and PR2 are provided. The performance aspects of sensors like range, resolution, linearity, and accuracy are defined. Case studies of laser rangefinders and infrared distance sensors are described in detail relating their physics and working principles to their performance capabilities and limitations. An exercise is proposed to design robots for vacuuming, lawn mowing, and ball collecting giving consideration to necessary sensors, algorithms, and mechanisms
Lecture 03 - Kinematics and Control
This document provides an introduction to robotics kinematics including forward kinematics, inverse kinematics, and maneuverability. It discusses calculating a robot's speed given its wheel speeds and geometry using forward kinematics, and determining required wheel speeds to achieve a desired speed using inverse kinematics. It also covers a robot's degree of mobility based on the number of independently controllable wheels and degree of steerability based on the number of independently steered wheels to determine its overall maneuverability. Examples are provided and the document concludes with assigning homework to read about forward kinematics and program a waypoint following robot.
Lecture 01
This document outlines the syllabus for an introduction to robotics course. It will cover topics like locomotion, kinematics, perception, localization, planning and navigation. Students will gain hands-on experience programming robots in simulation and debates. Assessments include weekly reading assignments, a midterm, debate and class participation. The course will not cover components building or software engineering, focusing instead on simulation. Students will design controllers for robots in a competition called Ratslife to practice perception, navigation and planning skills.
Lectures 11+12: Debates
What are the safety risks with autonomous robots? Are autonomous robot a threat to human workers? How can robots achieve intelligent behavior? What mechanisms are needed to reach human agility?
Lecture 09: Localization and Mapping III
This document provides an overview of localization and mapping techniques for robotics, including:
- Markov localization and particle filters for estimating robot location as a probability distribution.
- The Kalman filter for optimally fusing uncertain sensor measurements and updating location estimates.
- Simultaneous localization and mapping (SLAM) and the "hen-egg" problem of needing a map to localize and a location to build a map.
- Feature-based SLAM approaches that build maps from distinct environmental features.
- FastSLAM which uses a particle filter to estimate robot location and build maps from sensor measurements.
- Key challenges in SLAM like recognizing previously visited places and handling dynamic environments.
Lecture 10: Navigation
This document discusses navigation techniques for robots. It begins by reviewing localization methods like Markov localization and Kalman filters. It then discusses two approaches for navigation - local planning, which involves moving towards a goal while avoiding obstacles, and global planning, which calculates an offline shortest path. Various global planning techniques are described, including graph-based methods like Dijkstra's and A* algorithms, as well as cell decomposition and potential field planning. Potential field planning calculates a virtual force pulling the robot based on distance to obstacles and goal direction. The document concludes by discussing debates around social and technical topics related to robotics.
Lecture 08: Localization and Mapping II
This document discusses algorithms for localization and mapping in robotics, including Dijkstra's algorithm, A* search, odometry, GPS, landmarks, and gyroscopes. It introduces probabilistic localization using Markov localization on discrete state spaces like grids or topological maps. Bayes' rule is used to update the probability of a robot's location based on sensor readings and motion. Particle filters are presented as a way to reduce complexity by random sampling rather than maintaining a full probability distribution over all locations. Examples show mapping and localization in a grid world using a particle filter approach. The homework assignment is to read about Markov localization and particle filters, and next week will include design reviews from student groups.
Lecture 07: Localization and Mapping I
This document discusses localization and mapping for robotics. It introduces topics like gyroscopes, odometry, GPS, and landmarks for localization. It discusses uncertainty models using Gaussian distributions and error propagation. Methods for belief representation are presented, including parametric single/multi hypothesis and non-parametric particle filters. Environment representations like continuous, discrete, and topological maps are described. The document provides an example of Google Maps and discusses belief representation in topological maps. It also covers multi-hypothesis belief representation, sensor data to topological maps using exact and Voronoi decompositions, and adaptive cell-size. The document assigns homework on navigation algorithms and reactive vs. deliberative planning.
Lecture 06: Features
This document provides an introduction to robotics features for computer vision. It discusses low-level image features like edges, colors and corners that can be extracted from sensors. Higher level features allow reasoning about the environment like object detection and segmentation. Examples demonstrate visual servoing using image features to grasp objects as well as fruit detection using filtering, segmentation and the Hough transform. The document also covers corner detection methods like Harris corners and scale-invariant feature transform (SIFT). It concludes with discussing using features to implement a robot controller and assigning project groups to work on different aspects.
Lecture 05: Vision
Vision is a challenging task for robots due to various ambiguities, including: depth discontinuities, surface orientation changes, reflectance changes, illumination changes, and different perspectives. Basic image processing techniques can help with tasks like edge detection, thresholding, morphological operations, and stereo vision calculations, but object recognition still requires combining these techniques with filters tuned to the specific objects. For homework, students should read about these topics and complete a questionnaire.
Lecture 04: Sensors
This document discusses robotics perception and sensors. It provides an overview of forward and inverse kinematics, feedback control concepts, and different types of sensors used in robotics like laser rangefinders, infrared sensors, and their performance characteristics. It also outlines an exercise for designing a robot capable of various tasks like vacuuming, lawn mowing, or ball collection and discusses the necessary sensors, algorithms, and mechanisms to address. Homework assigned is to read a section on perception and complete a questionnaire.
Lecture 03: Kinematics
The document provides an introduction to robotics kinematics. It discusses forward and inverse kinematics, which involve determining speed and position from wheel speeds and desired speeds respectively. It also covers feedback position control to calculate motion from position errors. Additionally, it defines concepts like mobility, steerability and maneuverability which relate to a robot's degrees of freedom based on wheel constraints and configurations. As homework, students are asked to read a chapter on kinematics and program a waypoint following robot.
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September 11, Deliberative Algorithms II
- 1. Multi-Robot Systems CSCI 7000-006 Friday, September 11, 2009 NikolausCorrell
- 2. So far Reactive vs. Deliberative Algorithms Both approaches are probabilistic for noisy sensors and actuators Robustness/Deterministic behavior can be increased by Combining different sensors Information exchange Actively validating hypothesis Redundancy
- 3. Today Exact and approximative algorithms Centralized vs. Distributed Systems Market-based algorithms
- 4. Exact Algorithms Find always the best solution Search the entire solution space Determine what “best” means (fitness function) Enumerate all solutions Pick best solution Some problems: dynamic programming Finding the best solution can be very time-consuming/impossible for NP-hard problems
- 5. Example: Traveling Salesman Problem Traveling Salesman Problem Find the shortest route connecting n cities Never visit any city twice Computational representation: sequence Brute force algorithm: calculate length of all possible permutations 60 cities -> 4.2 * 10^81 permutations NP hard, exact better than brute-force solutions exist (e.g. dynamic programming)
- 6. Course Question Come up with a reactive algorithm for solving the TSP. Hint: ants.
- 7. Reactive Algorithm for the TSP Use a population of ant-like agents starting at random cities Each ant randomly select a city that it has not yet visited on this tour (repeat until all cities are visited) Each ant calculates the length of this path and deploys an inverse amount of “pheromones” on the path In following iterations, ants are programmed to select paths from city i to city j with a higher likelihood Algorithm converges to a local optimum
- 8. Lessons from this example Exact problems can be very hard to solve Also “pure” CS offers a wide range of algorithmic solutions The design problem trades off provable optimality with speed In robotics algorithmic choice is constrained by sensors, actuators, computation and communication
- 9. Coverage example (Wednesday) Exact algorithm for single robot Approximative algorithm for multiple robots Robots might find the optimal solution Worst case: every robot covers everything
- 10. Course Question Come up with an exact algorithm for covering M cells with N robots as fast as possible. Hints: The problem reduces to allocate a subset of cells to each robot to minimize the maximum number of cells allocated to one robot. Identify sub-problems / algorithms
- 11. Possible Solution Enumerate all possible sets of allocations Calculate the cost of each allocation Cost: TSP path over all cells NP-Hard Stirling numbers of the 2nd kind for 3 and 4 cells and up to 4 robots. © Mathworld
- 12. Centralized vs. Distributed Algorithms Finding the best solution requires knowing all parameters of the system Usually requires “leader” or centralized agent Course Question: What problems do you expect in a centralized system?
- 13. Centralized Systems Information needs to be sent to a central unit Commands need to be sent to each robot Problems Information get lost both ways Process needs to be repeated when individuals fail Individual failure needs to be detected …
- 14. How to distribute an algorithm? Smart way: using the optimal substructure of the problem (dynamic programming) Not all problems can be efficiently distributed Robust: Every robot solves the whole problem for the entire team Problem: ambiguous solutions Resolution: conflict resolution rules, e.g. lower id goes first Example: Market-based task allocation
- 15. Market-based task allocation Tasks are offered by auctioneer Every robot bids with the cost that it would need to do the task Robot with the lowest cost gets the job Simplest auction: greedy, non-optimal ordering Variations: bidding on all possible permutations
- 16. Example: Box Pushing Two tasks: watch the box, push the box Three robots, only one can watch the box Watch the box requires LMS Watcher auctions off “push left” and “push right” tasks "Sold!: Auction methods for multi-robot coordination". Brian P. Gerkey and Maja J Mataric´. IEEE Transactions on Robotics and Automation, Special Issue on Multi-robot Systems, 18(5):758-768, October 2002.
- 17. Example: Coverage Robots calculate cost for covering a blade by solving the TSP Sequential biddingapproximates near optimal Deterministic bid evaluation allows for decentralized auction-closing Re-Allocation upon error P. Amstutz, N. Correll, and A. Martinoli. Distributed Boundary Coverage with a Team of Networked Miniature Robots using a Robust Market-Based Algorithm. Annals of Mathematics and Artifcial Intelligence. Special Issue on Coverage, Exploration, and Search, Gal Kaminka and Amir Shapiro, editors, 52(2-4):307-333, 2009.
- 18. Re-Auctioning example Bids during auction Robot 1 “slips”
- 19. 9/20/2007 Nikolaus Correll 19
- 20. Results DFS/A* No collaboration Market-based coordination DFS/A* Information exchange
- 21. Summary The better you plan, the better the performance Noise requires you to re-plan all the time Feasible algorithms determined by robot capabilities: sensors, actuators, computation and communication Algorithmic complexity exponential for NP hard problems Potentially very high cost for marginal improvements!
- 22. Outlook Control-based approaches (in two weeks) Modeling: examining resource trade-offs on paper (in three weeks) Next week: building week
Editor's Notes
- Optimal Substructure: solution can be constructed from solutions to its subproblemsOverlapping subproblems: solutions to subproblems can be used multiple times in finding the solution