introduction to robot algorithms cse 410/510robplatt/lecture_intro.pdfproblem: find a path from...
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Introduction to robot algorithmsCSE 410/510
Times: MWF, 10-10:50Location: Clemens 322
Course web page:http://people.csail.mit.edu/rplatt/cse510.html
Office Hours: 11-12 MW, 330 Davis HallTA:
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What is robotics?
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Answer from science fiction:a mechanical person
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What do robotics researchers do?
...try to build mechanical people
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The hard part?
Hardware? Smarts?or
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The hard part?
Hardware? Smarts!or
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• SRI, 1967
• Sense-think-act paradigm
1. Sense the world using vision, sonar range finder
2. Plan a sequence of actions that achieves specified goal (STRIPS)
3. Execute plan
• Tasks: navigation around blocks and over bridges, rearranging blocks by pushing them
Charles Rosen, Nils Nilsson
An enduring approach to robotics
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This course: objectives
1. Understand “the” basic problems in robotics
2. Understand a few key algorithms in detail
3. Learn mathematical/algorithmic tools that you can use elsewhere
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1. Planning
2. Control
3. Localization and mapping
4. Planning/Control as Optimization
Topics
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Topics
1. Planning
- configuration space, topology, rotation- dynamic programming- sample-based methods- cell methods- A^* and its variants- kinodynamic planning
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Motion Planning
Problem statement:
Given: model of state space
Given: a model obstacles in state space
Problem: find a path from start to goal
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Motion Planning
Applications:
1. mobile robot path planning
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Motion Planning
Applications:
2. “Piano movers problem”
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Motion Planning
Applications:
3. articulated arm motion planning
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Motion Planning
Applications:
3. articulated arm motion planning
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Motion Planning
Two main algorithms:
1. Probabilistic Road Maps (PRM)
2. Rapidly Exploring Random Tree (RRT)
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Motion Planning
Also kinodynamic applications:
- inverted pendulum
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Motion Planning
Also kinodynamic applications:
- “Acrobot”
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Topics
2. Control
- Markov Decision Processes- Value iteration, policy iteration- continuous state spaces- function approximation- linear optimal control- differential dynamic programming
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Reinforcement learning
Given: the ability to take actions
Given: the ability to perceive state exactly
Given: “rewards”
Objective: gradually calculate a policy for acting optimally with respect to the reward function.
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Topics
3. Localization and mapping
- Bayes filtering- particle filtering- EKF, UKF, etc.- Rao-blackwellization- scan matching- gMapping, EKF-SLAM, FastSLAM, etc.
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Estimation: localization
Problem statement:
Given: noisy sensors that measure partial information
Given: a model of the system
Problem: estimate state
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Estimation: localization
For example:
Given: mobile robot with laser scanners moving in an office building
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Estimation: localization
For example:
Given: mobile robot with laser scanners moving in an office building
Given: a map of the building, model of how wheels move
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Estimation: localization
For example:
Given: mobile robot with laser scanners moving in an office building
Given: a map of the building, model of how wheels move
Objective: localize robot
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Estimation: localization
Potential algorithms: variants of Bayesian filtering:
1. Extended Kalman filter (EKF)2. Unscented Kalman filter (UKF)3. Ensemble Kalman filter4. Histogram (Markov) filter5. Particle filter6. Others?
Potential applications:1. mobile robot localization2. localization of object held in hand3. ?
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Estimation: localization
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Estimation: localization
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MappingIn principle, same as localization:
Given: mobile robot with laser scanners moving in an office building
Given: no map!
Objective: localize robot, estimate map
Algorithms:- same as for localization- new problem: high dimensionality of estimation problem- other problems too...- solutions: various tricks to deal w/ high dimensionality
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Mapping
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Ground truthOdometry
Reconstructed
Mapping
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Topics
4. optimization in planning and control
- standard convex optimization problems- model predictive control- sequential quadratic programming- semi-definite relaxations- polynomial optimization, controller stability
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Convex optimization
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Model predictive control
1. Parameterize trajectory by a sequence of via points.2. define cost function and dynamics constraints3. solve the following optimization problem:
Minimize: cost functionSubject to: dynamics constraints
Under certain circumstances, this problem is convex...
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Course Prerequisites
1. Ability to program in Matlab (of the ability to learn to do this)
2. Comfortable with linear algebra.
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Reading material, notes
1. There is no single assigned text. I will assign papers and chapters as we go. This will be posted to my webpage.
2. I'll try to have my notes posted the day prior to lecture.
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Course Requirements
1. Approximately four homework/lab assignments
2. Final exam- you can be tested on things that I say in class as well as what's in the notes and reading.