1. CS790E Planning Algorithms Lecture 1: Applications and Basic Ingredients of Motion Planning 19 January 2010 Instructor: Kostas Bekris Computer Science & Engineering, University of Nevada, Reno

2. CS790E “Planning” Algorithms? The term “planning” corresponds to multiple research challenges: e.g., scheduling tasks, path planning, action selection, etc. We will focus on planning in an algorithmic way motions and actions for “physical” systems, e.g., objects with geometry, mass and velocity, etc.  This includes “real-world” systems such as: ✓ 3D rigid-bodies, robots and vehicles, machines in factory floors, molecules, etc.  But also includes “virtual” agents such as: ✓ animated characters, simulated environments, etc. Many different fields are related to this challenge: Robotics Artificial Intelligence Control Theory Computer Graphics Computer Animation Scientific Simulation Computer Games Algorithms: Computational Geometry Computational Biology & Bioinformatics Virtual prototyping in manufacturing Architectural Design Aerospace Engineering Computational Geography

3. CS790E Planning Challenges in Various Fields Artificial Intelligence Originally:  Search & Automated Planning: How to search for a sequence of operations that transform an initial problem state into a desired goal state Today:  Decision-theory: How to make optimal decisions or sequence of decisions under the presence of uncertainty? ✓ imperfect state information, markov-decision processes (MDPs), game-theory  Reinforcement learning: Learn the right decisions or sequence of decisions that must be executed for every possible state from experience. In general: Machine planning is the complement to machine learning  Once learning is being successfully performed, planning deals with the decisions that have to be made AI focuses on discrete problems, we will mostly focus on continuous ones

4. CS790E AI Examples Discrete Puzzles, Operations and Scheduling Mars Rovers - NASA Kasparov vs. Deep Blue - IBM Earth Observing 1 - NASA 15-puzzle Rubic’s Cube

5. CS790E Planning Challenges in Various Fields Robotics Originally:  Motion Planning: How to move a rigid body without collisions (i.e., a piano from one room to another without collisions) Today, new complications are being considered:  Trajectory Planning: How to compute feasible paths for robots/vehicles with constrains in velocity and acceleration (systems with dynamics)  Planning under Uncertainty: How to plan the motion of a moving system if we are not absolutely certain about its location  Motion Coordination: How to move in coordination with other robots or in the presence of other moving systems? Many other problems are involved in building robots: state estimation, task allocation, mechanism design, dynamical system modeling, feedback control, sensor design, computer vision, inverse kinematics, humanoid robots, etc.

6. CS790E Benchmarks Traditional Motion Planning Alpha Puzzle - James Kuffner - Carnegie Mellon Univ. Piano Mover’s Problem - Gamma Group Manocha & Lin - Univ. of N. Carolina, Chapel Hill Piano Mover’s Problem - Gamma Group Manocha & Lin - Univ. of N. Carolina, Chapel Hill Kostas Bekris - Rice University

7. CS790E Manipulators Traditional Motion Planning 3 Manipulators moving a Piano - Juan Cortes & Tierry Simeon - LAAS-CNRS France 3 Manipulators moving a Piano - Juan Cortes & Tierry Simeon - LAAS-CNRS France Lydia Kavraki - Rice University Jean-Claude Latombe - Stanford University

8. CS790E Traditional Motion Planning Automotive Applications Motion planning company: Kineo CAM Customers: Renault Ford Airbus Optivus Volvo cars plant

9. CS790E From Traditional Planning to Planning with Dynamics

10. CS790E From Traditional Planning to Planning with Dynamics

11. CS790E From Traditional Planning to Planning with Dynamics

12. CS790E Motion Planning with Dynamics & Under Uncertainty Mobile Robots & Vehicular Applications CMU DARPA Urban Challenge CMU DARPA Urban Challenge Stanford DARPA Urban Challenge Stanford DARPA Urban Challenge A robot pulling a trailer Jean-Paul Laumond - LAAS - France A robot pulling a trailer Jean-Paul Laumond - LAAS - France PLEN Scating Robot - Japan Honda - Japan James Kuffner CMU James Kuffner CMU

13. CS790E Planning Challenges in Various Fields Control Theory Originally:  Traditional Control: Optimal operation of continuous systems under differential constraints (constrains expressed through differential equations) ✓ focusing on dynamics, stability, optimality, feedback (closed-loop control) ✓ ignoring obstacles Today:  Open-loop non-linear control: Feasible open-loop trajectories for non-linear syst. In this course initially the focus will be on:  open-loop trajectories instead of closed-loop  feasibility as opposed to optimality  rigid bodies without dynamics Eventually, we will include: closed-loop problems, optimality and dynamics but from an algorithmic perspective instead of an analytical

14. CS790E Planning Challenges in Various Fields Algorithms Combinatorics and complexity theory are important for planning algorithms Important questions: are the algorithms complete? Most related sub-areas:  Path finding in graphs  Computational geometry Computer Animation / Graphics / Simulation / Games Originally:  Animated characters and agents moved in a cartoonish way  As long as the agent reaches the goal that is enough  Cool graphics more important than reasonable AI Today:  Simulated Motion: It becomes increasingly important for simulated motion to be physically realistic  Game AI: Becomes the most important selling point for new games  Industrial Simulation: Physics-based simulation is increasingly used before real experiments are conducted - real products are produced - real factories are built

15. CS790E Virtual Characters James Kuffner - Carnegie Mellon University Gamma Group University of North Carolina, Chapel Hill Gamma Group University of North Carolina, Chapel Hill

16. CS790E Types of Problems Discrete Continuous 3D Free moving Constrained Motion Differential Constraints & Dynamics 2D Other complications: sensor-based problems (i.e., partial-observability) uncertainty in sensing and acting multi-agent systems real-time requirements

17. CS790E Class Overview Plan for CS790E (check schedule online: http://www.cse.unr.edu/robotics/bekris/cs790_s10/event) : http://www.cse.unr.edu/robotics/bekris/cs790_s10/even 1. Applications and Basic Ingredients of Motion Planning 2. 2D Planning: Combinatorial Algorithms and Potential Functions 3. 3D Planning: The Configuration Space Abstraction 4. Sampling-based Motion Planning for Free-Flying Rigid Bodies 5. Extensions of Basic Motion Planning 6. Presentations I: Literature Survey and Project Proposal 7. Dynamics and Trajectory Planning 8. Planning for Cars and Trailers 9. Safety in Replanning with Dynamics 10. Feedback Planning & Planning for Hybrid Systems 11. Planning under Uncertainty 12. Presentations II: Experimental Results and Conclusions

18. CS790E Basic Ingredients of Planning State Planning problems involve a state space: all possible situations that could arise  e.g., position and orientation of a robot  e.g., the locations of tiles in a puzzle  e.g., the position, orientation, and velocity of a helicopter Typically, too large to represent and store explicitly Time We have to make a sequence of decisions over a period of time Time can be modeled explicitly:  e.g., driving a car as quickly as possible through an obstacle course (when velocity is important, time is important) Time may be modeled implicitly:  e.g., in solving the Rubik’s cube, actions just have to be executed in succession  e.g., the Piano Mover’s problem, the speed of the object is not important

19. CS790E Basic Ingredients of Planning Actions A plan generates actions that manipulate/change the state.  AI: actions and operators, Control theory and Robotics: inputs and controls How does the state change when actions are applied?  Discrete time: State-valued function  Continuous time: Ordinary differential equation Initial and Goal States Start at an initial state and select actions so as to reach a goal state Criterion Additional requirement the plan must satisfy:  Feasibility: Find a plan that causes arrival at a goal state given the motion capabilities of a system, regardless of its efficiency (already hard)  Optimality: Find a feasible plan that optimizes performance in some carefully specified manner, in addition to arriving in a goal state (even harder) Feasible solutions are preferable to having no solutions at all

20. CS790E Basic Ingredients of Planning Plan A plan may be:  simply a sequence of actions to be taken  a time-sequence of controls  (uncertainty in action) an assignment of actions to all states (AI: policy, Control theory: feedback control - feedback/reactive plan) Once a plan is available, there are three ways to use it: 1. Execution  Execute it either in simulation or on a physical device 2. Refinement 3. Hierarchical inclusion

21. CS790E “Simpler” Planning: Planning in Discrete Spaces