CS790E Planning Algorithms

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

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

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

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

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

9. From Traditional Planning to Planning with Dynamics

10. From Traditional Planning to Planning with Dynamics

11. From Traditional Planning to Planning with Dynamics

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

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

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

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

18. 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. 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. 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: • Execution • Execute it either in simulation or on a physical device • Refinement • Hierarchical inclusion

21. “Simpler” Planning: Planning in Discrete Spaces