Path Following & Motion Control

1. Path Following & Motion Control

2. One Theme – Two paper • Pedestrian path following • Control using physics • Controlling Physical Simulations • Control of physics

3. Reactive Pedestrian Dynamics

4. Reactive Pedestrian Dynamics • Premise: • Building visualizations are more compelling with moving people • Need a simple to place moving virtual people in models • Approach: • Let users specify path • Make agents follow it naturally Reactive Pedestrian Path Following from Examples, Ronal Metoyer Oregon State, Jessica Hodgins CMU (2004)

5. Agent Model • Create “Intelligent” Agents to follow path • Intelligence comes from force models in the environment and on other agents • Example forces:

6. User Defined Paths • Exploits humans’ natural ability to general realistic paths • Convert paths into forces: • f(s) – Unit vector along path (at nearest point) • f(dmax) – unit vector perpendicular to f(s) • p – the perpendicular distance to the path • d – max is the largest allowed distance • kp – the path gain

7. Path Following Diag. • Example application of forces • Note the direction of force changes with distance from path

8. Hazard’s of Potential Based Models • The authors state: “The intelligence model alone should produce correct 2D motion in terms of avoiding the defined obstacles and reaching goals, but will not necessarily produce natural motion for navigating complex scenes.” • Reading between the lines: • Our approach (like any potential based method) can mess up when two dynamic agents are involved • Solution – Let the user fix it • User warned of collisions and asked how to handle: • Yield • Cut in front • Go-around-right (or left) • No action

9. Implementing Avoidance Primitives • Cut-In Front and Yield: • Change the agent’s speed to avoid collision • Go Around Right: • Change the agent’s direction to avoid collision

10. Automating Avoidance Primitive • Somehow we’ve moved away from our goal of an automatic system for path following • Key Idea - Learn from previous user corrections (Machine Learning/AI) • Record data needed to repeat user decisions: • Layout of scene • Position of agents • Speed of agents

11. Training • Build a naïve Bayes classifier • Inputs: • Is the path around left blocked (Y or N) • Is the path around right blocked (Y or N) • Relative speed of the colliding pedestrians (5) • Approach direction of the colliding pedestrians (8) • Colliding pedestrian’s distance to collision (5) • Pedestrian’s distance to collision (5) • Desired travel direction (3) • Outputs: • Yield • Cut in front • Go-around-right (or left) • No action • aj – jthaction • hi – ith avoidance technique • H – set of all avoidance techniques • nhi – number of times user selected hi • |N| – total number of user selections

12. Results • No videos (dead links ) • Simulation snapshot --> • Bayes Classification

13. Sampling Plausible Solutions to Multi-body Constraint Problems

14. Solution Sampling for Constraint Satisfaction • Premise • Extreme sensitivity makes multi-body simulations difficult to control • Users general want a goal, more than the care how the goal is achieved • Approach • Allow users to specify constraints (goals) • Explore simulation space • Return animations which likely satisfied constrains Chenney, S., and Forsyth, D. A. 2000. Sampling plausible solutions to multi-body constraint problems. In Proceedings of ACM SIGGRAPH 2000, 219–228.

15. Simulation Randomness • Simulation needs randomness for this technique to work • Needs variations in simulations to explore • Authors argue randomness is good anyway • Models small variations in otherwise flat surfaces • Closer to real world • Closer to user expectation

16. Incorporating Uncertainty • Define function pw(A) (prob. of animation A) which is low for unlikely As and high for likely As • Consider a bouncing ball (2D) • A is collection of normals i • Vertical normals likely:

17. Constraints Satisfaction • We want pw(A | C) ‘s distribution in A • Return animations with high likely in pw • Example Constraints • Ball must go from here to there • Ball much have final velocity of foo • Ball must bounce through hoop • Finding pw(A|C) is not (generally) possible

18. Constrain Approximation • Can’t use pw(A|C) • Instead use p(A) = pw(A)*pc(A) • pc(A) depends on how well A satisfies constraints • For ball example (d is target distance form center) • And • Sample according to p(a) • Mainly likely events • Occasionally unlikely events

19. Defining Plausibility • Moves past “it it looks right to me its right” • Plausibility is statistically defined be P(A) • Possible to validate important parts of P(A) against a real world model • But there are other approaches • (See next paper)

20. Markov Chain Monte Carlo (MCMC) • Markov Chain Model • Given a sequence of events, next state is dependant only on current state • Monte Carlo Algorithms • Using random numbers to help (probably) solve problems • MCMC • Generate sequence of animations: A1, A2, A3, … • An dependant only on An-1 • A is distributed following p(A)

21. Algorithm • initialize(A0) • simulate(A0) • Repeat • propose(Ac, Ai) • simulate(Ac) • u <- random(0,1) • if u < min(1, ) • Ai+1 <- Ac • else • Ai+1 <- Ai q(X | Y) is probability of transitioning from X to Y

22. Example – 2D Ball • Generating Ai+1: • 50% of adding between -5 and 5 degrees to each normal of the previous animation • q(X|Y): • Choosing d is tricky • Too small – no variation • Too large – constraints aren’t well satisfied

23. Example - Bowling • Rank resulting pin-condition with Gibbs distribution • pc(A) = k+m •  > 1 • k number of correct pins • m number of undisturbed pins •  has the same constraints as d did before • Author’s claim less sensitivity • Proposing new Ai • Sample new values for all variables • Change the radius, density, or initial conditions of the ball • Change the initial position of some pins

24. Bowling – Videos (1/2) • 3 Different strike animations • Was easy to get strikes given simulations

25. Bowling – Videos (2/2)

26. Bowling 7-10 split

27. Example – Spelling Balls • Similar to bowling • Gibbs distribution • Similar Parameters varied • Spelling “Hi” • “A few hours” on an Pentium 200 MHz

28. Example - Dice • Approach from simple ball example won’t work • Need a smooth change in normals • Create “surface” using b-splines • Vary control points of b-spline • ~ 1 hour per die

29. Future Work • Issues • Not real time • Not interactive (is this an issue?) • Very slow • Unclear how to best build p(A|C) (std. dev issues) • Unclear how to best build the proposal function • “Multi-body constraint problems are good candidates for a Design Galleries interface, in which a user browses through sample solutions to locate the one they prefer. Our work addresses the sampling aspect …, but we do not consider other aspects of the interface.”

30. Many-Worlds Browsing for Control of Dynamics Simulations

31. Many-Worlds Browsing for Control • Premise • Passive physical simulations are great… • But artists often need more control • Existing techniques are basically • Convert user’s goals to a function • Minimize this function numerically • This is slow on non-linear simulations • Approach • Leverage human flexibility • Provide user options at interesting points Christopher D. Twigg and Doug L. James. Many-worlds browsing for control of multibody dynamics. ACM Transactions on Graphics (SIGGRAPH 2007), 26(3), August 2007.

32. Keeping the User in the Loop • Previous work used offline Markov Chain Monte Carlo to reach goals (Chenney and Forsyth) • Authors argue it’s good to keep the user in the loop • Gives feedback on the simulation • Even w/ ideal optimizations, user would need to give feedback on simulation setup

33. Basic Technique • Specify initial simulation state • Create various physical simulations, until a collision • Report various results/options to user • Allow user to choose path • Allow user to insert new objects • Repeat • It’s important to return a variety of results, but they all need to be plausible

34. Plausibility • Studies have been performed on how much users notice wrong results [O’Sullivan] • Variations users don’t mind/notice are considered plausible • Users were unable to detect distortions of up to: • 40% in magnitude of linear velocity • 20 degrees in direction of linear velocity • 20% in angular velocity • Assumes that chains of plausible actions are also plausible

35. Practicalities • Parallelization • Running multiple simulations is slow • Each simulation is independent • Split over a cluster! • Data transfer • Simulation from each comp. needs to be sent to user • Need efficient representation (or lots of bandwidth) • Represent the position as a piecewise quadratic spline • Represent the rotation as a piecewise linear skew-symmetric matrix

36. User Interaction • Spatial queries • Allow the user to section areas where the chosen objects should or should not go through • Ranking metrics – allows the user to specity additional metrics to sort valid queries by • Angular velocity, running time, collisions, orientation, desired constraints • Refinement – allow user updates in realtime

37. Results • UI was vary fast, able to show user over 1,500 simulation results at once screen • Creating interesting simulations was quick • Refrigerator Toy – 5½ minutes • Spelling SIGGRAPH – 1 hour (w/ backtracking) • Spiral Staircase – 25 minutes • Trebuchet – Simulation took 14 hours so no realtime refinement was possible

38. Result • SIGGRAPH Video • Live Demo

39. Comparison • The three control techniques were radically different • The first – worked to follow users path (with a physically inspired model) • The second – gave user several options which fit their constraints • The third – allowed the user to naturally explore physically based options • Some similarities • Leverage user input when it makes sense • Physics! (making life better)

40. Questions ?

41. References Ronald Metoyer, and Jessica Hodgins, Reactive Pedestrian Path Following from Examples, (2004). Christopher D. Twigg and Doug L. James. Many-worlds browsing for control of multibody dynamics. ACM Transactions on Graphics (SIGGRAPH 2007), 26(3), August 2007. Chenney, S., and Forsyth, D. A. 2000. Sampling plausible solutions to multi-body constraint problems. In Proceedings of ACM SIGGRAPH 2000, 219–228. O’Sullivan, C., Dingliana, J., Giang, T., And Kaiser, M. K. 2003. Evaluating the visual fidelity of physically based animations. ACM Transactions on Graphics 22, 3 (July), 527–536.