Path Following & Motion Control Stephen J. Guy Stephen J. Guy

One Theme – Two paper ► Pedestrian path following  Control using physics ► Controlling Physical Simulations  Control of physics

Reactive Pedestrian Dynamics

► Premise:  Building visualizations are more compelling with moving people  Need a simple to place moving virtual people in models ► Approach: 1.Let users specify path 2.Make agents follow it naturally Reactive Pedestrian Path Following from Examples, Ronal Metoyer Oregon State, Jessica Hodgins CMU (2004)

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

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  k p – the path gain

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

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

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

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

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 ► a j – j th action ► h i – i th avoidance technique ► H – set of all avoidance techniques ► n hi – number of times user selected h i ► |N| – total number of user selections

Results ► No videos (dead links  ) ► Simulation snapshot --> ► Bayes Classification

Sampling Plausible Solutions to Multi-body Constraint Problems

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 Sampling plausible solutions to multi-body constraint problems. In Proceedings of ACM SIGGRAPH 2000, 219–228.

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

Incorporating Uncertainty ► Define function p w (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:

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

Constrain Approximation ► Can’t use p w (A|C) ► Instead use p(A) = p w (A)*p c (A)  p c (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

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)

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: A 1, A 2, A 3, …  An dependant only on An-1  A is distributed following p(A)

Algorithm 1. initialize(A 0 ) 2. simulate(A 0 ) 3. Repeat 4. propose(A c, A i ) 5. simulate(A c ) 6. u <- random(0,1) 7. if u < min(1, ) 8. A i+1 <- A c 9. else 10. A i+1 <- A i q(X | Y) is probability of transitioning from X to Y

Example – 2D Ball ► Generating A i+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

Example - Bowling ► Rank resulting pin-condition with Gibbs distribution  p c (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 A i  Sample new values for all variables  Change the radius, density, or initial conditions of the ball  Change the initial position of some pins

Bowling – Videos (1/2) ► 3 Different strike animations  Was easy to get strikes given simulations

Bowling – Videos (2/2)

Bowling 7-10 split

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

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

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.”

Many-Worlds Browsing for Control of Dynamics Simulations

Many-Worlds Browsing for Control ► Premise  Passive physical simulations are great…  But artists often need more control  Existing techniques are basically 1. Convert user’s goals to a function 2. 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.

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

Basic Technique 1. Specify initial simulation state 2. Create various physical simulations, until a collision 3. Report various results/options to user 4. Allow user to choose path 5. Allow user to insert new objects 6. Repeat ► It’s important to return a variety of results, but they all need to be plausible

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

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

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

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

Result ► SIGGRAPH Video ► Live Demo

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)

Questions ?

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 Chenney, S., and Forsyth, D. A 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 Evaluating the visual fidelity of physically based animations. ACM Transactions on Graphics 22, 3 (July), 527–536.