1. 1 Control of Articulated Bodies Lecture for COMP 768 presented by Georgi Tsankov Oct 30, 2007

2. 2 Control of Articulated Bodies Overview  Control system.  One-legged hopper and dynamic locomotion.  Animating human athletics.  Automatically generated controllers.  Composable controllers, more intelligent behavior.

3. 3 Control System The Control Problem:  Question: how do we control the muscles in order to achieve a desired motion (walking) ? What motions are we interested in:  grasping - easier (stable, less DOF).  walking/running - cyclic, unstable, many DOF. The most important movement a human can perform. Most of the work is concentrated here.

4. 4 Control System

5. 5 Disciplines involved and Applications Robotics Computer Animation  Feature films  Computer games Biomechanics  Provides real-world data.  Uses simulations for analysis of problems, high- performance athletics. Artificial Intelligence

6. 6 Properties of a good control system Realistic. Keeping balance. Adaptable to different characters (proportions, weights). Various speeds and gaits. Changing direction, variable step length. Handling uneven terrain, obstacles, external forces.

7. 7 A typical control system: Finite state machine:  Small number of states (2-10)  Types of transitions: Timed – after fixed amount of time. Sensor-based – after certain event has happened.

8. 8 A typical control system: Example FSM (running for one-legged robot) :

9. 9 Open vs. Closed-loop control: Open-loop control doesn’t consider feedback.  The behavior is hard-coded (only timed transitions).  Cheap, simple, sometimes sufficient for computer animation. Closed-loop control observes its output.  More realistic model, required for robotics and biomechanics.  Can be learned. http://www.motivationwarehouse.com/images/product_images/chatterbox.jpg

10. 10 Open vs. Closed-loop control: Controller Input signal Joint Output signal (Force) New body position Feedback Controller Input signal Joint Output signal (Force) New body position Open-loop Closed-loop

11. 11 Proportional-Derivative controller (PD servo) PD controller - a simple closed-loop controller. Input:  desired pose (angles) and velocities.  current pose. Output:  force.  k d – derivative gain  k v – velocity feedback gain  The gains determine the strength of the joint http://www.library.cmu.edu/ctms/ctms/examples/pitch/pidplot3.gif

12. 12 Control of Articulated Bodies Overview  Control system.  One-legged hopper and dynamic locomotion.  Animating human athletics.  Automatically generated controllers.  Composable controllers, more intelligent behavior.

13. 13 First Approach: [Raibert83], MIT - 3D one-legged hopping robot. The control system is divided into three independent parts:  Control of the forward speed.  Control of the body attitude.  Control of the hopping height.

14. 14 One-legged hopper 4 DOF:  1 for length of the leg.  3 for the joint. Only 2 DOF in 2D. Modeled as spring and inverted pendulum. Video

15. 15 One-legged hopper Many papers in late 80s, early 90s are based on this control design. Especially separation of the control into 3 components. We will focus on [Hodgins91].

16. 16 Animation of Dynamic Legged Locomotion Based on the one-legged hopper. Present three hopping robots:  One-legged planar kangaroo  Biped  Quadruped

17. 17 Animation of Dynamic Legged Locomotion 5 states. Can be simplified to:  Support phase.  Flight phase. All the transitions are event-driven.

18. 18 Animation of Dynamic Legged Locomotion Controlling forward velocity: we can only influence step length, i.e. the next footstep.  Neutral point – the velocity is preserved.  Step before the neutral point – increased velocity. (after–decreased).  x fh – forward displacement of the foot.  t s – duration of the support period.   – the angle of the leg at touchdown.  k x’ – gain, determined experimentally.

19. 19 Animation of Dynamic Legged Locomotion Controlling body attitude:  Estimate the torque at the hip, given: Desired angle –  d. Current angle –   Use PD control:  – hip torque  k    b  – gains.

20. 20 Animation of Dynamic Legged Locomotion Controlling hopping height:  Depends on the force exerted by the leg.  The leg is modeled as spring with adjustable rest length (L d ).  L d – rest length – can be modified to control the hop height.  k L, b L – gains, again experimentally.

21. 21 From hopper to biped Active and idle leg changing at each step. The active leg behaves as before. Strategies for the idle leg:  In flight – mirror the active leg (for balance) (Here the active and idle leg are swapped.)  In compression/thrust – keep short (not to penetrate the ground)

22. 22 From hopper to biped

23. 23 Quadruped The four legs are coordinated in two pairs - two virtual legs. The controller is essentially the same as for the biped (operating on the virtual legs). Different grouping for different gaits  diagonal for trotting.  front and rear for bounding. Video

24. 24 Animation of Dynamic Legged Locomotion What we have?  Realistic motions for hopping robots. How to extend them to virtual humans? [Hodgins95]  Use the same FSM.  The control is again divided into three parts (forward velocity, balance, vertical velocity).

25. 25 Control of Articulated Bodies Overview  Control system.  One-legged hopper and dynamic locomotion.  Animating human athletics.  Automatically generated controllers.  Composable controllers, more intelligent behavior.

26. 26 Animating human athletics What is new ?  The runner has 17 body segments, 30 DOF.  Legs can still be modeled as springs, the length is controlled by the knee and hip joints.  The hands follow the same pattern as the legs (to reduce the torque of the upper body). Similar techniques for bicycling and vaulting are presented in the same paper ([Hodgins95]). (video1, video2, video3)video1video2video3

27. 27 Walking vs. Running How is walking different ?  Has double-support phase.  No flight phase.  The legs are not springy (no energy is saved in them). [Yin,Panne07] present control system for walking and running based on PCG:  Very small number of parameters.  Different gaits (including sideways and backwards walking).  Can handle pushes in all directions, unexpected steps and slopes. (Video)Video Walking cycle Running cycle Left Right Left Right

28. 28 Control of Articulated Bodies Overview  Control system.  One-legged hopper and dynamic locomotion.  Animating human athletics.  Automatically generated controllers.  Composable controllers, more intelligent behavior.

29. 29 Ways to generate controllers automatically Motivation: the techniques so far give good results, but require a lot of hand-tuning for new characters and motions. Techniques for automatic generation of controllers:  SAN – Sensor-Actuator Networks [Panne,Fiume93].  PSM – Parametrized State Machines [Panne96].

30. 30 SAN – Sensor-Actuator Networks The controller is a directed network (similar to neural network):  Input nodes – sensors (positions, angles, contact with ground).  Output (actuator) nodes - produce force/torque at a specific joint.  Intermediate nodes – compute the weighted sum of the inputs with some time delay.

31. 31 SAN – Sensor-Actuator Networks Generate random controllers, take the best 1-5% and do fine tuning on them. Measure: distance traveled in T seconds. Results:  Desk lamp.  Fish.  Video (Karl Sims’ Alife – not SAN, but similar results). Video

32. 32 SAN – Sensor-Actuator Networks Advantages:  Able to generate controllers for arbitrary bodies Disadvantages:  Can not create complex motions.  The generated controller is hard to understand (and modify) by human.

33. 33 PSM - Parametrized State Machines Based on PCG – pose-control graph.  Each state represents a pose. (like key-framing)  Transition times are fixed.  No feedback! (i.e. open-loop control).

34. 34 PSM - Parametrized State Machines Again, random generation and local search for best solution. Measure - the same - distance traveled in T seconds of simulation. Results:  Walking Monster (3D)  Cheetah (2D)

35. 35 PSM - Parametrized State Machines Advantages:  Simple architecture and allows for interpolation between controllers (slow and fast walk).  Can be used to integrate aperiodic motions in walking. Disadvantages:  Hard to generate complex motions.  No feedback. The balance is entirely dependant on the poses.  Very hard to generate unstable motions!

36. 36 Control of Articulated Bodies Overview  Control system.  One-legged hopper and dynamic locomotion.  Animating human athletics.  Automatically generated controllers.  Composable controllers, more intelligent behavior.

37. 37 A higher level system with multiple controllers [Faloutsos01] Motivation :  Ability to integrate various behaviors in the same system.  Response to external forces and switching between behaviors: Falling Getting up Walking again.

38. 38 A higher level system with multiple controllers The control system consists of:  A pool of controllers.  Supervising controller. The individual controllers have:  pre-conditions: initial and target state, environment parameters, balance.  post-conditions: target state, environment parameters, balance.

39. 39 A higher level system with multiple controllers The supervising controller chooses which controller to execute:  Must satisfy the pre-conditions. (e.g. fallen)  If able to reach the goal position - even better. (crawling vs. standing-up)

40. 40 A higher level system with multiple controllers A controller can be deactivated for one of 3 reasons:  successfully performs the motion.  fails because of external forces/obstacles.  after user input.

41. 41 A higher level system with multiple controllers The hardest problem is determining the pre- conditions for each controller. Can be solved efficiently by off-line learning.  Various states are sampled and a simulation is run.  SVM (support-vector machine) is used to do the learning.  10,000 simulations can be learned in several minutes to a few hours (depending on SVM parameters).

42. 42 Summary Controllers so far:  Produce realistic animation in automated way.  Improved flexibility and diversity of motions. What else can be done:  Reduce the number of parameters (simplify the design).  Add individual style to the motions.  Use motion data to generate controllers.  Motion planning for uneven terrain, error recovery.  More work on composable controllers.

43. 43 Acknowledgments Many pictures and formulas were taken from [2]. Also from [1]. And the other cited papers.

44. 44 References 1. M. van de Panne - Control for Simulated human and animal motion, 2000. 2. J. Hodgins – Building Control Systems for Robot Locomotion, GDC 2000. 3. Multon, France, Cani-Gascuel, Debunne - Computer Animation of Human Walking: a Survey, 1999. 4. M. Raibert - 3D One-legged Hopper - http://www.ai.mit.edu/projects/leglab/robots/3D_hopper/3D_hopper.html, 1983. http://www.ai.mit.edu/projects/leglab/robots/3D_hopper/3D_hopper.html 5. J. Hodgins, M. Raibert - Animation of Dynamic Legged Locomotion, Proceedings of SIGGRAPH 1991. 6. J. Hodgins, W. Wooten, D. Brogan, J. O'Brien - Animating Human Athletics, SIGGRAPH 1995. 7. K. Sims - Evolving Virtual Creatures, SIGGRAPH 1994. 8. K. Yin, K. Loken, M. van de Panne - SIMBICON: Simple Biped Locomotion Control, SIGGRAPH 2007. 9. M. van de Panne, E. Fiume - Sensor Actuator Networks, Proceedings of SIGGRAPH 1993. 10. M. van de Panne – Parameterized Gait Synthesis, 1996. 11. P. Faloutsos, M. van de Panne, D. Terzopoulos - Composable Controllers for Physics-Based Character Animation, SIGGRAPH 2001.