Control of Articulated Bodies Lecture for COMP 768

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

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

Control System n The Control Problem: q n Question: how do we control the muscles in order to achieve a desired motion (walking) ? What motions are we interested in: q q 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. 3

Control System 4

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

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

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

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

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

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

Proportional-Derivative controller (PD servo) n n PD controller - a simple closed-loop controller. Input: q q n desired pose (angles) and velocities. current pose. Output: q force. n q q q kd – derivative gain kv – velocity feedback gain The gains determine the strength of the joint http: //www. library. cmu. edu/ctms/examples/pitch/pidplot 3. gif 11

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

First Approach: n n [Raibert 83], MIT - 3 D one-legged hopping robot. The control system is divided into three independent parts: q q q Control of the forward speed. Control of the body attitude. Control of the hopping height. 13

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

One-legged hopper n n Many papers in late 80 s, early 90 s are based on this control design. Especially separation of the control into 3 components. We will focus on [Hodgins 91]. 15

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

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

Animation of Dynamic Legged Locomotion n Controlling forward velocity: we can only influence step length, i. e. the next footstep. q q q Neutral point – the velocity is preserved. Step before the neutral point – increased velocity. (after–decreased). xfh – forward displacement of the foot. ts – duration of the support period. q – the angle of the leg at touchdown. kx’ – gain, determined experimentally. 18

Animation of Dynamic Legged Locomotion n Controlling body attitude: q q Estimate the torque at the hip, given: n Desired angle – fd. n Current angle – f. Use PD control: n t – hip torque. n kf , bf – gains. 19

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

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

From hopper to biped 22

Quadruped n n n 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 q q n diagonal for trotting. front and rear for bounding. Video 23

Animation of Dynamic Legged Locomotion n What we have? q n Realistic motions for hopping robots. How to extend them to virtual humans? [Hodgins 95] q q Use the same FSM. The control is again divided into three parts (forward velocity, balance, vertical velocity). 24

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

Animating human athletics n What is new ? q q q n 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 ([Hodgins 95]). (video 1, video 2, video 3) 26

Walking vs. Running cycle n How is walking different ? q q q Has double-support phase. No flight phase. The legs are not springy (no energy is saved in them). Left Right Walking cycle Left Right n [Yin, Panne 07] present control system for walking and running based on PCG: q q q Very small number of parameters. Different gaits (including sideways and backwards walking). Can handle pushes in all directions, unexpected steps and slopes. (Video) 27

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

Ways to generate controllers automatically n n 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: q q SAN – Sensor-Actuator Networks [Panne, Fiume 93]. PSM – Parametrized State Machines [Panne 96]. 29

SAN – Sensor-Actuator Networks n The controller is a directed network (similar to neural network): q q q 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. 30

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

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

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

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

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

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

A higher level system with multiple controllers n [Faloutsos 01] n Motivation: q q Ability to integrate various behaviors in the same system. Response to external forces and switching between behaviors: n n n Falling Getting up Walking again. 37

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

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

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

A higher level system with multiple controllers n n The hardest problem is determining the preconditions for each controller. Can be solved efficiently by off-line learning. q q q 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). 41

Summary n Controllers so far: q q n Produce realistic animation in automated way. Improved flexibility and diversity of motions. What else can be done: q q q 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. 42

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

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