A Survey Of Robotic Juggling And Dynamic Manipulation

by Matt Mason

This is a somewhat cursory survey of work in robotic juggling. I interpret juggling broadly, to include pretty much any machine that controls the motions of flying objects by catching, throwing, or hitting. Thus running is a kind of self-juggling, and ping-pong is adversarial juggling.

I. Shannon's machine

Claude Shannon seems to be generally credited with building the first juggling machine. It juggles three balls using two hands. Shannon has not described the machine in print, but see [11] for a description of Shannon's machine and a variant machine that juggles five balls. Shannon's machine consists of two cups, padded with an energy-absorbing material, mounted at either end of a roughly horizontal rocker arm. The arm oscillates about its center. Each cup is mounted so that at the zenith of its travel, the ball rolls out of the cup, falls to a drumhead below, and bounces into the opposite cup, as that cup nears its nadir. The throwing motion is simple, because the hand does not have to produce precisely the desired motion of the ball, nor is there an elaborate mechanism to release the ball at precisely the right time.

II. Raibert's running machines [8, 5]

Hopping and running can also be viewed as a form of batting. Marc Raibert started by building a single-legged running machine that works in two-dimensions, then extended the principles to a variety of machines using 1, 2, or 4 legs, in 2 or 3 dimensions. Although Raibert and his collaborators used sophisticated dynamic models in the analysis and design stages, the machines used simple feedback control systems. The machines performed a variety of running gaits (trotting, pacing, bounding), and also performed some gymnastic maneuvers: aerials and flips.

III. Andersson's ping-pong machine [3]

Russ Andersson built a system to play ping-pong at Bell Labs. (Robots play a modified form of ping-pong: The table dimensions are smaller, the net is higher, and the ball must pass through square wire frames at each end of the table.) There were multiple cameras to track the ball in three dimensions. A small industrial arm wielded a paddle with an extra-long handle. It was good enough to beat me, although I think I could have beaten it given enough time with it.

The robot's planner incorporated a model of ball flight and impact, and used these models to plan a nominal trajectory for the paddle. This nominal trajectory was then refined by iterated simulations, with concurrent adjustment of goals as better estimates of the ball's motion became available.

IV. Koditschek's juggling machines [4, 9]

Batting means generating a single collision between effector and projectile in order to redirect the projectile. It combines catching and throwing in a single collision. Buhler and Koditschek [4] describe a machine using a single bar pivoting about its center to bat pucks sliding on an inclined plane. The goal is to achieve a cyclic bouncing of the puck, with stable height, at a stable location along the bar. Buhler and Koditschek found a very simple feedback law that will stabilize one or two bouncing pucks simultaneously. Rizzi and Koditschek [9] describe a machine that extends the principles to three dimensions, batting two ping-pong balls in columns. The feedback law has terms to keep the ball in the right location, to maintain the right height, and to keep the two balls out of phase. It bats the two balls in columns.

V. Atkeson's machines [1, 2, 11]

Chris Atkeson and his group have developed a number of juggling machines, and use them to explore issues in machine learning. Aboaf, Atkeson, and Reinkensmeyer [2] describe a robot that iteratively improves its throwing motion to throw a ball more accurately. Aboaf, Drucker, and Atkeson [2] describe a system that bats a single ball in three dimensions. It also improves with experience.

Schaal, Atkeson, and Botros [11] built a special devil sticking robot. The problem is simplified by mounting the devil stick so that it has only three degrees of freedom, rather than the usual six. A long rod is attached perpendicular to the center of the devil stick. The other end of the long rod is attached to ground by a ball and socket joint. In effect the devil stick is confined to the surface of a sphere.

The machine has two `effector sticks' mounted by springy joints to a `torso'. The effector stick contacts the devil stick at its center of percussion, halting the effector stick and storing its energy momentarily at a springy joint. The collision is effectively inelastic, resulting in a catch. The energy is then transferred back to the devil stick, throwing it to the other effector stick.

The same paper describes other juggling machines, including a machine similar to the Shannon juggler, that bounce-juggles five balls.

VI. Others

This just scratches the surface. There are many other machines that demonstrate dynamic walking, or other dynamic tasks. For example, Hirofumi Miura at the University of Tokyo has built several small walking robots with a motion that resembles a person walking with stilts. He also has constructed robots that can play a Japanese ball-in-cup (kendama) game and spin a top (koma) by throwing it with a string [6].

Tad McGeer [13] built a walking machine with a gait resembling a human's, including the knees. The machines does not have motors, sensors, or computers. It was designed so that the intrinsic dynamic behavior produces stable walking patterns. Note the similarity to Shannon's juggler.

Sakaguchi, Masutani, and Miyazaki [10, 7] obtain robot juggling of one or two balls with a single robot hand. The hand makes an elliptical motion, modified by the perceived path of a ball. The hand is a simple funnel, and the balls appear to be very soft. They also describe a robot to play the ball-in-cup game.

Slotine [12] has programmed a robot to throw and catch balls. Using stereo vision to predict the ball's path, the arm very quickly matches velocities while the fingers close on the ball.

References

[1] E. W. Aboaf, C. G. Atkeson, and D. J. Reinkensmeyer.  1987.
    Task-level robot learning:  Ball throwing.
    A.I. Memo 1006, Massachusetts Institute of Technology.

[2] E. W. Aboaf, S. M. Drucker, and C. G. Atkeson.  1989.  
    Task-level robot learning: Juggling a tennis ball more accurately.
    Proceedings 1989 IEEE Int Conf Robotics and Automation, pages 1290--1295,
    Scottsdale AZ.

[3] R. L. Andersson.  1989.
    Understanding and applying a robot ping-pong player's expert
    controller. 
    Proceedings 1989 IEEE Int Conf Robotics and
    Automation, pages 1284--1289, Scottsdale AZ. 

[4] M. Buhler and D. E. Koditschek.  1990.
    From stable to chaotic juggling: Theory, simulation, and experiments. 
    Proceedings 1990 IEEE Int Conf Robotics and
    Automation, pages 1976--1981, Cincinnati OH.

[5] J. K. Hodgins and M. H. Raibert.  1990.
    Biped gymnastics.
    Int J Robotics Research, 9(2):115--132.

[6] H. Miura.  Private communication.  
    See also H. Miura and I. Shimoyama,
    "Dynamical Walk of Biped Locomotion", 
    in Robotics Research: The First International Symposium.
    Cambridge:  MIT Press.

[7] F. Miyazaki.  1992.  
    `Motion Planning and Control for a Robot Performer' (videotape).

[8] M. H. Raibert.  1986.  
    Legged Robots That Balance. Cambridge: MIT Press.

[9] A. A. Rizzi and D. E. Koditschek. 1992.
    Progress in spatial robot juggling.
    Proceedings 1992 IEEE Int Conf Robotics and Automation,
    pages 775--780, Nice, France.

[10] T. Sakaguchi, Y. Masutani, and F. Miyazaki.  1991.  
    A study on juggling task.  
    IEEE/RSJ International Workshop on Intelligent
    Robots and Systems IROS '91, Osaka, Japan, pages 1418--1423.

[11] S. Schaal, C. G. Atkeson, and S. Botros.  1992.  
    What should be learned?  
    Proceedings Seventh Yale Workshop on Adaptive and
    Learning Systems, pages 199--204.

[12] J. Slotine.  1992.  
    `Vision Guided Motion Control'  (videotape).

[13] T. McGeer.  1990. 
    Passive dynamic walking.  
    Int J Robotics Research, 9(2):62--82.

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