By not grasping, a simple robot with few degrees-of-freedom can control an object with more degrees-of-freedom by exploiting dynamic effects, such as centrifugal and Coriolis forces. These extra degrees-of-freedom come from manipulation phases such as controlled slipping and rolling. In contrast, a robot that carries an object with a firm grasp requires as many degrees-of-freedom as those of the object it wishes to control.
We have shown that a one-degree-of-freedom revolute robot, with just a two-dimensional state space, can take a planar object to a six-dimensional subset of its six-dimensional state space (linear position and velocity, angle and angular velocity).
Experiments with a one joint robot
Experiments in dynamic rolling manipulation
Experiments with an underactuated robot
Experiments in batting and juggling
Other videos: Parts feeding
The videos below show some dynamic tasks that were planned automatically using a dynamic manipulation planner that we have developed. The plans have been implemented on a one-degree-of-freedom robot powered by an NSK direct-drive motor.
The manipulator snatches the object from the table by accelerating
into it, causing it to roll back onto the palm of the manipulator and
come to rest in a stable equilibrium. After snatching the object,
the manipulator throws and catches it to rotate it by 90 degrees on
the palm. Quicktime, 990K
The manipulator dynamically rolls a part to a new stable face. Quicktime,
662K
The manipulator causes the part to begin rolling before throwing it,
much like a pitcher allows a ball to roll off the fingers. This allows
the arm to impart an angular velocity to the part different than that
of the arm at the release.
In the first example (Quicktime,
2305K), the object rotates a quarter revolution clockwise and lands
in a different location.
In the second example
(Quicktime, 276K), the object rotates a half
revolution clockwise and lands with a final location identical to the
initial.
Here the task is to roll the disk from one side of the "hand" to the
other side. The hand is a one joint robot, and the disk is floating
on an air table inclined at 5 degrees, giving effective gravity of
approximately 0.09 g. A trajectory is planned offline using a rolling
simulation, and the trajectory is stabilized using vision
feedback. This task is called a "butterfly," after the juggler's
skill of rolling a ball from the palm of the hand to the back of
the hand. Quicktime, 588K
In 2006, a student group in my ME 333 Introduction to Mechatronics
course revisited the butterfly problem and built their own version.
Their version used a metal ball rolling on two wires as the
wiper of a potentiometer to determine the ball's position on the
butterfly. A much more elegant solution than using vision!
A picture and video are shown at right. They also included a manual
mode to allow a user to try to accomplish the motion. You can
see their project webpage
here.
Students of Giuseppe Oriolo at the University of Rome "La Sapienza" also built their own butterfly, which you can see here.
Here the task is to simply balance the disk at the top of the hand.
We found that by giving the controller high gains, it's possible
to make the disk spin while the hand looks essentially motionless.
(Vibrations of the hand cause the disk to bounce.) This "breaks"
the holonomic rolling constraint between the disk and hand.
Quicktime, 3404K
This video demonstrates collision-free trajectory planning for an
underactuated robot. This robot has three degrees-of-freedom,
operates in a horizontal plane, and the third joint is passive. This
robot can be shown to be small-time locally controllable -- it can
accomplish essentially any pick-and-place task that a fully actuated
robot could. Naturally, motion planning and control are much harder.
The video demonstrates collision-free trajectory planning and feedback
control for this robot, which we believe is the first working
implementation for an underactuated manipulator.
Quicktime, 1485K
This video shows a repetitive juggling task on Flatland. An overhead
vision system tracks the puck, and the controller uses the vision
data and a predictive impact model to continually update its estimate
of the best possible bat to hit the puck to the goal state.
The updates are generated using fast nonlinear optimization.
The result is stable, robust juggling to a fixed point. The air
table here is tilted 5 degrees from horizontal, slowing down
motions by a factor of 3.4 from full gravity.
Quicktime, 2136K