compare the forward kinematics of a nonholonomic robot to those of a holonomic robot
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Compare the forward kinematics of a nonholonomic robot to those of a holonomic robot. Note that our textbook Craig will provide a very useful and general way to develop the forward kinematics of a Holonomic robot. E P A P Recall, that a holonomic robot will (kinematically) “repeat”.

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slide2
Note that our textbook Craig will provide

a very useful and general way to

develop the forward kinematics of a

Holonomic robot.

slide3
EP

AP

recall that a holonomic robot will kinematically repeat5
Recall, that a holonomic robot will (kinematically) “repeat”.
  • In general, by returning the internal, servo-controlled angles to earlier, taught values, you will bring about a return of the borne load to its corresponding location in space.
slide7
However there is a subtle distinction between holonomic robots and nonholonomic robots that can be appreciated with this animation.
slide8
The nonholonomic robot will not repeat by merely returning the internal angles of rotation to their previous values.
slide10
Let’s consider a “bird’s eye view” of the axis that connects the wheelchair’s two wheels.
slide25
The wheelchair can get away with a three-degree-of-freedom movement using just two servomechanisms, one for each wheel, precisely because it is a nonholonomic system.
slide26
How will we control such a robot if teach/repeat, the standard for holonomic robots, cannot be applied?
also tracking of a physical line doesn t permit deviation from the path in the event of an obstacle
Also tracking of a physical line doesn’t permit deviation from the path in the event of an obstacle.
you could track a wall instead
You could track a wall instead.
  • Many early developments of this kind.
  • Shakey
  • The Kent floor-cleaning robot
slide32
Alternatively, create sensor-based autonomy and reasoning, such as “simultaneous localization and mapping”, SLAM.
slide33
So far SLAM methods have not produced much fruit. Hard to achieve absent humans’ ability of object recognition. The “correspondence problem”.
slide46
EP

AP

z y x euler angles48

Z-Y-X Euler Angles

- Just three numbers are needed to specify the orientation of one set of axes relative to another.

z y x euler angles49

Z-Y-X Euler Angles

Just three numbers are needed to specify the orientation of one set of axes relative to another.

One possible set of these numbers is the Z-Y-X Euler angles

slide51
How can we define just three quantities from which we can express all nine elements of the rotation matrix that defines the relative orientations of these frames?
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