Loading in 5 sec....

Compare the forward kinematics of a nonholonomic robot to those of a holonomic robot.PowerPoint Presentation

Compare the forward kinematics of a nonholonomic robot to those of a holonomic robot.

- By
**jana** - Follow User

- 377 Views
- Updated On :

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”.

Related searches for Lectures 5

Download Presentation
## PowerPoint Slideshow about 'Lectures 5' - jana

**An Image/Link below is provided (as is) to download presentation**

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript

### Compare the forward kinematics of a nonholonomic robot to those of a holonomic robot.

### Bird’s eye view of axle. connects the wheelchair’s two wheels.

### Bird’s eye view of axle. connects the wheelchair’s two wheels.

### Z-Y-X Euler Angles achieve absent humans’ ability of object recognition. The “correspondence problem”.

### Z-Y-X Euler Angles achieve absent humans’ ability of object recognition. The “correspondence problem”.

### Z-Y-X Euler Angles achieve absent humans’ ability of object recognition. The “correspondence problem”.

Note the rotation matrix between {A} and {B’} express all nine elements of the rotation matrix that defines the relative orientations of these frames?

Note the rotation matrix between {A} and {B’} express all nine elements of the rotation matrix that defines the relative orientations of these frames?

Note that our textbook Craig will provide those of a holonomic robot.

a very useful and general way to

develop the forward kinematics of a

Holonomic robot.

E those of a holonomic robot.P

AP

Recall, that a those of a holonomic robot.holonomic robot will (kinematically) “repeat”.

Recall, that a those of a holonomic robot.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.

Recall, that a those of a holonomic robot.holonomic robot will (kinematically) “repeat”.

However there is a subtle distinction between holonomic robots and nonholonomic robots that can be appreciated with this animation.

The nonholonomic robot will not repeat by merely returning the internal angles of rotation to their previous values.

What is the nature of the forward kinematics of this nonholonomic robot?

Let’s consider a “bird’s eye view” of the axis that connects the wheelchair’s two wheels.

Development of nonholonomic equations for numerical integration.

Imperfect tracking won’t affect the holonomic robot’s terminal pose.

Imperfect tracking won’t affect the holonomic robot’s terminal pose.

Imperfect tracking won’t affect the holonomic robot’s terminal pose.

Imperfect tracking won’t affect the holonomic robot’s terminal pose.

But imperfect tracking has a cumulative effect on the nonholonomic robot.

But imperfect tracking has a cumulative effect on the nonholonomic robot.

But imperfect tracking has a cumulative effect on the nonholonomic robot.

But imperfect tracking has a cumulative effect on the nonholonomic robot.

For all their disadvantages, nonholonomic, wheeled robots offer some distinct advantages.

For all their disadvantages, nonholonomic, wheeled robots offer some distinct advantages.

The wheelchair can get away with a offer some distinct three-degree-of-freedom movement using just two servomechanisms, one for each wheel, precisely because it is a nonholonomic system.

How will we control such a robot if teach/repeat, the standard for holonomic robots, cannot be applied?

One possibility is to track a line in the floor. standard for holonomic robots, cannot be applied?

One possibility is to track a line in the floor. But this standard for holonomic robots, cannot be applied?can get messy!

Also tracking of a physical line doesn’t permit deviation from the path in the event of an obstacle.

And line tracking doesn’t permit pivoting in tight spaces. from the path in the event of an obstacle.

You could track a from the path in the event of an obstacle.wall instead.

- Many early developments of this kind.
- Shakey
- The Kent floor-cleaning robot

Alternatively, create sensor-based autonomy and reasoning, such as “simultaneous localization and mapping”, SLAM.

So far SLAM methods have not produced much fruit. Hard to achieve absent humans’ ability of object recognition. The “correspondence problem”.

Random motion. achieve absent humans’ ability of object recognition. The “correspondence problem”.

Intelligent achieve absent humans’ ability of object recognition. The “correspondence problem”. random motion.

Compare Jacobians for our two two-degree-of-freedom robots. achieve absent humans’ ability of object recognition. The “correspondence problem”.

E achieve absent humans’ ability of object recognition. The “correspondence problem”.P

AP

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

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

Consider the {A} and {B} frames shown below. achieve absent humans’ ability of object recognition. The “correspondence problem”.

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?

Beginning with the {A} frame, rotate a positive express all nine elements of the rotation matrix that defines the relative orientations of these frames?a about the ZA axis.

Call this new frame {B’} express all nine elements of the rotation matrix that defines the relative orientations of these frames?

Note the rotation matrix between {A} and {B’} express all nine elements of the rotation matrix that defines the relative orientations of these frames?

Note the rotation matrix between {A} and {B’} express all nine elements of the rotation matrix that defines the relative orientations of these frames?

Note the rotation matrix between {A} and {B’} express all nine elements of the rotation matrix that defines the relative orientations of these frames?

Next consider just the intermediate {B’} frame. express all nine elements of the rotation matrix that defines the relative orientations of these frames?

Consider a positive rotation express all nine elements of the rotation matrix that defines the relative orientations of these frames?b about the YB’ axis.

Suppose the second rotation express all nine elements of the rotation matrix that defines the relative orientations of these frames?b had instead occurred about the original YA axis?

Suppose the second rotation express all nine elements of the rotation matrix that defines the relative orientations of these frames?b had instead occurred about the original YA axis?

Suppose the second rotation had instead occurred about the original YA axis?

Returning to the Z-Y-X Euler Angles … original Y

… take the last rotation original Yg to be about the XB” axis.

Download Presentation

Connecting to Server..