Discussion of our Many Victorious Battles

Problems we encountered and overcame throughout our project.

One of the things we are very proud of is our use of homework as a resource to make our trajectory as smooth as possible. We incorporated 6-th order polynomials for all x-y-z axis to accomplish this. Therefore we had to solve for 18 unknown coefficients.

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Initial End Effector trajectory:

Trajectory Equations:

Compare this trajectory graph and equations to the one posted in the Results section. It is clear that this is a straight line, hence the shortest path between the End Effector Start position and End Effector End position (on top of the space bar).

As you may discover when solving the 'Final Question', we the Decepticons had to change our initial trajectory due to the our physical body constraints and the fact that the straight line trajectory forced us outside the boundary of our workspace.

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Also, a lot of our trials can be deemed unsuccessful if our home position is incorrectly set. Meaning it is crucial that the home position of the robot (which we are experts at eye balling) be consistent so that when the Matlab code is run the space bar is hit only once to play the music.

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One of our first learning experiences with the hardware was learning to build our own H-bridge (before we acquired industry made ones).

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We were also successful in building both our own circuit and the Bumble Bee's original control box. This was unfortunately not helpful because the control box interfered with the H-Bridges by stopping the Arduino microprocessor from sending signal to the motors.

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Final Exam Question

Part 1)

The toy robot arm is a four-link manipulator with four motors that control the End Effector position. The schematic D-H diagram of the robot with the constraints 0<θ1<2π radians, 0<θ2<π/2, 0<θ3<π/2 and 0<θ4<π/2 is shown below:

Please draw the workspace of this toy robot.

Part 2)Now, suppose the limits of the joint angles of our toy robot are:

-2.35<θ1<2.35 radians, 0<θ2<2.4, -2.4<θ3<2.4, and -0.7<θ4<0.7

The desired trajectory is represented by the following plot:

And the following graphs represent the values of the joint angles that need to be performed by the robot in order to achieve this trajectory.

Do you think the robot can perform this motion (is the trajectory staying within the work space)?

Final Exam Solution

Part 1)

Workspace of robot:
Part 2)

The trajectory is out of the workspace and the robot cannot physically perform this trajectory. This is due to the fact that joint 2 and 3 are out of the range of the joint angle limits.

Results (Matlab Graphs) - From Keyboard to Home Position

Posted are graph results of movements of different parts of the robot with the use of Inverse Kinematics. This set of graphs represents the movement of the robot after it has pressed the space bar and is returning to its original home position.

Final End Effector Position over time(10 sec):

Trajectory Equations for this trajectory follow the same model as those for the initial movement.

Theta (Motor) 1 vs. time:

Theta (Motor) 2 vs. time:

Theta (Motor) 3 vs. time:

Theta (Motor) 4 vs. time:

Results (Matlab Graphs) - Home Postion to Hit Keyboard

Posted are graph results of movements of different parts of the robot with the use of Inverse Kinematics. This set of graphs represents the movement of the robot as it makes its way to the keyboard and pauses right above the space bar.

Final End Effector Position over time(10 sec):

**Notice the Parabolic shape of the End Effector Trajectory (this will be helpful for the final).

Trajectory Equations:

Theta (Motor) 1 vs. time:
Theta (Motor) 2 vs. time:
Theta (Motor) 3 vs. time: Theta (Motor) 4 vs. time:

Videos 2 and 3

Below is master Bumble Bee performing its duties and responsibilities with pride. It is following a smooth continuous trajectory that goes from its home position to entertain itself (playing some tunes) by hitting the space bar. This task not only uses inverse kinematics but many hours of labor.

Task Attempt 1, with Inverse Kinematics (4/19).

Here Master Bumble Bee plays music and returns to its original starting position. This shows control and manipulation of trajectories.

Task Attempt 2, with Inverse Kinematics (4/20).

Video 1

Below is our young Bumble Bee learning its duties without the use of Inverse Kinematics -- a task that is a right of passage for us Decepticons.

Task Attempt without the use of Inverse Kinematics, (4/6).

Block Diagram

The following is our secret war strategy/map( aka our control loop block diagram ). This is how we will destroy the Primes and conquer Planet Earth.

Pictures

Here are photographs of our valiant soldiers in battle. If you think they look beaten up, you should have seen the other guys!


Photo A

A. Pictured here is Bumble Bee in its original box, the way he is born to be.


Photo B

B. Pictured here is Bumble Bee in what we call its 'HOME' Position. Motor 1* is inline with the battery box, and the remaining motors are positioned so that the robot arms are in an 'elbow up' orientation.


Photo C

C. Pictured is our H-bridges connected to the Arduino microprocessor (under the hood stuff).



Photo D

D. This picture shows a malfunctioning Decepticon that is no longer self-aware. It moves without regard to its own limbs (outside of its work space -- physical constraints). This was one of the main issues we encountered when implementing inverse kinematics to move the robot arms. Our initial trajectory and corresponding thetas were resulting in self-hindrance by the robot. This stopped the motors from reaching their end goal and if allowed to continue could result in damage to the motors.


* The motors are labeled 1-5 in sequential order starting with the base motor with is touching the table.

Project Description

Our fearless leader Megatron (Prof G.) put us in charge of wiping Bumble Bee's (our toy robot) memory and have him 'focus on trajectory following with the use of inverse kinematics by integration of differential kinematics, which exercises the many properties of the Jacobian.'

But the Decepticons do not settle for just mind-wiping 'The Good' we go above and beyond what is required of us and that is why Megatron will be pleased with our evolved changes in our objective, which we will present on Friday the 22nd.

Here is a block representation of the tasks that Bumble Bee will perform:

Objectives

We started our project with one goal in mind -- to defeat the Autobots. But as the semester went on we discovered that we neither had the resources or the motivation to bring down Optimus Prime, rather our time would be better served by learning how to operate our humble toy Bumble Bee robot. **

As the Professor may have seen in our Project Proposal, we started off wanting our robot's end effector to follow the trajectory of the initials LT, in honor of our brilliant team member Leo Tse. By doing this we would incorporate what we learned in regards to inverse kinematics and trajectory following. Not only would we be getting first hand experience but we would have to teach ourselves about the Ardiuno microprocessor and how to manipulate it.

However, as the semester went by, we felt our Bumble Bee robot was capable of doing even more -- such as trying to play a song by himself! Our objective for this task is to teach Bumble Bee how to use a computer to play its favorite song. We will compute the inverse kinematics so that Bumble Bee can press the space-bar on the keyboard which will trigger his song to start. Once his song starts, he will return back home and show-off some sweet dance moves.

**Reference made to Transformers

Decepticons

is our group name/project title. Our wonderful group consists of Rajen Kumar (rkumar1@gmail.com), Leo Tse (laiyutse@gmail.com) and Radhika Bhargav (rbhargav7@gmail.com).

Project Title:
Member Names (with emails):
Brief Project Description:
Objectives:
Picture:
Model, including Jacobian:
Block Diagram:
Control Design:
Implementation Notes:
Results: (MATLAB plots)
Discussion: