How Robots Use Maths to Move

Summary

This video script details the creation of a simple robot arm project with an inverse kinematic model, designed to move a ping pong ball through a contraption. The project uses basic servos, 3D-printed parts, and an Arduino Uno for control. It demonstrates the arm's ability to move in a straight line in 2D space and includes a gripper for ball manipulation. The script also discusses the use of potentiometers for analog input and the 'ramp' library for smooth motion interpolation. The project is part of a larger 'Great Ball Contraption' and is shared as open-source on GitHub.

Takeaways

• 🤖 The video discusses the application of inverse kinematics in robotics, which is essential for positioning a robot's end effector in a specific location within a known coordinate system.
• 📐 The presenter has used inverse kinematics in robot dog projects to coordinate the feet for movement in three dimensions, allowing for translation and rotation.
• 🔧 The project involves a simple robot arm with a basic inverse kinematic model, which is part of a larger 'Great Ball Contraption' project demonstrating science and engineering concepts.
• 🛠️ The robot's base consists of a sliding axis with V-wheels and a frame for stability, using drop-in T-nuts for easy assembly.
• 🔩 The robot arm uses basic servos with metal brackets for easy mounting, creating a limb with multiple joints that can be controlled via a servo PWM signal.
• 🔄 The arm includes a linear axis for shoulder movement, an elbow joint, and a gripper at the end controlled by another servo, designed to pick up and move ping pong balls.
• 🔋 A 7.4-volt 2-cell LiPo battery powers the servos and a DC motor for the linear axis, managed by an L298 motor driver.
• 📊 The inverse kinematic model for the robot is simple, suitable for an 8-bit Arduino Uno, and involves calculating joint positions based on the desired end effector position.
• 📐 The arm's design uses a triangle with two equal sides, simplifying the math for calculating joint angles using Pythagoras' theorem.
• 📊 The video includes a demonstration of the arm's movement in a straight line controlled by potentiometers, showing the effectiveness of the inverse kinematics model.
• 💻 The project's code and CAD files are open source and available on GitHub for modification and inspiration for other projects.

Q & A

What is the purpose of an inverse kinematic model in robotics?

An inverse kinematic model in robotics is used to calculate the joint positions required to place the end effector, such as a robot's foot, at a specific point in a known coordinate system.

How does the inverse kinematic model enable a robot to move its feet in a coordinated manner?

The model allows the robot's feet to move from point A to point B in a straight line by calculating the joint positions at each waypoint between the two positions, enabling coordinated movement in three axes of translation and rotation.

What is the 'Great Ball Contraption' project mentioned in the script?

The 'Great Ball Contraption' is an ongoing project that involves creating a series of machines to pass ping pong balls from one stage to another, demonstrating various science and engineering concepts.

What materials and components are used for the main base of the robot in the project?

The main base of the robot consists of a simple sliding axis with V wheels attached to a 3D print using M5 bolts and lock nuts, with the wheels fitted with bearings and spacers for smooth rotation.

How are the servos used in the robot arm project mounted and connected?

The servos are mounted using metal brackets and connected by screwing them onto 3D prints with self-tapping screws, allowing for easy assembly of the robot arm's multiple joints.

What role does the servo mounted on top of the first servo play in the robot arm?

The servo mounted on top of the first servo provides an additional mechanical stage to the robot arm, functioning as the shoulder joint, which, along with the elbow joint, allows for a wide range of positions.

What is the function of the gripper's fingers and how are they constructed?

The gripper's fingers are 3D printed and consist of two parallel plates that are spaced apart and screwed together to grip the ping pong balls. They are actuated by a servo that pulls strings attached to the plates to open and close the gripper's jaw.

What is the computational requirement for the kinematic model of the robot arm?

The kinematic model for the robot arm is simple enough to be controlled by an 8-bit Arduino Uno, which calculates the necessary joint positions based on the desired end effector position.

How is the linear sliding axis of the robot arm powered and controlled?

The linear sliding axis is powered by a 7.4-volt 2-cell LiPo battery, which provides sufficient current to operate the servos and the DC motor. The motor is controlled using an L298 motor driver and an encoder for precise movement.

What modifications were made to the robot arm to ensure the gripper does not crush the ping pong balls?

An elastic band was used to pull the gripper fingers together for gripping the ping pong balls, and the gripper activation servo was adjusted to ensure the fingers move freely and do not apply excessive force.

How does the Arduino ramp library help in making the robot arm's motion smoother?

The Arduino ramp library allows for interpolation between positions, enabling the servos to move at a controlled speed and reach their target positions smoothly over a specified time period.

What is the final function of the robot arm in the 'Great Ball Contraption' project?

The robot arm is programmed to move through set motions using the kinematic model to pick up ping pong balls at a sensor-triggered ramp, transport them to the other end, and drop them into the next stage of the contraption.

Outlines

00:00

🤖 Introduction to Inverse Kinematics and Robot Arm Design

The script introduces the concept of inverse kinematics in robotics, which is essential for calculating joint positions to achieve a desired end-effector position in a known coordinate system. The speaker discusses their experience with inverse kinematics in robot dog projects and presents a new project involving a simple robot arm with an inverse kinematic model. The robot arm is part of a larger 'Great Ball Contraption' project that demonstrates various scientific and engineering concepts. The base of the robot consists of a sliding axis with V-wheels and a frame for stability. The arm itself is constructed using servos with metal brackets for easy assembly, and the project is sponsored by 3D Fuel, which provided the filament for 3D printing components.

05:01

🔧 Building the Robot Arm and Writing Inverse Kinematics Code

The paragraph details the construction of the robot arm, which includes a linear sliding axis, servos for shoulder and elbow movements, and a gripper at the end controlled by another servo. The servos are connected using 3D printed parts and screws, creating a simple yet functional design. The kinematic model is kept basic, requiring only an 8-bit Arduino Uno for control. The script also describes the process of writing code for the inverse kinematics, which involves calculating joint positions based on the arm's length and desired end-effector position. The use of trigonometry and potentiometers for analog input is explained, allowing the arm to move in a straight line along one axis. The code and CAD files for the project will be open-sourced on GitHub.

10:02

📈 Refining Motion Control with Arduino Ramp Library

This section discusses the refinement of the robot arm's motion using the Arduino Ramp library, which provides smooth interpolation between positions. The script explains the initial jerkiness of the servos' motion and how the Ramp library helps to create a smoother movement. The library's example code is used to demonstrate a linear rise in values, which is applied to both the z and x positions of the arm. The result is a more controlled and fluid motion that can be adjusted by varying the interpolation time. The script also mentions the use of a sensor to detect the presence of balls and trigger a series of motions to pick up and pass the balls along the contraption.

15:11

🎥 Finalizing the Robot Arm and Future Enhancements

The final paragraph wraps up the project by showing the robot arm in action, picking up balls and moving them to the next stage of the 'Great Ball Contraption'. The script describes the safeguards in the code to ensure the arm completes one cycle before being triggered again, allowing it to continue picking up balls until the ramp is empty. The speaker expresses satisfaction with the functional aspect of the project and suggests future enhancements, such as adding LED strips to visually represent the inputs to the axis as the arm moves. The script concludes by inviting viewers to like, subscribe, and support the channel through Patreon or YouTube membership, with links provided in the video description.

Keywords

💡Inverse Kinematics

Inverse kinematics is a method used in robotics to determine the joint parameters required to position the end effector (like a robot's hand or foot) at a specific location in space. It's crucial for tasks that require precise movements. In the video, the creator uses inverse kinematics to control a robot arm, enabling it to move its 'feet' or end effectors to designated points in a coordinated manner, which is essential for the robot's movement in 3D space.

💡End Effector

The end effector is the terminal component of a robot's arm that interacts with the environment to perform tasks such as grasping, moving, or manipulating objects. In the context of the video, the end effector is the gripper at the end of the robot arm designed to pick up ping pong balls, demonstrating the practical application of robotic limbs in a specific task.

💡Coordinate System

A coordinate system is a well-ordered set of mathematical rules for assigning a pair of numbers, known as coordinates, to every point. In robotics, a known coordinate system is used to define positions for the robot to move to or interact with. The video script mentions calculating joint positions to place the end effector at specific points within a known coordinate system, which is fundamental to the operation of the robot arm.

💡Robot Dog Projects

Robot dog projects refer to the development and construction of robotic mechanisms that mimic the movement and behavior of dogs. In the video, the creator mentions using inverse kinematic models in multiple robot dog projects, which allows the robot's legs to move in a lifelike manner, enhancing the robot's ability to navigate and perform tasks in three dimensions.

💡Great Ball Contraption

The Great Ball Contraption is an ongoing project mentioned in the video that involves creating a series of machines to pass ping pong balls from one stage to another. Each stage demonstrates different science and engineering concepts. The robot arm designed in the video is intended to be a part of this contraption, showcasing the practical integration of robotics in a larger, interactive system.

💡Servo PWM Signal

A servo PWM (Pulse Width Modulation) signal is a type of control signal used to command the position of a servo motor. In the video, the servos used in the robot arm operate with a servo PWM signal, which makes them easy to control for precise movements. The servos are mounted with metal brackets to facilitate the assembly of the robot's limbs with multiple joints.

💡Gripper

A gripper is a mechanical device that is used to grasp, hold, or move objects. In the context of the video, the gripper is a crucial part of the robot arm, designed with 3D printed fingers that can open and close to pick up and hold ping pong balls. The gripper's operation is controlled by a servo, demonstrating the application of robotics in manipulating objects.

💡Arduino Uno

The Arduino Uno is a microcontroller board based on the ATmega328P. It is widely used in robotics and other DIY projects for its ease of use and versatility. In the video, an Arduino Uno is employed to control the servos and the overall movement of the robot arm, highlighting its role in managing the inverse kinematics model.

💡L298 Motor Driver

The L298 is a dual full-bridge driver designed to drive inductive loads, such as relays, solenoids, DC, and stepping motors. In the video, an L298 motor driver is used to power the motor for the linear axis of the robot, indicating its importance in enabling the robot's movement along a straight path.

💡Ramp Library

The Ramp library is an Arduino library that allows for smooth motion control by ramping the speed of motors or servos over time. In the video, the creator uses the Ramp library to make the robot arm's movements smoother by interpolating between positions over a set amount of time, improving the overall functionality and visual appeal of the robot's motion.

💡Potentiometers

Potentiometers are electronic components that provide a variable resistance that can be adjusted manually. In the video, the creator uses potentiometers as an analog input to control the movement of the robot arm along one axis, demonstrating a simple method for adjusting the position of the arm and testing the inverse kinematics model.

Highlights

Inverse kinematic models enable robots to calculate joint positions for placing end effectors at specific coordinates.

The speaker has applied inverse kinematics in robot dog projects for coordinated multi-axis movement.

A simple robot arm project with an inverse kinematic model is part of the 'Great Ball Contraption', demonstrating scientific and engineering concepts.

3D Fuel provided filament for the project, showcasing the importance of materials in 3D printing.

The robot's base consists of a sliding axis with V wheels and a sturdy frame for stability.

Basic servos with metal brackets are used for the robot arm, allowing for easy assembly and control.

The robot arm design includes a shoulder and elbow joint for a wide range of motion.

A gripper with 3D printed fingers and a servo-activated jaw is designed to pick up ping pong balls.

An 8-bit Arduino Uno is sufficient to control the simple kinematic model of the robot arm.

A 7.4V 2-cell LiPo battery powers the servos and the DC motor for the linear axis.

The L298 motor driver and an encoder are used for smooth motion control of the linear axis.

Elastic bands and strings are used for the gripper's compliant mechanism to hold ping pong balls.

Trigonometry and Pythagoras theorem are applied in the inverse kinematic calculations.

Arduino code is used to convert mathematical solutions into servo control signals.

Potentiometers provide an analog input for testing the arm's motion in a straight line.

The speaker's approach to inverse kinematics simplifies calculations for a two-link arm.

PCBWay is highlighted for their PCB manufacturing and assembly services.

The robot arm's motion is tested for smoothness using the Arduino Ramp library.

A sensor is used to detect the presence of ping pong balls and trigger the gripper.

The robot arm is programmed to move through set motions for the 'Great Ball Contraption'.

The project's code and CAD files are open source and available on GitHub for community use.

LED strips are suggested for visual representation of the robot arm's axis inputs.

The robot arm successfully demonstrates inverse kinematics in a functional and educational manner.

Transcripts

i get many questions about inverse

kinematics for robotics

an inverse kinematic model gives us the

ability to request to position the foot

or end effector of a robot limb at a

specific point in a known coordinate

system

and calculate all the joint positions in

order to place it there

i've used inverse kinematic models in

multiple robot dog projects which allows

the feet to be coordinated so that the

robot's body can move in three axis of

translation and three axis of rotation

this allows us to move the robot's foot

from point a to point b

in a straight line by visiting all the

waypoints between the two positions one

after the other

and calculating the inverse kinematics

at each position

so for this video i thought i'd make a

simple robot arm project with a very

simple inverse kinematic model and also

make this part of the great ball

contraption

this is an ongoing project built in

multiple parts which passes ping pong

balls along from one stage to another

by using machines which demonstrate

science and engineering concepts

these will eventually all be linked

together so let's get the core parts of

the design printed and i'll explain the

concept

thanks to 3d fuel for the filament for

this project and lots of other projects

so check out my channel for more 3d

printing projects and check out

3dfuel.com

the main base for the robot is a very

simple sliding axis

so i've got some v wheels and i've

attached those with the right spacing to

a 3d print with some m5 bolts and lock

nuts

these v wheels came fitted with bearings

and also spacers so you can do the bolts

up nice and tight and they still rotate

freely

and that allows the carriage to run on a

piece of v-slot extrusion that's going

to make up the main base for the robot

i've built a frame which goes at each

end of the v-slot to make up four legs

so we've got a nice sturdy base for the

robot

and i'm using drop-in t-nuts here so

that we can attach all the pieces

together

as i have with many other projects so

that makes one linear sliding axis which

we can mount the robot

arm on i'm using fairly basic servos for

this project which work with a servo pwm

signal so they're easy to control

but these particular servos come with

metal brackets so that we can mount them

easily together to make up a limb with

multiple joints

they come with small screws and brackets

so we can just screw those down to the

3d print

and screw the servos on each one has an

arm which has another 3d print attached

to it to make the next section of the

robot

arm and again they come with

self-tapping screws which easily screw

in

and that makes it really easy to connect

the servos together

on top of the first servo is mounted

another servo so i have two mechanical

stages to my robot arm as well as the

linear axis that everything sits on

this gives me a shoulder and an elbow so

we should be able to achieve quite a

wide range of positions

but of course we need a gripper to

actually grip the ping pong balls to

pick them up and move them through the

machine so i fitted another servo

on the very end which is going to

control the end effector

and that one's fitted at right angles i

3d printed some fingers for my gripper

which are two parallel plates

and those are spaced apart and screw

together with countersunk self-tapping

screws

i've used m4 bolts and lock nuts again

to make sure we can tighten those up but

not over tighten them

so the fingers move really freely and

the idea is that servo has two pulleys

on

which is simply just going to pull

strings to open the jaw and they'll be

sprung back together

the kinematic model for this robot is

going to be really simple so we don't

need anything more than an 8-bit arduino

uno to control

all of it the servos i'm using need a

minimum of 6 volts so i'm using a 7.4

volt 2 cell lipo battery

which has got more than enough current

capability to power all of the servos

as well as the dc motor on the sliding

axis

and to power the motor for the linear

axis i'm using an l298 which is a fairly

archaic motor driver but it does two

amps and axis so that should be more

than sufficient

the motor itself is driven with an

encoder hung on the back and i 3d

printed a t5 pulley for it

so this is just going to be a simple

belt drive that goes all the way up and

down the axis

to move the carriage a bit like a 3d

printer bed

or tool head i've used an elastic band

to pull the gripper fingers together so

they can grip the ping-pong ball

and i've also added the strings that go

around those pulleys on the gripper

activation

servo so you can see the whole thing in

operation

obviously with the elastic band there we

can't crush the ping pong ball

and that makes the gripper pretty much

compliant

now the arm's assembled it's time to

write some code for the inverse

kinematic model

and that allows to position the end

effector where it picks up the ball

in a known coordinate system and work

out the joint positions

for the other two or three joints

my approach to this is to write some

code that allows us to enter

the resulting length of the arm and

output the two joint positions

at the shoulder and at the elbow and

you'll have notice

i've made this a triangle with two equal

length sides

for both the upper arm and the lower arm

that makes the maths quite a lot easier

that's a pretty easy type of triangle to

solve but looking at the website

mathsisfun.com we can find out how to

solve various triangles

in this case we know three sides and we

want to find the missing angles

this uses pythagoras theorem which is a

simple piece of maths

i converted that mass into arduino code

which gives us the answers in radians

which then need to be turned into

degrees and into the milliseconds for

the pwm that drives the servo

of course once we've got one angle of

the arm we can easily work out the

others

and since two sides of the triangle are

equal two angles are also

equal i took some potentiometers off a

previous project from the junk pile i'm

only going to use two of them but this

allows me to have an analog

input that allows me to sweep through a

range of values and see if the maths

works

i'm only using one axis to start with

but we should see that the arm moves in

a straight line as i turn the pot

and that straight line should be a 45

degree angle with its origin at the base

joint of the base servo

the reason that it's at 45 degrees is

because that was the default position

for the servos

basically the shoulder axis pointing

straight up and the elbow axis at 90

degrees

i put that offset in the code and now

everything is based off that offset

and that 45 degree angle

now we've taken care of the length of

the arm and that's all dealt with with

the first bit of code

we now want to be able to enter two

other axes to position the arm in at

least 2d

space that can be done with simple

trigonometry though

and the rest of the arm is already dealt

with by the previous piece of code

the trigonometry looks like this cos of

theta the angle at the base

equals the adjacent over the hypotenuse

and so the hypotenuse simply equals the

adjacent

over cos theta that's just one line of

code so that we can work out the arm

length from the two other coordinates

we do need one more piece of simple

trigonometry though so that we can

modify the shoulder angle based on its

new angle

i converted that to degrees and taken

away the existing 45 degree offset

and i've also converted that to servo

pwm which is roughly 11 milliseconds

per degree but before we look at that

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so now i'm using two potentiometers to

control the arm one of them moves the

arm

up and down in a pretty much perfectly

straight line there will be some issues

with servo calibration

here because the pots are probably low

tolerance inside the servo itself that

gives it feedback

so it may not run perfectly linearly but

that looks pretty good for cheap hobby

servos

and some code i wrote on an 8-bit

arduino

the other part causes the arm's reach to

move in another

almost perfectly straight line given the

servo's tolerances

and we can see that both joints are

working together there to move that arm

pretty much in a perfectly straight line

horizontally and vertically

all the code as well as the cad for this

project will be published and you can

find that on github and the link is in

the description to this video

it's open source so feel free to modify

it and do what you like with it or use

it for inspiration in your own projects

the last axis in this project is very

simple because it moves in a straight

line anyway so we don't really need to

do

any math to control it but check out my

previous robot dog projects if you want

to see something more complicated

i've programmed the rover arm to move

through some set motions

using the kinematic model so it moves in

x and z positions

in order and there's three positions in

this sequence

however you'll notice that it's very

jerky because the servos move at full

speed

and also for some moves one servo

doesn't need to move as far

so it gets there first that means we

don't have a very smooth motion

so i'm going to be using the arduino

ramp library from site swap juggler

which is open source and you can find it

on github

it has various parameters but ultimately

allows us to interpolate through

positions from one point to another

and make our motion really smooth the

example code that ships with the ramp

library is pretty simple all we need to

do is my ramp go

give it a value to interpolate 2 and a

time we want to interpolate over

so if we now open the serial plotter we

can see we get a linear rise here

straight from one value to the other

without a step

there are various other responses in

this library as well but for now we're

just going to use the linear one

so now i'm feeding both the z and the x

positions over the ramp library and i'm

feeding them

over the same amount of time so now my

step sequence is allowing those joints

to move over the same amount of time

and the end effector of the robot should

be moving in a perfectly straight line

between them

so this is a much smoother motion and

also we can control how fast it moves by

interpolating each move

over a longer or shorter time if we wish

to do so

but now we need to pick up some balls

and pass them along so the arm can be

part of the great ball contraption

i'm using one of these sensors that i've

used in the past so we can sense when

balls are present and trigger a series

of motions

i made a short ramp to feed the arm

which has the sensor on eventually this

will be fed by a reservoir and a longer

ramp

and that means we can throttle the

amount of balls pass through this stage

and the rest of the great ball

contraption

when it sees a ball present it picks it

up takes it to the other end and drops

it which will take it on to the next

stage

perhaps into the high voltage ball

accelerator that i made last time

if i stack multiple balls in the ramp

i've put various safeguards in the code

that means it finishes one cycle before

being triggered again

so this means it will keep coming round

picking up the balls taking them to the

other end and dropping them

until the ramp is empty in which case it

stops

this

i'm pretty happy with this from a

functional point of view to demonstrate

inverse kinematics what would be great

from an educational and visual point of

view would be to have perhaps two led

strips one vertical

and one horizontal that show the inputs

to the axis

as the robot arm moves so we can show

that what goes in is lines in a straight

line

and what comes out is the rotation of

these joints but for now this is a great

addition to my great ball contraption

look at the other parts in my channel

i'm going to be building a few more and

then stringing them all together

so that balls get passed all the way

around and hopefully back to the

beginning again

if you liked the video don't forget to

like and subscribe for more pieces of

this

more robotics and more open source

designs and you can find all my designs

which are open source on github the

links in the description to this video

so if you'd like to support me through

patreon or youtube channel membership

then those links are in the description

as well and patrons and youtube channel

members get access to all the videos up

to a week early

and sneak peeks and pictures of what's

coming up so you can be involved in all

of that discussion

alright that's all for now

[Music]

you