Scaling Fixed Robots Using Brian Mechanisms

This article is about a new class of mechanisms called Brian Mechanisms. For progress on the work of building the worlds cheapest robots using Brian Mechanisms, read the articles here

In the search for an affordable and scalable design of an agricultural robot, the design has been established of a mechanism for turning both fixed as well as mobile robots into compound robots, thereby (1) scaling up fixed robots and (2) increasing the precision of mobile robots, as well as (3) reducing the complexity currently involved in the positioning systems of mobile robots. The new mechanism, called Brian Mechanism, can be used to build robots for the agricultural and construction industrial which don't require high precision. But it is also theoretically possible to build large scale cartesian robots for use in 3D printers, laser cutters and other application that require high precision. It is left to the imagination of the creative and inventive minds to conceive many other uses for the mechanism.

Based on the degree of mobility, robots are traditionally classified into two classes: (1) fixed robots and (2) mobile robot. Fixed robots do not move with respect to certain components in their environment while mobile robots travel in their environments by using various means of locomotion. But there is yet another new class of robots called compound robots. Compound robots integrates the functions of a mobile robot and a fixed robot. Fixed robots mainly replace the functions of human arms and hands; while mobile robots, namely, replace the walking functions of human legs and feet. The compound robot uses both hands and feet, combining two functions. This way it has, with a few trade-offs here and there, the advantages of fixed robots as well as those of mobile robots.

Fixed robots are mainly designed for high endurance, speed, and precision, while mobile robots are bulit for scalability. By scale we mean not the number of robot working together, but rather the size of its workspace. Combining the two we get the precision of fixed robots as well as the workspace scalability of mobile robots into our compound robots.

Mobile robots can also be grouped into two categories: guided (AGVs) and autonomous(AMRs). AGVs rely on guidance devices that allow them to travel a pre-defined navigation route in relatively controlled space, while AMRs are capable of navigating an uncontrolled environment without the need for physical or electro-mechanical guidance devices. The components of a mobile robot are a controller, sensors, actuators and power system. The sensor systems required for AMRs such as self driving cars are quite complicated and therefore quite expensive. AGVs have far less complicated sensor systems while fixed robots can work without position feedback sensors since a number of them are cable of being controlled by open loop systems.

Brian mechanisms, to a large degree take away the need for guidance systems for AGVs as well as the complicated sensor systems for AMRs while increasing the area over which fixed robots can work. The result is a means which, it is suggested, provides the cheapest means of producing large scale robots.

The Concept

The Brian Mechanism concept is this: a fixed robot carries a mobile robot. The workspace/environment of the fixed robot is the mobile robot while that of the mobile robot is the world. When the fixed robot needs to work an area greater than its workspace, the mobile robot carries it to the area adjacent to its current workspace of the same size as its current workspace. The mobile robot moves over a fixed distance each time. The motion and position of the fixed robot does not depend upon that of the mobile robot. That is, the position of the fixed robot is only a function of that of the mobile robot in as far as the position of its workspace is determined by the mobile robot. For instance, the position in the y direction can be calculated as:

Where
n is the number of times the mobile robot has moved.
L is the distance by which the mobile robot moves
yf is the position of the fixed robot end effector in its workspace.

Comparison with Wheels and Walking Mechanisms

Brian Mechanisms can be made from wheels, tracks or legs. Therefore it is easy to confuse them with any of these, especially with walking mechanisms. But the difference lies in the way in which the fixed robot/payload is moved. When using wheels or tracks, the displacement of the payload is equal to that of wheel axles. For example, a person sitting in a car has the same displacement from some location as that of the wheel axles. If the tires spin and the vehicles does not move, the person also does not move. That is:

Where
S_p - is the displacement of the payload and
S_w - is the displacement of the wheel axel.

The same is true for tracks. Walking mechanisms also have the displacement of their payloads equal to the amount by which the joint of the leg to the payload has been displaced.

But its different in Brian Mechanisms. The position of a person walking in a car from a point of reference outside the car depends not entirely on the posision of the car. This is the case in Brian Mechanisms.

But there is another difference. A car's position is continuous making it, as has been mentioned under AGVs difficult to locate. The position of the mobile part of Brian Mechanisms is moved by discrete steps as opposed to the continuous displacement of the car. At any point t:

This is the mechanism provided by the mechanism for locating the mobile robot in its environment. While not entirely eliminating errors, it reduces the error significantly compared to normal wheels or tracks.

In summary:

1. Mobile robot part of Brian mechanisms have discrete position while normal mobile robots have continuous positions.
2. The position of the payload of Brian mechanisms is only partially dependent on the position of the mobile robot part. This point is capture in point 1 above.

A Practical example

The video shows an implementations of the Brian Mechanism using a chain driven mechanism.