# 2D Robotic Movement

### 2D Overview

The goal of this semester’s progress was to extend the robotic system from 1D adaptive movement to allow it to move freely on a 2D surface. Doing this provides the system with a number of different types of movement it can use in order to optimize microphone placement. Working with 1 dimensional movement, the robots could only shift sideways and converge/diverge. With 2D movement the robots can physically approach the source, point each of their microphone pairs to best face the source individually, and rotate around themselves to collectively face the source, in addition to sideways movement and converging/diverging. This provides a much more robust system for resolution improvement compared to using only 1D movement.

The freedom which 2D movement provides makes the problem of deciding upon physical limitations for movement important in creating an algorithm to optimize microphone placement. If for example the sound source is within the 2D surface in which the robots are allowed to travel, we saw that the highest resolution results from moving the microphones very close to the source and surrounding it, as can be seen from the configuration of the web of points, with the highest density in the center. The challenges change though when the system is limited to say a rectangular area and the source is located outside of this region. The optimal configuration might then be to rotate the robots to collectively face the source, approach the physical boundary, and the source itself, as closely as possible, and then converge/diverge to until an optimal position is found. For this reason we found it important to keep the specific physical constraints in mind when designing an algorithm for adaptive movement in 2D.

### Illustration

• P, the red ring, indicates the midpoint between the robots.
• Stars indicate the location of microphones.
• Black circles indicate the midpoints of the microphone pairs which are synonymous with the robot positions.
• Red lines show the direction in which the robots are pointing, which is perpendicular to the line between the two microphones of one robot and indicate where the robots have maximum individual resolution.
• Green arrow indicates the U vector, the vector that points from the position of robot 2 to the position of robot 1.
• Theta indicates the angle formed by the U vector with the horizontal axis. This is the means of tracking the direction of the U vector and the T vector.
• The gold arrow indicates the T vector, the vector perpendicular (90 cclwise) to the U vector. This vector determines the path followed by the robots during approach/retreat.
• The sound source is the speaker, instrument, or machine which is emitting the sound of interest.
• Alpha indicates the rotation of Robot 1 with respect to the U vector.
• Beta indicates the rotation of Robot 2 with respect to the U vector.
• Alpha and Beta are used in conjunction with Theta to determine the orientation of the robots in an absolute coordinate system based off of the X Axis.
• The robot midpoint positions are fully described by P, Theta, and |U|. The microphones are described by the robot midpoint positions in conjunction with the distance between the microphones, “pair D”, Alpha, and Beta.
• Each one of these parameters is adaptable through the controller which selectively chooses which parameters to change using its 4 different modes shown below.