Question $4$

Wavefront$-$based robot path planning.

In our class, we delved into a fundamental wavefront$-$based path planning methodology, which

forms several variations, indeed. The concept we explored involves using a wavefront approach

to plan paths for robots by labelling numbers in a workspace. The process involves labeling cells

in a workspace with numbers to facilitate this path planning.

$(1)$ We have a workspace that has labeled numbers with starting location $S$ and goal location

$G$ as follows. Please complete the following steps how you fill out the number and find

the robot path. Note that the first two steps are given as follows.

Step $1$:

Discretize space by imposing a grid $($define cell neighbors $4-$ or $8-$connectivity$).$ You can choose

to connect cells either in a $4-$connectivity or an $8-$connectivity manner.

Step $2$:

Assign the label $"1"$ to cells that are either partially or fully occupied by obstacles.

Now, please proceed with the following steps:

Step $3$:

$(2)$ Additionally, please create a visual representation of the path generated using the

Gradient Descent rule.