# Motion Planning Algorithms Series

Motion planning is a critical component of robotics and automation systems that enables a machine to plan its path from an initial configuration to a goal configuration while avoiding collisions with obstacles in its environment. This process involves solving complex mathematical problems that require sophisticated algorithms and computational techniques. In recent years, various motion planning algorithms have been developed to meet the demands of different applications, each with its strengths and limitations. These algorithms are classified based on their underlying principles and methodologies, and understanding their differences is crucial for selecting the most suitable algorithm for a specific task. This article provides an overview of motion planning algorithms and their classifications, highlighting their key features and applications.

There are several types of motion planning algorithms, and they can be classified based on their underlying principles and methodologies. Here are some common classifications:

## 1. Sampling-based algorithms:

These algorithms randomly sample the configuration space and build a roadmap that connects the sampled points to generate a collision-free path. Examples of sampling-based algorithms include Rapidly-exploring Random Trees (RRT) and Probabilistic Roadmaps (PRM).

## 2. Grid-based algorithms:

These algorithms discretize the configuration space into a grid and perform a search to find a collision-free path. Examples of grid-based algorithms include Dijkstra’s algorithm and A* algorithm.

## 3. Optimization-based algorithms:

These algorithms optimize a cost function that represents the desired properties of the path, such as smoothness, shortest distance, or minimum time. Examples of optimization-based algorithms include **Gradient Descent** and **Sequential Quadratic Programming.**

Gradient descent can be used to iteratively update the robot’s configuration along the path by following the direction of steepest descent of the cost function. The gradient of the cost function with respect to the robot’s configuration provides the direction of steepest descent, and the learning rate controls the size of the steps taken in that direction.

To implement gradient descent programming in motion planning for robotics, one needs to define the cost function and its gradient based on the robot’s kinematics and dynamics, as well as the environment’s constraints. The robot’s initial and goal configurations are also specified, and the optimization algorithm updates the robot’s configuration iteratively until a satisfactory path is found.

One challenge with gradient descent programming in motion planning for robotics is that the cost function may have multiple local minima, which can lead to suboptimal or even invalid paths. To address this issue, one may use a hybrid approach that combines gradient descent with other optimization algorithms, such as sampling-based or search-based methods, to improve the search space exploration and avoid local minima.

## 4. Hybrid algorithms:

These algorithms combine two or more of the above techniques to improve their performance and robustness. Examples of hybrid algorithms include **PRM*** and **RRT***.

RRT* algorithm works by randomly sampling the configuration space and building a tree of connected configurations, starting from the robot’s initial configuration. Unlike the original RRT algorithm, RRT* uses a cost function to evaluate the quality of each path and guide the search towards more promising regions of the configuration space.

The cost function used in RRT* is based on the length of the path from the initial configuration to the sampled configuration, as well as the distance between the sampled configuration and its nearest neighbor in the tree. By using this cost function, RRT* ensures that the generated paths are both collision-free and optimal.

One of the key advantages of RRT* algorithm is its ability to handle high-dimensional configuration spaces efficiently. It achieves this by using a local rewiring step that attempts to improve the connectivity of the tree and reduce the number of nodes needed to cover the configuration space.

To implement RRT* algorithm, one needs to define the sampling strategy, the cost function, and the local rewiring step. The algorithm iteratively generates new configurations by randomly sampling the configuration space and connecting them to the nearest node in the tree. Then, it evaluates the cost of each path and updates the tree by rewiring the nodes with lower cost paths.

RRT* algorithm has been successfully applied in various robotic applications, such as autonomous vehicles, mobile robots, and manipulators. Its ability to generate optimal and collision-free paths in high-dimensional spaces makes it a valuable tool for motion planning in complex environments. However, its performance heavily depends on the choice of the cost function and the sampling strategy, and choosing the appropriate parameters can be challenging.

Thanks for reading this article on motion planning algorithms! As I’ve discussed, motion planning is a fundamental problem in robotics and AI, and there are many different approaches and algorithms that can be used to tackle it.

In this series, I’ve introduced some of the most common classifications of motion planning algorithms, including sampling-based algorithms, optimization-based algorithms. In upcoming articles, I’ll take a deeper dive into each of these classifications and explore some of the most popular algorithms within each category.

So if you’re interested in learning more about motion planning and how it can be applied in robotics and its space applications, be sure to stay tuned for the rest of this series. I hope you’ve found this introduction informative and engaging, and I look forward to exploring this topic in more detail with you soon!