# Robotic path planning

What methods do you all use for robotic arm path planning? Do you use linear algebra to determine global minimums of a configuration space, or are there now simpler ways/existing software for that?

Thanks,
Colby Sherman

I posted your question verbatim to ChatGPT and got this:

“Robotic arm path planning generally uses a combination of approaches, including some rooted in linear algebra but also leveraging more advanced algorithms and software frameworks. Here are some of the common methods used today:

1. Sampling-Based Algorithms:

• Probabilistic Roadmaps (PRM) and Rapidly-exploring Random Trees (RRT) are popular algorithms. They explore the configuration space by randomly sampling points and then trying to connect them, avoiding obstacles along the way. These methods don’t directly compute global minimums but rather try to find feasible paths efficiently.
2. Optimization-Based Methods:

• Trajectory optimization techniques, like CHOMP (Covariant Hamiltonian Optimization for Motion Planning) or STOMP (Stochastic Trajectory Optimization for Motion Planning), formulate path planning as an optimization problem. These methods aim to minimize a cost function (e.g., distance, energy, or time), and often use gradient descent-like methods. Linear algebra plays a role in formulating and solving these optimization problems.
3. Search Algorithms:

• Classical algorithms like A*, Dijkstra, or Dynamic Programming are still widely used for grid-based or discretized configuration spaces, especially for finding optimal paths in terms of a cost metric. These methods can give the shortest or least costly path but can be computationally expensive for high-dimensional spaces.
4. Linear Algebra and Inverse Kinematics:

• For solving inverse kinematics (finding joint angles for a desired end-effector position), linear algebra is often used. For example, Jacobian matrices are used to solve for velocity control, and pseudo-inverse methods help deal with singularities. However, these methods are typically part of low-level control rather than full path planning.
5. Reinforcement Learning (RL):

• RL-based methods are emerging for robotic path planning, where the robot learns optimal paths through trial and error in a simulation environment. These methods don’t require direct computation of global minima but instead find policies that maximize rewards over time.
6. Software and Frameworks:

• Existing software frameworks like ROS MoveIt!, OMPL (Open Motion Planning Library), and Drake implement many of these algorithms. They offer ready-to-use tools for path planning without needing to directly engage with the underlying mathematics.

So, while linear algebra is still crucial in certain aspects (like inverse kinematics or cost function formulation in optimization), modern path planning often relies on more sophisticated algorithms that handle the complexities of high-dimensional spaces more effectively than trying to compute a global minimum from scratch.

Is there a specific type of robotic arm or application you’re working with that could benefit from these methods?“

This is way beyond me.