What do you do if you're struggling to grasp mathematical concepts in Robotics?

Imagine you're in the lab late at night, and after staring at the same equation for the 47th time, you start thinking, "Maybe I should just build a robot to learn this for me." You start drafting designs for a robot whose sole purpose is to tackle the dense forest of calculus. It would have modes like "Explain Like I'm Five". Just as you're about to submit your Nobel Prize nomination for inventing a robot that could potentially replace math teachers (and possibly take over the world, but you'll deal with that later), you remember something crucial: Robotics is all about problem-solving, and every challenge is an opportunity to learn and grow. So, you decide to give MathBot a metaphorical rest and tackle the problem head-on.

Mathematics plays a pivotal role in all the engineering streams, especially robotics and AI-ML. If one is struggling to grasp the mathematical concept in robotics, go for the specialized courses designed for robotics. refresh your previous mathematical concepts. Identify experts in your network, organization, and neighborhood. Don't hesitate to seek help and guidance. Robotic concepts demand practice, do more and more practice.

YouTube and Khan Academy are a great resource to learn about topics that you are struggling with. They are free, and I have found them to be very helpful.

I have experienced that consistency and dedication have not only solved mathematics problems but many others. In robotics, at least the basics of algebra, geometry, calculus, linear algebra, and trigonometry are necessary. Use software libraries and modules in our existing robotic projects without needing to know the algorithms & their functionality. As they are already tested & approved for errors, this will reduce dependency on mathematics. Take a few free online classes and do small and simple projects on robotics that utilize basic math implementations. Practice solving mathematical problems related to robotics regularly. Start with simpler problems and gradually increase the complexity as you become more comfortable with the concepts.

Going back to basics always helps. It's necessary to have good foundation in algebra, calculus, matricies, etc. which can be learned through any coursework or online lectures.

Start from basics and focus on applied mathematics. Robotics usually involves maths in the areas of instrumentation, control systems, navigation and 3d point control. A plethora of simulation tools are available that allows you to manipulate algorithms on the go along with visual interpretation.

It's very important to know how to breakdown problems and look for solutions. While doing so, it is more important than the newer solutions collectively solve the bigger problem. More important is that the newer solutions don't create newer problems. Some of the basic approaches in robotics is to have a good understanding of the robot space , kinematics and range of motion. The concept and true application of vector algebra, linear algebra, calculus and basic physics are what are really needed to be understood well.

A very simple way that helped me tremendously is solving for very specific values. In computer vision, solving the filters for a few pixel values in the whole image made it much easier to understand the effect on the entire image. Similarly, for kinematics and controls, using a few control values to get desired angles and outputs help understand and verify the effect on the robot.

Most mathematics is very hard to grasp. Even professionals sometimes seem to struggle with it. Main idea is to develop intuition about what the input is and how the output is generated, what terms appear and how they are connected. Keeping it simple not only helps the complete process, it also helps develop new ideas. Coding implementation is mostly available, so grasping the intuition is enough at earlier stages without getting frustrated. Then, going deeper by solving problems using these intuitions help grasp even complex ideas.

Mathematics=Imagination 1. Understanding "Primitive Notions". 2. Constructing a Mind-Tower on Four Pillars (example in kinematics): - Logical-Philosophical Pillars: Connect mathematical concepts to philosophical underpinnings, reflecting on historical insights from Zeno to Newton - Mathematical Language Pillars: Stress the importance of fluency in mathematics' symbolic language for articulating kinematic principles. - Visualization Pillars: Master visual representation in geometry, algebra, and topology, using 2-D time-space graphs for kinematic motion. - Applications Pillars: Transition abstract concepts to real-world applications, showing how kinematics applies to fields like robotics and engineering.

In my opinion, going old school helps understand complex mathematical equations. To solve most, simply 'pen and paper' practice is the most effective way. Dedicate a time in day or week to solve at least one problem by hand, by writing down the problem, and its solution. Then, if necessary, go for the simulation. This is the only way getting through the complex mathematics in any field including robotics.

If you're struggling with a math concept in robotics, try these steps: 1. Break it Down: Simplify the concept into smaller parts and understand each step. 2. Practice Problems: Work on problems that apply the concept to help reinforce your understanding. 3. Ask for Help: Discuss the concept with a teacher or a classmate who understands it well. 4. Use Resources: Look for tutorials, videos, or books that explain the concept in different ways. 5. Apply It: Try to use the concept in a practical robotics project to see it in action.

In my experience, dedicating time to solving math problems related to robotics has been significant. Initially focusing on simple scenarios "lab-prototype," I gradually tackled more complex scenarios, which significantly deepened my understanding. Integrating this practice with coding and constructing miniature robotic models provided a hands-on approach that bridged theory with practical application. This method not only honed my analytical skills but also cultivated an intuitive sense of how mathematical principles manifest in the physical world, making the learning process both stimulating and effective.

1) Sensor Fusion - Analyzing inertial data for displacements and tilts. Required knowledge of mathematical analysis 2) SLAM - Constructing maps and determining the robot's position using data from Sensor Fusion. Knowledge of linear algebra is important here. 3) Navigation - Path planning using SLAM data. Requiring graph theory and search algorithms. 4) Interpolation - Curve formation from node lists, a facet of computational mathematics. 5) Trajectory Simplification - Breaking down curved trajectories into manageable actions for the robots. 6) Execution - Implementing actions with appropriate feedback. Additionally, a scheduler layer manages tasks. Here planning, logistics, and addressing challenges like the traveling salesman problem.

Mathematics is a skill that improves with practice. Dedicate time each day to solving problems, working through exercises, and applying mathematical concepts to robotics-related scenarios. Repetition helps reinforce understanding and build confidence.

Online sources are much helpful to fill the gaps between the technology and mind measures. So far, I have not faced any kind of problems pertaining to DK and IK problems of manipulators. I have slight difficulty in MATLab simulation. I am practicing it now.

Coursera and Udacity offer great courses on robotics. The best thing about these courses is that they have interesting tools that help you build a strong understanding of complex concepts, such as inverse kinematics and Jacobian matrices. However, there's no easy shortcut – you still need to study hard.

Check out - Khan Academy, edX, Coursera or MIT OpenCourseWare. These platforms provide some really good fundamentals that are most of the time the reason to grasp some math problems

Take advantage of online resources such as tutorials, video lectures, and interactive exercises available on educational platforms and robotics forums. These resources offer diverse perspectives and alternative explanations to enhance your comprehension.

In navigating complex mathematical principles within robotics, I've found that initially focusing on the broader goal, while not fully understanding every detail, can be effective. It’s essential to keep a record of what succeeds and what doesn’t. Retrospectively analyzing these outcomes, with the goal already achieved, offers valuable insights. This reverse-engineering approach not only demystifies the functions in play but also enhances understanding of the underlying mathematics, as practical data points guide you toward clear, conclusive insights.

Sometimes your preferred methods wont work for the application. Find a problem that you already know the solution for and find different ways to solve it. Then weigh out the pros and cons of each method. Being an expert is not simply being the best at doing something one way, but being able to identify the different options and discern which is best for the current situation.

Make connections between mathematical concepts and their applications in robotics. Understand how mathematical principles such as linear algebra, calculus, and statistics are utilized in robot kinematics, dynamics, control algorithms, and sensor data processing.'

In Robotics Mathematics, the key to resolving solution struggles is understanding the deep conceptual connections across disciplines like mathematics, computer science, and engineering. Challenges often stem from applying abstract mathematical theories—such as linear algebra for robotic movements or calculus for control systems—to tangible mechanical and electronic implementations. Building a strong foundational knowledge and linking these principles to real-world robotics applications are crucial. This approach not only enhances application skills but also fosters innovation and intuitive problem-solving, making it easier to address complex issues in robotic systems.

Reflect on your learning process and identify strategies that are most effective for you. Be flexible and willing to adapt your approach if certain methods are not yielding the desired results. Experiment with different study techniques until you find what works best for you.

Have a solid science base is the angular stone to adapt your strategies. Simplify Ideas and then you have better tools to find a path. For me it's necessary to have small victories to confirm the path or to undestand the problem better.

Begin by reviewing fundamental mathematical principles such as algebra, calculus, and linear algebra, which form the foundation of robotics. Don't hesitate to seek clarification from instructors or peers, and utilize various resources like textbooks, online tutorials, and practice problems to reinforce your learning. Also, applying these concepts directly to robotics projects or simulations can provide practical insight and enhance comprehension.

Don't get discouraged by setbacks or challenges along the way. Stay patient, persistent, and proactive in your learning journey. Celebrate your progress and accomplishments, no matter how small, and stay motivated to overcome obstacles and achieve your goals.

I would start with solving basic problems related to Linear Algebra. Then I will explore Rotation Matrix, Jacobians, Relationship between Joint Velocities to Cartesian Velocities. The Math is fascinating! Keep learning.

Don't fret, many engineers grapple with the math side of robotics! Here's a four-line approach: 1. Visualize: Sketch or build physical models to see how math translates to robot movement. 2. Break it down: Simplify complex concepts into smaller, more manageable steps. 3. Practice: Solve real-world robotics problems to solidify your understanding. 4. Seek help: Ask professors, peers, or online forums for explanations and alternative approaches.