Robot Path Tracking Techniques

2–6 DOF Robotic Manipulators Trajectory Tracking using PID in MATLAB ➡ Simulation of 2-DOF to 6-DOF robotic manipulators ➡ Detailed modeling of serial manipulators including UR5 ➡ Forward & Inverse Kinematics implementation for all DOF systems ➡ PID-based joint control for smooth and stable motion ➡ Trajectory tracking: Circle, Rectangle, and Infinity (∞) paths ➡ Real-time 3D visualization and animation in MATLAB ➡ Modular and well-structured code for scalability and learning ✨ Why this matters: Trajectory tracking is a fundamental problem in robotics, where a manipulator must precisely follow a desired path while maintaining stability and accuracy. This becomes increasingly complex as the number of degrees of freedom increases due to nonlinear kinematics, joint coupling, and control challenges. This project demonstrates how classical control techniques like PID can be effectively applied to multi-DOF robotic systems to achieve smooth and reliable motion. By integrating kinematic modeling with control strategies, the system reflects real-world industrial applications where robotic arms are required to perform precise tasks such as assembly, welding, and pick-and-place operations. 📊 Key Highlights: ✔ Complete kinematic modeling (FK & IK) for 2–6 DOF manipulators ✔ PID-based trajectory tracking for accurate motion control ✔ Implementation of multiple trajectories (circle, rectangle, infinity) ✔ Real-time simulation and visualization in MATLAB ✔ Clean and reusable code structure for educational use ✔ Industrial-level modeling with UR5 6-DOF manipulator 💡 Future Potential: This framework can be extended to: ➡ Advanced control (Adaptive, MPC, Fuzzy, AI-based control) ➡ Obstacle avoidance and path planning ➡ Integration with ROS 2 for real robot deployment ➡ Dynamic modeling and torque control ➡ Digital twin and industrial automation systems 🔗 For students, engineers & robotics enthusiasts: This project provides a complete hands-on approach to understanding robotic manipulators, control systems, and trajectory planning. It is ideal for learning how robotic arms achieve precise motion in real-world applications. 🔁 Repost to support robotics innovation & engineering learning! #Robotics #MATLAB #PIDControl #RobotManipulators #UR5 #ControlSystems #Automation #Mechatronics #EngineeringProjects #Simulation #STEM #EngineeringEducation

Researchers at Hong Kong University MaRS Lab have just published another jaw dropping paper featuring their safety-assured high-speed aerial robot path planning system dubbed "SUPER". With a single MID360 lidar sensor they repeatedly achieved autonomous one-shot navigation at speeds exceeding 20m/s in obstacle rich environments. Since it only requires a single lidar these vehicles can be built with a small footprint and navigate completely independent of light, GPS and radio link. This is not just #SLAM on a #drone, in fact the SUPER system continuously computes two trajectories in each re-planning cycle—a high-speed exploratory trajectory and a conservative backup trajectory. The exploratory trajectory is designed to maximize speed by considering both known free spaces and unknown areas, allowing the drone to fly aggressively and efficiently toward its goal. In contrast, the backup trajectory is entirely confined within the known free spaces identified by the point-cloud map, ensuring that if unforeseen obstacles are encountered or if the system’s perception becomes uncertain, the system can safely switch to a precomputed, collision-free path. The direct use of LIDAR point clouds for mapping eliminates the need for time-consuming occupancy grid updates and complex data fusion algorithms. Combined with an efficient dual-trajectory planning framework, this leads to significant reductions in computation time—often an order of magnitude faster than comparable SLAM-based systems—allowing the MAV to operate at higher speeds without sacrificing safety. This two-pronged planning strategy is particularly innovative because it directly addresses the classic speed-safety trade-off in autonomous navigation. By planning an exploratory trajectory that pushes the speed envelope and a backup trajectory that guarantees safety, SUPER can achieve high-speed flight (demonstrated speeds exceeding 20 meters per second) without compromising on collision avoidance. If you've been tracking the progress of autonomy in aerial robotics and matching it to the winning strategies emerging in Ukraine, it's clear we're likely to experience another ChatGPT moment in this domain, very soon. #LiDAR scanners will continue to get smaller and cheaper, solid state VSCEL based sensors are rapidly improving and it is conceivable that vehicles with this capability can be built and deployed with a bill of materials below $1000. Link to the paper in the comments below.

I am delighted to share an interesting example of stabilizing a Car-like mobile robot (CMR) using a Nonlinear Model predictive controller (NMPC) optimal controller, to avoid obstacles and overcome barrier limitations. This is achieved by integrating the Artificial Potential Field (APF) method, with extended Kalman Filter (EKF) to estimate longitudinal and lateral position and drive the mobile robot to track a given trajectory while adhering to environmental constraints. CMR is typically modeled using its kinematic equations, capturing its nonholonomic constraints and motion characteristics.this often involves a bicycle model, where the robot is simplified to two wheels, a steerable front wheel and a fixed rear wheel. The state variables usually include the robot's position, orientation, and steering angle, while the control inputs are the linear velocity and Ang velocity.This model is essential for designing controllers. NMPC works by repeatedly solving an optimization problem over a finite prediction horizon at each control step. For a car-like robot, this involves using a dynamic model of the robot to predict its future states, such as position, orientation, and velocity, based on the current state and a sequence of control inputs. 'fmincon' solver in MATLAB solve this constrained nonlinear optimization, it aims to minimize a cost function that typically includes terms for trajectory tracking error, control effort, and adherence to constraints like obstacle avoidance, actuator limits, or road boundaries. By solving this problem in real-time, NMPC generates optimal control actions that drive the robot toward its goal while respecting system constraints and adapting to changes in the environment, if the robot detects an obstacle, NMPC can replan its trajectory to avoid collisions while still progressing toward the target. The integration of APF ensures smooth obstacle avoidance, while EKF provides accurate state estimation for robust control. This combination makes NMPC highly effective for CMRs operating in dynamic or uncertain environments, ensuring safe, efficient, and precise navigation. Overall, this approach showcases a powerful framework for autonomous navigation and control of CMR. In the future, the proposed framework for stabilizing a CMR can be further enhanced by exploring alternative techniques and solvers. For instance, Reinforcement Learning or Deep Learning could be incorporated to improve obstacle avoidance and trajectory planning in highly dynamic environments, enabling the robot to learn from experience and adapt to complex scenarios. solvers like IPOPT or CasADi could be tested alongside `fmincon` to improve computational efficiency and scalability, especially for large-scale problems. These advancements would not only improve the performance and robustness of the CMR but also expand its applicability to more challenging environments, such as urban autonomous driving or multi-robot coordination.

The robotics algorithm library every engineer should know! 📚 PythonRobotics is an open-source collection of Python code and textbook for robotics algorithms, created by Atsushi Sakai. It has 27.2k stars on GitHub and 7k forks, so it's a no brainer to bookmark it! 🔖 The project covers everything from localization (EKF, particle filters, histogram filters) to SLAM (FastSLAM, ICP matching), path planning (A*, RRT*, Dijkstra, D*, potential fields, state lattice), path tracking (Stanley, LQR, MPC), arm navigation, aerial navigation, and even bipedal planning. What makes this special? It's designed to be easy to read and understand, with minimal dependencies and practical, widely-used algorithms. Each algorithm comes with visual animations, mathematical explanations, and working code. The documentation is essentially a full textbook on robotics algorithms, available free online at https://lnkd.in/dvuuVy6e. Requirements are simple: Python 3.13+, NumPy, SciPy, Matplotlib, and cvxpy. That's it. This a learning resource with 2,201 commits, contributions from 138 developers, and active maintenance. The animations alone (stored in a separate repo) are worth studying. If you're learning robotics, building autonomous systems, or teaching algorithms, this is the resource. It's MIT licensed, so you can use it freely in research or commercial projects. Here's the link: https://lnkd.in/dNX5JzkX P.S. This is what good open-source looks like: educational, practical, well-documented, and community-driven. Bookmark it. 🔖 ~~ ♻️ Join the weekly robotics newsletter, and never miss any news → ziegler.substack.com

End-to-end motion planning simulation built on the CARLA simulator that seamlessly integrates advanced path planning, smooth trajectory generation, and real-time vehicle control 🚗 🔑 Key Features: - Path Planning with RRT*: I implemented sampling-based algorithms (RRT, RRT*, and Informed RRT*) to compute collision-free paths in a simulated urban environment. By dynamically sampling the CARLA world and avoiding obstacles, the planner finds viable routes even in challenging scenarios. - Smooth Trajectory Generation: Using motion primitives based on cubic polynomial interpolation, the system generates smooth trajectories between waypoints. This ensures that the vehicle’s motion is both safe and comfortable. - PID Control for Real-Time Vehicle Guidance: A combination of longitudinal and lateral PID controllers has been designed to accurately follow the planned trajectory. The vehicle’s throttle, brake, and steering commands are continuously updated in real-time. Repository: https://lnkd.in/d7qMqD-p 📖 Learn More: CARLA Open-source simulator for autonomous driving research: https://carla.org/ Robotic Path Planning RRT and RRT*: https://lnkd.in/dTqpGfJt The PID Controller & Theory Explained: https://lnkd.in/dMHYQdJB #autonomousdriving #CARLA #PathPlanning #PIDControl #Simulation #Robotics #RRT #RRT*

𝗠𝗮𝘀𝘁𝗲𝗿𝗶𝗻𝗴 𝗟𝗼𝗰𝗮𝗹 𝗣𝗮𝘁𝗵 𝗙𝗼𝗹𝗹𝗼𝘄𝗶𝗻𝗴: 5 Powerful Controllers in Nav2 You Should Know 𝗖𝗼𝗻𝘁𝗿𝗼𝗹𝗹𝗲𝗿𝘀 are the secret sauce behind smooth, reliable mobile robot navigation in ROS2. In the Nav2 stack, the right controller plugin can make the difference between jerky motion and elegant, obstacle-aware trajectories. Here are five of the most capable and widely used local controllers available today; each with unique strengths for different robotics challenges. 𝟭. 𝗗𝗪𝗕 𝗖𝗼𝗻𝘁𝗿𝗼𝗹𝗹𝗲𝗿 The battle-tested default in Nav2, built on the Dynamic Window Approach. It generates feasible trajectories and scores them using modular critics (obstacles, path adherence, velocity limits, etc.). 𝗕𝗲𝘀𝘁 𝗳𝗼𝗿: General-purpose navigation in dynamic environments with strong obstacle avoidance and goal-reaching behavior. 𝗗𝗼𝗰𝘀 → https://lnkd.in/dpVZ5CJ4 𝟮. 𝗚𝗿𝗮𝗰𝗲𝗳𝘂𝗹 𝗖𝗼𝗻𝘁𝗿𝗼𝗹𝗹𝗲𝗿 A lookahead-based controller engineered for smooth, exponentially stable motion. It intelligently selects target poses along the path to deliver clean, human-like driving with precise orientation control. 𝗕𝗲𝘀𝘁 𝗳𝗼𝗿: Indoor navigation, cluttered spaces, or missions where final heading accuracy really matters. 𝗗𝗼𝗰𝘀 → https://lnkd.in/dR_R894Y 𝟯. 𝗠𝗼𝗱𝗲𝗹 𝗣𝗿𝗲𝗱𝗶𝗰𝘁𝗶𝘃𝗲 𝗣𝗮𝘁𝗵 𝗜𝗻𝘁𝗲𝗴𝗿𝗮𝗹 𝗖𝗼𝗻𝘁𝗿𝗼𝗹𝗹𝗲𝗿 (𝗠𝗣𝗣𝗜) A modern sampling-based Model Predictive Control approach. It uses thousands of trajectory rollouts with Gaussian noise, then optimizes using critic-weighted scoring—delivering excellent performance even on mid-range hardware. 𝗕𝗲𝘀𝘁 𝗳𝗼𝗿: Confined spaces, dynamic obstacles, omnidirectional / Ackermann / differential drive robots that need smooth, predictive behavior. 𝗗𝗼𝗰𝘀 → https://lnkd.in/dkPwVJxb 𝟰. 𝗥𝗲𝗴𝘂𝗹𝗮𝘁𝗲𝗱 𝗣𝘂𝗿𝗲 𝗣𝘂𝗿𝘀𝘂𝗶𝘁 (𝗥𝗣𝗣) An improved take on classic Pure Pursuit. It dynamically regulates linear velocity based on path curvature and proximity to obstacles, plus adaptive lookahead distance to minimize cutting corners and overshoot. 𝗕𝗲𝘀𝘁 𝗳𝗼𝗿: Industrial AGVs, service robots, and environments with tight turns, narrow corridors, or blind corners. 𝗗𝗼𝗰𝘀 → https://lnkd.in/daYgZb2j 𝟱. 𝗥𝗼𝘁𝗮𝘁𝗶𝗼𝗻 𝗦𝗵𝗶𝗺 𝗖𝗼𝗻𝘁𝗿𝗼𝗹𝗹𝗲𝗿 A lightweight wrapper that rotates the robot in place to achieve the desired initial heading before handing control to the main controller. 𝗕𝗲𝘀𝘁 𝗳𝗼𝗿: Situations where the global planner produces paths with sharp initial turns, non-holonomic robots, or when you need clean orientation alignment at the start of motion. 𝗗𝗼𝗰𝘀 → https://lnkd.in/dzJP7Cg5 Stay tuned for the blog post soon! #ROS2 #Nav2 #Robotics #MobileRobots #RobotControllers