TEB Local Planner – Navigation

TEB Local Planner: A Comprehensive 4-Month Self-Study Course

Course Syllabus

Course Description

This comprehensive 4-month (approximately 16-week) self-study course is designed to take motivated beginners and intermediate learners through the fundamentals and advanced applications of the Timed Elastic Band (TEB) Local Planner. The TEB Local Planner is a powerful and widely used algorithm in robotics for local trajectory optimization, enabling robots to navigate complex environments smoothly and efficiently while avoiding obstacles.

This course will cover the theoretical underpinnings of TEB, its implementation in ROS (Robot Operating System), parameter tuning, and real-world application through practical examples and a culminating final project. By the end of this course, students will have a deep understanding of TEB and the ability to apply it to their own robotic projects.

Primary Learning Objectives

Upon successful completion of this course, students will be able to:

1. Understand the core concepts of local planning in robotics and the role of the TEB Local Planner.
2. Grasp the mathematical foundations of the Timed Elastic Band formulation, including cost functions and optimization.
3. Implement and configure the TEB Local Planner within a ROS/ROS2 environment.
4. Effectively tune TEB parameters for various robotic platforms and navigation scenarios.
5. Debug and troubleshoot common issues encountered when using the TEB Local Planner.
6. Integrate TEB into a complete robotic navigation stack for real-world applications.
7. Develop and execute a final project demonstrating proficiency in TEB-based robot navigation.

Necessary Materials

• A computer with Ubuntu 20.04 (or later) installed.
• ROS Noetic or ROS2 Foxy/Humble installed and configured.
• Gazebo simulator installed.
• Basic understanding of Linux command line.
• Familiarity with C++ or Python programming (intermediate level for practical examples).
• Optional: A physical robot (e.g., Turtlebot3, LIMO) for real-world testing (simulations will be sufficient for all practical examples).

Course Content

Week 1-2: Foundations of Local Planning and Introduction to TEB

Lesson 1: Introduction to Robot Navigation and Local Planning

• Learning Objectives:
• Understand the overall robot navigation stack (global vs. local planning).
• Identify the challenges and requirements of local planning.
• Be introduced to different local planning algorithms.
• Key Vocabulary:
• Global Planner: Generates a high-level path from start to goal.
• Local Planner: Generates a collision-free trajectory for immediate execution.
• Odometry: Measurement of a robot’s position and orientation over time.
• Localization: Determining a robot’s position within a map.
• Mapping: Creating a representation of the environment.
• Content: Robot navigation is a complex task that can be broken down into several components, primarily global and local planning. The global planner computes a path considering the entire known map, while the local planner is responsible for generating a short-term, collision-free trajectory that the robot can execute immediately. This involves reacting to dynamic obstacles, maintaining safe distances, and respecting robot kinematics. We’ll briefly touch upon algorithms like DWA, Eband, and then focus on TEB.
• Practical Hands-on Example: Setting up a basic ROS/ROS2 navigation stack without a local planner (just global path visualization) to understand the concept of a path.

Lesson 2: Overview of the TEB Local Planner

• Learning Objectives:
• Understand the fundamental concept behind the Timed Elastic Band.
• Identify the key advantages of TEB over other local planners.
• Gain an initial understanding of TEB’s role in a typical navigation stack.
• Key Vocabulary:
• Timed Elastic Band (TEB): A local planner that optimizes a robot’s trajectory by considering time and obstacle avoidance.
• Trajectory Optimization: The process of finding the best possible path or motion given certain constraints.
• Elastic Band: A metaphor for a flexible curve that can be stretched and compressed.
• Content: The TEB Local Planner treats the robot’s trajectory as an “elastic band” in time and space. This band is optimized to minimize various cost functions, such as distance to obstacles, deviation from a global path, and smoothness, while respecting the robot’s kinematic and dynamic constraints. This approach allows for very smooth and efficient trajectories, even in cluttered environments.
• Practical Hands-on Example: Running a pre-configured TEB navigation stack in a simple Gazebo environment (e.g., a straight corridor) and observing the robot’s smooth motion.

Week 3-4: Mathematical Foundations of TEB

Lesson 3: Trajectory Representation and Discretization

• Learning Objectives:
• Understand how a robot’s trajectory is represented in TEB.
• Grasp the concept of time parametrization in the trajectory.
• Learn about the discretization of the elastic band.
• Key Vocabulary:
• Trajectory Point: A single pose (position and orientation) and associated time.
• Time Parametrization: Assigning a time value to each point on the trajectory.
• Discretization: Representing a continuous function as a finite set of points.
• Content: In TEB, a trajectory is represented as a sequence of discrete robot poses, each associated with a specific time. This time component is crucial as it allows TEB to consider velocity and acceleration limits. The optimization process then manipulates these discrete points and their time intervals to find an optimal trajectory.
• Practical Hands-on Example: Visualize the discrete trajectory points generated by TEB in RViz using path or marker displays.

Lesson 4: Cost Functions: Obstacle Avoidance and Path Following

• Learning Objectives:
• Understand the primary cost functions used in TEB.
• Learn how obstacle avoidance is formulated as a cost.
• Grasp the concept of path following and its associated cost.
• Key Vocabulary:
• Cost Function: A mathematical function that quantifies the “badness” of a particular state or trajectory.
• Hard Constraint: A condition that must be strictly satisfied.
• Soft Constraint: A condition that is preferred but can be violated to some extent.
• Inflation Layer: Expands obstacles to account for robot size.
• Content: TEB optimizes the trajectory by minimizing a weighted sum of various cost functions. Two critical costs are obstacle avoidance, which penalizes trajectories that come too close to obstacles, and path following, which encourages the robot to stay close to the global path. We will delve into how these are mathematically represented.
• Practical Hands-on Example: Experiment with changing obstacle distances in a simulated environment and observe how TEB adjusts the robot’s trajectory to avoid collisions.

Week 5-6: Cost Functions: Robot Kinematics and Dynamics

Lesson 5: Kinematic and Dynamic Constraints

• Learning Objectives:
• Understand how robot kinematics (e.g., non-holonomic constraints) are incorporated.
• Learn about dynamic constraints (e.g., max velocity, acceleration).
• Grasp the impact of these constraints on trajectory optimization.
• Key Vocabulary:
• Kinematics: The study of motion without considering forces.
• Dynamics: The study of motion considering forces and torques.
• Non-holonomic Constraint: A constraint on a system’s velocity, e.g., a car cannot move sideways.
• Content: Robots have physical limitations. TEB accounts for these by including cost functions related to maximum velocity, acceleration, and even more complex kinematic constraints like those for differential drive or omnidirectional robots. These ensure that the generated trajectory is physically executable by the robot.
• Practical Hands-on Example: Modify the max velocity and acceleration parameters in TEB and observe the robot’s motion change in simulation, noting the impact on trajectory smoothness and speed.

Lesson 6: Other Important Cost Functions and Optimization Problem

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