Axon 05: Kinematics & Motion Planning

Welcome to the Kinematics & Motion Planning Axon. This track develops the mathematical models that translate high-level autonomous trajectory curves into real-time wheel speeds and steering angles.

Modules in this Axon

1. Chassis Speeds & Forward/Inverse Kinematics

• The Real-World Problem: How does a robot translate high-level desired forward, strafe, and rotational speeds into individual wheel commands?
• Key Concepts: ChassisSpeeds [vx, vy, omega], Differential drive kinematics, wheel velocity saturation, and desaturation algorithms.

2. Swerve Kinematics & 2nd-Order Twist Correction

• The Real-World Problem: Why do omnidirectional swerve robots drift in curved arcs during combined translation and rotation?
• Key Concepts: 4-module vector decomposition, azimuth angle optimization (180° speed flips), Lie group twist discretization, and continuous curvature compensation.

3. Motion Profiling (Trapezoidal & S-Curves)

• The Real-World Problem: How do we command mechanisms to move as fast as possible without exceeding physical motor velocity, acceleration, or jerk limits?
• Key Concepts: Trapezoidal profiles, constant jerk 7-segment S-curves, profile generation in time, and real-time state following.

4. Holonomic Trajectory Tracking

• The Real-World Problem: How does an autonomous robot follow a pre-computed spline trajectory across the carpet while compensating for wheel slip and defense?
• Key Concepts: Cubic and Quintic Hermite splines, HolonomicDriveController feedback, PathPlanner/Choreo trajectory execution, and dynamic obstacle repulsion.