Module backstepping_control 

Backstepping-style controller for a unicycle robot.

Uses a recursive Lyapunov-based control law in the robot body frame to drive the robot to a target pose.

References:

• Claude Samson, “Control of chained systems application to path following and time-varying point-stabilization of mobile robots”: https://ieeexplore.ieee.org/document/362899
• R. W. Brockett, “Asymptotic Stability and Feedback Stabilization”: https://hrl.harvard.edu/publications/brockett83asymptotic.pdf

Notes: A stationary unicycle posture cannot in general be asymptotically stabilized by smooth time-invariant pure-state feedback alone. To keep the API posture-regulation oriented while preserving robust convergence in practice, this module uses the backstepping tracking-form control law away from the goal and a terminal pose regulator close to the target.

Structs

BacksteppingConfig

Configuration for the backstepping controller.

BacksteppingController

Backstepping controller.

BacksteppingResult

Full backstepping simulation result.

BacksteppingStep

One recorded simulation step.

TimeVaryingBacksteppingConfig

Configuration for the time-varying pose stabilizer.

TimeVaryingBacksteppingController

Time-varying pose stabilizer based on a shrinking virtual-goal orbit.

Functions

backstepping_control

Runs the backstepping controller from start to goal.

normalize_angle

Normalizes an angle into [-pi, pi].

time_varying_backstepping_control

Runs the Samson-inspired time-varying backstepping controller.