DyadBotComponents

Dyad models of a two-wheeled balancing robot, together with controller architectures and controller-tuning scripts.

Models (dyad/)

Plant models:

• PlanarDyadBot: planar model of the robot. A wheel rolling without slip, an inverted-pendulum body mounted on the wheel axis through a motor (SimpleMotor), and an IMU-like sensor. Inputs/outputs: motor torque in, position/velocity/tilt/tilt-rate out.
• DyadBot3D: three-dimensional model with two individually spinning wheels with slip-based ground contact, allowing the body to tilt.
• RollingDyadBot3D: three-dimensional model with an ideal no-slip rolling wheel axle (MultibodyComponents.RollingWheelSet) and individually driven wheels, so the robot can be steered by differential torque. Outputs odometric path position/velocity, tilt angle/rate and yaw (heading) angle/rate. With equal torque on both wheels it is dynamically equivalent to PlanarDyadBot.

Closed-loop models around the planar plant:

• AngleControlledDyadBot: single PID loop stabilizing the tilt angle.
• CascadeControlledDyadBot: cascade control with an inner tilt-angle loop and an outer position loop; all six controller gains are exposed as tunable top-level parameters.
• CascadeFFDyadBot: the cascade extended with a feedforward generator (state-space system loaded from data/ff_*.csv) providing filtered position reference, tilt-angle feedforward and torque feedforward.
• LQGControlledDyadBot: LQG controller with reference feedforward and integral action (state-space system loaded from data/lqg_*.csv).
• LQGTuningDyadBot: analysis model used by the LQG design script.

Closed-loop models around the 3D plant:

• AngleControlledDyadBot3D: RollingDyadBot3D stabilized by the same AngleController as AngleControlledDyadBot; with in-plane motion the closed-loop response is identical to the planar model (test/test_stabilization.jl verifies this).
• YawControlledDyadBot3D: RollingDyadBot3D with the balance/position cascade (CascadeController, position reference held at zero) and a separate YawController tracking a heading reference that steps at t = 5; a ControlMixer combines drive and yaw torque into the two wheel torque commands, so the robot spins in place to the new heading.

Controller tuning scripts (scripts/)

Each script activates the scripts/ environment and can be run directly:

• tune_angle_pid.jl: PID autotuning of the inner angle loop (PIDAutotuningAnalysisSpec).
• tune_cascade_pid.jl: PID autotuning of the outer position loop, plus robustness analysis (sensitivity functions, disk margins).
• tune_cascade_structured.jl: structured tuning of all six cascade gains simultaneously (StructuredAutoTuningProblem) with per-loop sensitivity bounds and a pole-location constraint.
• compute_feedforward.jl: computes the feedforward generator for CascadeFFDyadBot and stores it in data/.
• tune_lqg.jl: LQG design (LQGAnalysisSpec) producing the controller used by LQGControlledDyadBot, stored in data/.

Julia utilities (src/)

• IMUKalmanFilter: discrete-time Kalman filter for tilt estimation from gyro and accelerometer measurements, suitable for embedded use.
• balance_original.jl: standalone Julia implementation of the original balance controller (not part of the package module).