Intelligent Control of Differential Drive Robots Subject to Unmodeled Dynamics with EKF-based State Estimation

1. Problem Statement

Differential Drive Robots (DDRs) are widely used in logistics and navigation but face significant challenges in dynamic, uncertain environments. The primary difficulties include:

• Unmodeled Dynamics: Real-world systems suffer from unknown nonlinearities such as friction, actuator dynamics, wheel slip, and external disturbances that are difficult to model analytically.
• Sensor Limitations: Relying on single sensors (e.g., wheel encoders, IMUs, or cameras) leads to vulnerabilities like drift, noise accumulation, and failure in specific conditions (e.g., low light for cameras, slip for encoders).
• Control Robustness: Traditional control methods (kinematic control, sliding mode, or linearized dynamic control) often rely on simplifying assumptions (perfect velocity tracking, known dynamics) that degrade performance when these assumptions are violated.

The paper addresses the need for a unified framework that simultaneously provides robust state estimation and adaptive control to handle unmodeled dynamics and sensor uncertainties.

2. Methodology

The authors propose a hybrid framework integrating Online Machine Learning Control with Multi-Sensor Fusion.

A. State Estimation (EKF-based Fusion)

To ensure reliable state feedback despite sensor degradation, an Extended Kalman Filter (EKF) is employed to fuse heterogeneous sensor data:

• Sensors: Inertial Measurement Unit (IMU), Wheel Encoders (Odometry), 2D-LiDAR, and a Monocular Camera.
• Fusion Strategy:
  • Wheel Encoders: Provide high-frequency, low-cost short-term displacement but suffer from long-term drift and slip.
  • IMU: Offers high-frequency acceleration and angular velocity but is prone to bias.
  • LiDAR & Vision: Provide absolute pose correction (using PLICP for LiDAR and ORB-SLAM3 for Vision) to correct drift.
• Robustness: The EKF is designed to handle partial sensor failures (e.g., visual feature loss) by dynamically weighting measurements based on covariance. If a sensor's uncertainty increases, the filter relies more on the motion model and other sensors.

B. Intelligent Control (RBF Neural Network + Lyapunov)

The control architecture combines Feedback Linearization (FBL) with an Adaptive Radial Basis Function (RBF) Neural Network:

• System Model: The DDR dynamics are modeled as a first-order velocity system. The control law is derived using Feedback Linearization to cancel known dynamics.
• Uncertainty Approximation: An RBF neural network acts as a universal approximator to estimate the "lumped" uncertainty term ($d$), which includes friction, unmodeled dynamics, and disturbances.
  • The estimate is given by $\hat{d} = w^T \phi(v)$, where $w$ are weights and $\phi$ are Gaussian activation functions.
• Adaptation Law: The weights of the RBF network are updated online using a Lyapunov-based adaptation rule ($\dot{w} = \eta \tilde{v} \phi$), where $\tilde{v}$ is the velocity tracking error and $\eta$ is the learning rate.
• Stability: A Lyapunov function is constructed to prove that the closed-loop system is stable and that the tracking errors converge asymptotically to zero, provided the approximation error is bounded.

C. Trajectory Tracking

For position tracking, an intermediate kinematic controller is used to generate a reference velocity ($v_c$) based on the pose error (position and orientation). This reference velocity is then fed into the intelligent dynamic controller to compute the required torque inputs.

3. Key Contributions

1. Unified Framework: Integration of an adaptive neural network controller with a multi-sensor EKF state estimator, addressing both control uncertainty and sensing unreliability simultaneously.
2. Theoretical Stability: Derivation of a Lyapunov-based control law that guarantees closed-loop stability and asymptotic convergence for trajectory tracking tasks, even with unmodeled dynamics.
3. Robust State Estimation: Implementation of an EKF that fuses IMU, encoders, LiDAR, and monocular vision, demonstrating resilience against sensor noise, drift, and partial failures (e.g., visual re-initialization).
4. Real-World Validation: Extensive testing on a physical DDR (iRobot Create3) in diverse environments (smooth, rugged, and soft floors), moving beyond pure simulation.

4. Experimental Results

The approach was evaluated using ROS2 (Humble/Jazzy) in Gazebo simulations and on a real iRobot Create3 platform.

• Simulation: The controller successfully tracked circular trajectories. While pure Feedback Linearization (without the NN) failed to track the pose accurately due to unmodeled dynamics, the intelligent controller showed decaying velocity errors.
• Real-World Experiments:
  • Setup: The robot navigated a 0.5m radius circle at 0.5 rad/s on various floor types.
  • Performance Metrics: The intelligent controller was compared against a baseline pure Feedback Linearization controller.
  • Error Reduction: The proposed method achieved significant reductions in steady-state Root Mean Squared Error (RMSE):
    • X-Position: Reduced by 80.67%
    • Y-Position: Reduced by 24.19%
    • Yaw Orientation: Reduced by 82.48%
    • Linear Velocity: Reduced by 53.91%
    • Angular Velocity: Reduced by 29.00%
  • Resilience: The system maintained stability and continued state estimation even when the visual odometry (VO) experienced feature loss and required re-initialization, demonstrating the effectiveness of the sensor fusion.

5. Significance

This work demonstrates that combining data-driven adaptation (RBF networks) with model-based control (Lyapunov/FBL) and robust estimation (EKF) creates a highly reliable control system for autonomous robots.

• It overcomes the limitation of traditional controllers that require precise dynamic models.
• It proves that intelligent controllers can learn and compensate for complex, real-world disturbances (friction, slip) in real-time without prior knowledge.
• The framework is scalable and applicable to various mobile robotics applications operating in unstructured environments, paving the way for more autonomous and resilient robotic systems in logistics and exploration.

Future Work: The authors suggest integrating Reinforcement Learning to automatically tune controller parameters and extending the framework to higher-level path planning and SLAM applications.