Reliable control and state estimation of differential drive robots (DDR) operating in dynamic and uncertain environments remains a challenge, particularly when system dynamics are partially unknown and sensor measurements are prone to degradation. This work introduces a unified control and state estimation framework that combines a Lyapunov-based nonlinear controller and Adaptive Neural Networks (ANN) with Extended Kalman Filter (EKF)-based multi-sensor fusion. The proposed controller leverages the universal approximation property of neural networks to model unknown nonlinearities in real time. An online adaptation scheme updates the weights of the radial basis function (RBF), the architecture chosen for the ANN. The learned dynamics are integrated into a feedback linearization (FBL) control law, for which theoretical guarantees of closed-loop stability and asymptotic convergence in a trajectory-tracking task are established through a Lyapunov-like stability analysis. To ensure robust state estimation, the EKF fuses inertial measurement unit (IMU) and odometry from monocular, 2D-LiDAR and wheel encoders. The fused state estimate drives the intelligent controller, ensuring consistent performance even under drift, wheel slip, sensor noise and failure. Gazebo simulations and real-world experiments are done using DDR, demonstrating the effectiveness of the approach in terms of improved velocity tracking performance with reduction in linear and angular velocity errors up to $53.91\%$ and $29.0\%$ in comparison to the baseline FBL.

翻译：在动态和不确定环境中运行的差速驱动机器人（DDR），其可靠控制与状态估计仍是一个挑战，尤其当系统动力学部分未知且传感器测量易受干扰时。本研究提出了一种统一控制与状态估计框架，该框架将基于李雅普诺夫的非线性控制器、自适应神经网络（ANN）与基于扩展卡尔曼滤波（EKF）的多传感器融合相结合。所提出的控制器利用神经网络的通用逼近特性实时建模未知非线性。在线自适应方案更新了径向基函数（RBF）的权重，RBF是为此ANN选择的架构。学习到的动力学被集成到反馈线性化（FBL）控制律中，通过类李雅普诺夫稳定性分析，为该控制律在轨迹跟踪任务中建立了闭环稳定性和渐近收敛性的理论保证。为确保鲁棒的状态估计，EKF融合了来自单目相机、二维激光雷达和轮式编码器的惯性测量单元（IMU）数据与里程计信息。融合后的状态估计驱动智能控制器，即使在漂移、车轮打滑、传感器噪声及故障条件下也能确保性能稳定。利用DDR进行的Gazebo仿真和真实世界实验表明，与基准FBL方法相比，该方法在线速度和角速度误差分别降低高达$53.91\%$和$29.0\%$，在速度跟踪性能方面验证了其有效性。