Intelligent Control of Differential Drive Robots Subject to Unmodeled Dynamics with EKF-based State Estimation
Authors: Amos Alwala, Yuchen Hu, Gabriel da Silva Lima, Wallace Moreira Bessa
Organizations: With the Smart Systems, Department of Mechanical and Materials Engineering, Faculty of Technology, University of Turku, 20520 Turku, Finland.
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.
Figures & tables
Fig. 1 : A time-lapse of the intelligent controlled Create3 DDR completing a circular trajectory
Fig. 2 : Schematic diagram of a differential drive robot
Fig. 3 : Gazebo simulation results showing trajectory tracking and velocity error of the intelligent controller.
Fig. 4 : Gazebo simulation results showing trajectory tracking and velocity error of the intelligent controller with an intermediate pose feedback velocity controller.
Fig. 5 : Results of feedback linearization controller on Create3 tracking a circle trajectory of 0.5m radius at 0.5rad/s angular speed.
Fig. 6 : Results of the intelligent controller on Create3 tracking a circle trajectory of 0.5m radius at 0.5rad/s angular speed.
Pure Feedback Linearization
Intelligent
Change (%)
Ex
0.0712
0.0138
80.67
Ey
0.0416
0.0315
24.19
Eθ
0.1242
0.0218
82.48
Ev
0.0416
0.0192
53.91
Eω
0.055
0.0391
29.00
TABLE I : A comparative analysis of the controller trajectory tracking performance on rugged floor with ηi=0.8 in terms of Steady State Root Mean Squared Error
Robust state estimation for highly dynamic motion of legged robots remains challenging, especially in dynamic, contact-rich scenarios. Traditional approaches often rely on binary contact states that fail to capture the nuances of partial contact or directional slippage. This paper presents CoCo-InEKF, a differentiable invariant extended Kalman filter that utilizes continuous contact velocity covariances instead of binary contact states. These learned covariances allow the method to dynamically modulate contact confidence, accounting for more nuanced conditions ranging from firm contact to directional slippage or no contact. To predict these covariances for a set of predefined contact candidate points, we employ a lightweight neural network trained end-to-end using a state-error loss. This approach eliminates the need for heuristic ground-truth contact labels. In addition, we propose an automated contact candidate selection procedure and demonstrate that our method is insensitive to their exact placement. Experiments on a bipedal robot demonstrate a superior accuracy-efficiency tradeoff for linear velocity estimation, as well as improved filter consistency compared to baseline methods. This enables the robust execution of challenging motions, including dancing and complex ground interactions -- both in simulation and in the real world.
Michael Baumgartner, David Müller, Agon Serifi +4
ETH Zurich, Switzerland · Disney Research, Switzerland
This paper addresses the challenge of simultaneously compensating for state-dependent uncertainties and enforcing time-varying state constraints in Euler-Lagrange systems, a common requirement in robotics that remains underserved by existing control designs. A novel adaptive control framework is developed that combines an artificial time-delay-based uncertainty estimation strategy, also known as time-delay estimation, with a barrier Lyapunov function to enforce constraint-aware control design. Specifically, a state-dependent upper bound on the time-delay estimation approximation error is analytically formulated, and an adaptive law is constructed to estimate its parameters online, enabling real-time state-dependent uncertainty compensation without relying on prior model knowledge. To ensure constraint compliance, the barrier Lyapunov function-based controller enforces time-varying bounds on both position and velocity. The resulting architecture is provably stable via Lyapunov analysis. Experimental results on a five-degree-of-freedom robotic manipulator validate the framework's capability, compared with the state of the art, in maintaining strict adherence to safety-critical constraints under dynamic uncertainties.
Saksham Gupta, Rishabh Dev Yadav, Sarthak Mishra +5
Robotics Research Center, International Institute of Information Technology Hyderabad, India · Department of Computer Science, University of Manchester, UK · Autonomous Systems and Automatic Control in School of Engineering, Newcastle University, UK +1
The control of agile quadrotors in dynamic and uncertain environments remains an open area of investigation to this day, particularly when the complete system dynamics are partially known or highly nonlinear. This work introduces a novel machine learning-based feedback-linearization control framework that employs a Gaussian Radial Basis Function (RBF) neural network (NN) to model and compensate for unmodeled dynamics in real time. The proposed controller leverages the universal approximation capability of RBF networks to model nonlinearities and uncertainties. An online adaptation of the RBF NN updates the network's weights without prior training. The control law is derived using the Lyapunov stability theory, herein guaranteeing closed-loop stability and providing theoretical guarantee of asymptotic convergence of a trajectory tracking task. Gazebo simulation and real flight experiments are conducted using the Bitcraze's Crazyflie 2.1 quadrotor subject to unmodeled air drag, actuator dynamics, and external disturbance. Despite incomplete knowledge of prior dynamics and presence of external disturbance such as air drag and drift in state estimation, the proposed controller improves trajectory tracking with rapid convergence and reduction of position-norm and yaw orientation RMSE by more than 7.13% and 49.27% respectively compared to baseline feedback linearization controller.
Amos Alwala, Gabriel da Silva Lima, Wallace Moreira Bessa
Smart Systems, Department of Mechanical and Materials Engineering, Faculty of Technology, University of Turku, 20520 Turku, Finland.