Abstract:
Two-wheeled robots, with a centre of mass above the wheel axles, are statically unstable systems. Therefore, a controller is required to actively stabilize the system. Conventional controllers are unaware of traction limits on low-traction surfaces, so when the wheels lose traction, the two-wheeled robot topples. The main objective of this work is to develop a controller suitable for low-traction surfaces and increase the performance envelope of the two-wheeled robot. In this thesis, a robust linear model predictive controller (MPC) suitable for low-traction surfaces is developed. MPC explicitly accounts for motor and traction constraints so it can optimally track a reference velocity unless a constraint would be violated. The linear MPC is made robust against linearization error and model uncertainty by using the constraint tightening approach, which requires no additional online computation. The constraint tightening margins are minimized using Disturbance Feedback Mapping Optimization (DFMO), a novel method developed to find the optimal non-linear time-varying control policy. Implementation on a mobile robot demonstrates that the proposed MPC design is practical. A conventional linear quadratic regulator (LQR) is designed as a baseline controller, with a cost function that matches the MPC. To allow LQR to balance on low-traction surfaces, a reference governor is used to limit the reference velocity and acceleration. Assuming advance knowledge of transitions in friction coefficient, a method of dynamically changing the traction constraints in MPC is demonstrated in simulation. The system parameters are experimentally measured and also estimated by system identification, showing that the derived equations of motion substantially represent the longitudinal 2D dynamics of the two-wheeled robot. Friction and wheel slip behaviour of the two-wheeled robot are experimentally investigated and a friction model is parameterized to approximate the test surfaces. In simulation and experimental testing, both MPC and reference governor approaches prevent toppling if properly tuned. However, MPC is more flexible with a model-based approach, whereas tuning the reference governor depends on empirical testing. Results show that the proposed MPC with a Coulomb friction model is robust to the behaviour of friction of real surfaces as well as different models of friction.