Extended Kalman Filtering-Based Nonlinear Model Predictive Control for Underactuated Systems With Multiple Constraints and Obstacle Avoidance

Underactuated systems are a class of systems in which the number of control inputs is less than the degrees of freedom (DoFs) to be controlled. With the increasing demand for the control performance of underactuated systems, the current research on their optimization of steady-state performance is no longer sufficient. However, owing to limited control inputs, ensuring their transient performance is often difficult. Moreover, some specific composite variables in underactuated systems should be kept within the preset ranges, which poses a significant challenge to collision avoidance safety. In addition, the sensor noises are also an issue that cannot be ignored. To this end, an extended Kalman filtering-based nonlinear model predictive control method for underactuated systems is developed in this article. The key feature of this method is that it simultaneously ensures accurate positioning, multiple constraints, and obstacle avoidance. Specifically, by adding an artificial potential field as an obstacle avoidance penalty term in the cost function and dynamically assigning weight coefficients, efficient collision avoidance control is achieved. Furthermore, it is combined with the extended Kalman filtering and jointly applied to underactuated systems with sensor noises. To the best of our knowledge, it is the first control method that simultaneously considers full-state constraints, specific composite variable constraints, control input and its increment constraints, as well as obstacle avoidance in underactuated systems. The satisfactory control performance of the proposed method is validated by implementing it on two typical underactuated systems, that is, four-DoF overhead cranes and five-DoF tower cranes.