Purpose
The purpose of this paper is to simplify the Explicit Nonlinear Model Predictive Controller (ENMPC) by linearizing the trajectory with Quantum-behaved Pigeon-Inspired Optimization (QPIO).
Design/methodology/approach
The paper deduces the nonlinear model of the quadrotor and uses the ENMPC to track the trajectory. Since the ENMPC has high demand for the state equation, the trajectory needed to be differentiated many times. When the trajectory is complicate or discontinuous, QPIO is proposed to linearize the trajectory. Then the linearized trajectory will be used in the ENMPC.
Findings
Applying the QPIO algorithm allows the unequal distance sample points to be acquired to linearize the trajectory. Comparing with the equidistant linear interpolation, the linear interpolation error will be smaller.
Practical implications
Small-sized quadrotors were adopted in this research to simplify the model. The model is supposed to be accurate and differentiable to meet the requirements of ENMPC.
Originality/value
Traditionally, the quadrotor model was usually linearized in the research. In this paper, the quadrotor model was kept nonlinear and the trajectory will be linearized instead. Unequal distance sample points were utilized to linearize the trajectory. In this way, the authors can get a smaller interpolation error. This method can also be applied to discrete systems to construct the interpolation for trajectory tracking.
A bilevel optimization approach for D-invariant set design**The research leading to these results has benefited from the financial support of the European Union’s 7th Framework Programme under EC-GA No. 607957 TEMPO - Training in Embedded Model Predictive Control and Optimization