When Prioritization Meets Input-output Linearization: A Prioritized Multi-objective Control and Case Study with Two-link Manipulator

We discuss a control strategy to handle singularity of input gain matrix in the input-output linearization of a dynamical system with multiple outputs. The key idea is to prioritize the outputs and designate available control inputs to the outputs in the order of priority, by which tracking control for higher priority outputs is possibly maintained even in the presence of the singularity. This strategy of prioritization (called the prioritized control) allows to successfully deal with critical control objectives (such as stability and/or collision avoidance) by assigning higher priority to the relevant outputs. In this paper, we first explain how the prioritization can be applied to the process of input-output linearization and provide a definition of the prioritized control law on the framework of the multi-objective optimization with the lexicographical ordering. Then, a simple case study is performed for a two-link manipulator along with simulation results, where we further discuss an intrinsic degenerate property of prioritization that the prioritized control law can be discontinuous.