Nonlinear Control of Two-Wheeled Robot Based on Novel Analysis and Design of SDRE Scheme

This brief presents a nonlinear control design for a two-wheeled inverted pendulum robot, based on new analysis of the classical state-dependent Riccati equation (SDRE) scheme and a novel alternative strategy. The solvability of pointwise algebraic Riccati equations (AREs) corresponding to the nonunique state-dependent coefficients (SDCs) of the SDRE scheme is analyzed from a new perspective. This is formulated as a simple equivalence condition with reduced dimensionality, which circumvents the excessive online computational effort to check the solvability of classical SDRE. The condition is derived in a way to facilitate the generalization to all meaningful SDCs. Moreover, due to unsolvable AREs, all conflicts against the primary objective of posture balance of the robot are revealed and illustrated, with a connection to the robot physical parameters. At the system states that cause such conflicts and other unsolvable AREs, a simple analytical solution via alternative SDC constructions is suggested. More potential advantages of this SDC construction over the classical scheme are revealed in simulations, e.g., the maximum input/torque and total energy consumption.