Computational Enhancement of the SDRE Scheme: General Theory and Robotic Control System

Li Gang Lin, Ming Xin

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


This article presents a new efficient variant of the state-dependent Riccati equation (SDRE) scheme in a general scope, by analytically alleviating the computational burden in solving the pointwise algebraic Riccati equations (AREs). The novel contributions include a more efficient construction of feasible state-dependent coefficients (named alternative SDRE), which is critical at the early design stage, and more efficient solvability check for the classical SDRE scheme. For the selected robotic application-balance control of a two-wheeled robot, the contribution lies in the system-specific analysis that further enhances the computational performance toward an agile mobility. This novelty is with respect to a state-of-the-art ARE solver. An offline/a priori analytical formulation replaces the very first stage of the solving process, which more efficiently integrates the ARE solver into the SDRE design framework. Notably, all the results not only benefit the classical SDRE scheme but, more significantly, favor the proposed alternative SDRE owing to its much better computational efficiency-mainly in terms of time while promisingly for memory saving. In addition, simulations reveal more potential advantages using the variants-such as the control effort efficiency or required regulation time-within and beyond the scope of SDRE.

Original languageEnglish
Article number9082821
Pages (from-to)875-893
Number of pages19
JournalIEEE Transactions on Robotics
Issue number3
StatePublished - Jun 2020


  • State-dependent Riccati equation (SDRE)
  • computational analysis
  • two-wheeled robot (TWR)
  • underactuated and nonholonomic system


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