Department: Center for Control Systems and Dynamics (CCSD)
Name: David Szeto
Email: dszeto @ ucsd.edu
Grad Year: 2007
Sean Summers, ssummers @ ucsd.edu | David Zhang, solarbikedz @ gmail.com
A model predictive control (MPC) approach is presented here for unstable mobile robots. We are currently applying this approach to two unstable robotic systems in our lab: a dual inverted pendula system and a three-wheeled rover that can swing up and balance in a "Segway"-like two-wheel configuration. These two canonical examples contain the essential features of a wide range of other mechanical systems that may be controlled using this technique. The former system is smoothly differentiable but the system trajectory must be constrained because of the physical limitations of the experimental hardware; in addition, the actuator inputs must be constrained to avoid saturation. The latter system presents the additional complication of a sudden change in the system model when the rover goes from one configuration to another. In order for these robots to complete a variety of difficult maneuvers, MPC determines the appropriate sequence of actuator inputs (a.k.a. control sequence), assuming accurate knowledge of the system model and the system's initial conditions. The desired trajectory is determined by the model, system's initial conditions and the control sequence. This MPC approach is an adjoint-based optimization, which is a gradient-based optimization. Though this iterative approach does not guarantee global minimization of the non-convex optimization problem, it usually leads to a satisfactory control sequence that accurately achieves the desired result even in the complex nonlinear systems considered in this investigation.
In real world application, deviations from the desired trajectory arise from modeling errors, external state disturbances and measurement noise during the actual maneuver. The deviations from the desired trajectory are minimized by using linear quadratic Gaussian (LQG) feedback control. The calculation of the necessary control and estimation gains consist of two stages: a finite-horizon linear time varying (LTV) stage and an infinite-horizon linear time invariant (LTI) stage. The LTV stage rejects disturbances from the desired trajectory during the maneuver, while the LTI stage stabilizes the possibly unstable state equilibrium reached after the maneuver.
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