Stabilizing Model Predictive Control for Wheeled Mobile Robots with Linear Parameter-Varying and Different Time-Scales

Control of Flexible Manipulator Robots Based on Dynamic Confined Space of Velocities: Dynamic Programming Approach

“…Since h(q, q) can be associated with unknown dynamics, acceptable control performance of (1) depends on efficient computing of h(q, q). Although algorithms based on the inverse dynamic method 2 , as well as corrective methods for systems with fast and slow dynamics 3 , have been widely used to solve this problem, the work reported here, likewise in [55], considers that E 1 (θ) Z 3 (q)h(q, q) and E 2 (θ) G 3 (q)h(q, q) admit a polytopic representation.…”

“…Without loss of generality, by using the T. Kato's method [66], like in [55], the system ( 5)-( 6) can be decoupled in two time-scales, as follows:…”

“…Model predictive control (MPC) has also become a suitable control strategy for handling constrained manipulator robots with input constraints that aim for reasonable behavior forecasts [50]- [54]. However, although MPC performs better than LQR due to its moving time horizon window, in robotic systems, its numeric complexity is increased when two time-scales and parameter varying related to links' guidance are considered [6], [38], [55]. Currently, some techniques suggest a lower computational effort using polytopic representations of the input/output constraints on dynamic programming (DP) methods for linear parameter varying (LPV) [52], [55], [56].…”

“…However, although MPC performs better than LQR due to its moving time horizon window, in robotic systems, its numeric complexity is increased when two time-scales and parameter varying related to links' guidance are considered [6], [38], [55]. Currently, some techniques suggest a lower computational effort using polytopic representations of the input/output constraints on dynamic programming (DP) methods for linear parameter varying (LPV) [52], [55], [56]. But, although DP's methods reduce the computational cost, this approach is poor for velocity changing.…”

Oriented manifold-based error tracking control for nonholonomic wheeled autonomous vehicles on Lie group for curvilinear approach

“…The global feedback control uε = uε(q, v) is projected by using the inverse dynamics of (2) and the second derivative of (1). Thus, Eliminating Lagrange multipliers in (2) and using the relation (23) give consequently, the law uε is defined by the inverse of ( 24): By substituting ( 25) in ( 24) is obtained ρ = ˙v, and, by substituting ( 16) and ( 1 techniques when the slipping is included into the dynamic model [29,20] whenever the kinematic controller is synthesized on an oriented manifold M. Unlike contributions which use manifolds of µ in order to linearize the dynamic model [17,41,14,15], the work reported here includes the flexibility (represented by parameter ε) within the kinematic model (see the inclusion of ε and ξ in ( 10)-( 12) and ( 15), respectively).…”