Abstract
Trajectory tracking is a common application method for manipulators. However, the tracking performance is hard to improve if the manipulators contain flexible joints and mismatched uncertainty, especially when the trajectory is nonholonomic. On the basis of the Udwadia–Kalaba Fundamental Equation (UKFE), the prescribed position or velocity trajectories are creatively transformed into second-order standard differential form. The constraint force generated by the trajectories is obtained in closed form with the help of UKFE. Then, a high-order fractional type robust control with an embedded fictitious signal is proposed to achieve practical stability of the system, even if the mismatched uncertainty exists. Only the bound of uncertainty is indispensable, rather than the exact information. A leakage type of adaptive law is proposed to estimate such bound. By introducing a dead-zone, the control will be simplified when the specific parameter enters a certain area. Validity of the proposed controller is verified by numerical simulation with two-link flexible joint manipulator.
Highlights
Define the link angle vector q1 = [q11 q12 ] T ; the joint angle vector q2 = [q21 q22 ] T ; m1, m2 are the mass of links; l1 is the length of the first link; lc1, lc2 are the centroid of the links; i11, i12 and i21, i22 are the moment of inertia of link and angles, respectively; τ = [τ1 τ2 ] T denotes the torques from motors; K1, K2 are the stiffness of linear torsional springs; and g is the gravity coefficient
This research is on the basis of the frame built by Udwadia and Kalaba
The desired trajectory is not used to obtain the position error directly. It is treated as a constraint applied to the system and utilized to acquire the constraint force
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. As manipulators are widely used in aerospace, medical, machining, and other fields, the flexibility is a non-negligible problem while optimizing the control performance [3,4,5] In practical applications, it is often necessary for flexible joint manipulator (FJM) to follow a prescribed trajectory. Chen illustrated the conception of constraint-following control systematically ( called constraint servo control) [20,21,22] On this basis, Xu et al designed the trajectory tracking control law for uncertain systems by combining with fuzzy control [23]. The existing applications have proved the validity of UKFE It would be an efficient method for the control of trajectory tracking for FJM, as such field is not sufficiently investigated. A leakage type adaptive law is designed for the estimation of such unknown bound information
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