Robust tracking control of kinematically redundant robot manipulators subject to multiple self-motion criteria

Abstract

SUMMARYIn this study, we consider a model based robust control scheme for kinematically redundant robot manipulators that also enables the use of self motion of the manipulator to perform multiple sub-tasks (e.g., maintaining manipulability, avoidance of mechanical joint limits, and obstacle avoidance). The controller proposed ensures uniformly ultimately bounded end-effector and sub-task tracking despite the parametric uncertainty associated with the dynamic model. A Lyapunov based approach has been utilized in the controller design and extension to a non minimum set of parameters for orientation representation has been presented to illustrate the flexibility of the approach. Extensive simulation studies performed initially on a 3 link planar robot arm (for the planar case) and on a six degree of freedom (DOF) Puma type robot arm (for the 3D case with quaternion feedback) are presented to demonstrate the capabilities and the performance of the controller. The results were then experimentally tested on an actual Puma 560 robot to illustrate the feasibility of the proposed method.

Robust Task Space Finite-Time Chattering-Free Control of Robotic Manipulators

“…denotes a filtered tracking error signal [38,39]; Y = Y (e,ė, q,q) ∈ R 2×4 is the regression matrix; = max = 5. In order to speed up the convergence process of differentiators (39)- (40), (39)- (40), they are assumed for simplicity of computations in all the simulations to be equal, i.e., L e (t) = L q (t).…”

“…Moreover,Ḋ is equal toḊ = θ 5q + θ 6q . The control law proposed in [38,39] for linearly parametrizable continuous term D is given by the following expression: are assumed in this experiment to be fully known, i.e., the following equalities are now fulfilled:ˆ = nm ,θ 5 = θ 5,nm andθ 6 = θ 6,nm , respectively. In order to attain the convergence of task errors e less or equal to 10 −3 in approximately the same time, the following numerical values of gain coefficients for both controllers are taken:…”

“…In the absence of disturbances and under some sufficient conditions on gain parameters, control law from [47] is shown to ensure only globally ultimately bounded Cartesian tracking error. In the third approach, model based robust control schemes were proposed in works [38][39][40]. The controllers from [38,39] ensure uniformly ultimately bounded endeffector and sub-task tracking despite the parametric uncertainties associated with the dynamic equations, an upper bound on the parameter accuracy and globally bounded external disturbances.…”

“…In the third approach, model based robust control schemes were proposed in works [38][39][40]. The controllers from [38,39] ensure uniformly ultimately bounded endeffector and sub-task tracking despite the parametric uncertainties associated with the dynamic equations, an upper bound on the parameter accuracy and globally bounded external disturbances. A neural network based adaptive asymptotically stable control scheme, in the presence of model uncertainties and globally bounded external disturbances, has been designed in [40].…”

Nonlinear Robust Control of Tendon–Driven Robot Manipulators

“…Specifically, for the restrictive case of full state feedback (i.e., position and velocity information of both the actuators and robot links and tension measurements of each tendon) being available, and the robot dynamic model and the actuator dynamics including uncertain parameters is considered. Adding the dynamics of the power transmission system and considering tendon elasticity yield a complicated dynamic model, and the resulting system dynamics mandates the use the backstepping technique twice (unlike our previous work [18], where robust backstepping was applied only once). After fusing the backstepping design procedure with Lyapunov-type analysis tools, we design the auxiliary backstepping control inputs and the control input applied to the actuators.…”