Adaptive control of redundant robot manipulators with sub-task objectives

Abstract

In this paper, adaptive control of kinematically redundant robot manipulators is considered. An end-effector tracking controller is designed and the manipulator's kinematic redundancy is utilized to integrate a general sub-task controller for self-motion control. The control objectives are achieved by designing a feedback linearizing controller that includes a least-squares estimation algorithm to compensate for the parametric uncertainties. I. INTRODUCTIONWhen the number of joints of a robot manipulator is greater than the dimension of its task-space position vector then it is called a kinematically redundant robot manipulator. In many applications, robot manipulators with such additional degrees of freedom are preferred to execute complicated tasks. This kinematic redundancy can result in joint motion in the null space of the Jacobian matrix that does not affect the end-effector position, this phenomenon is commonly referred to as self-motion. There are generally an infinite number of solutions for the inverse kinematics of redundant robot manipulators [1], [2], [3], this complicates the control of kinematically redundant robot manipulators since it is difficult to select a reasonable desired joint trajectory for a given desired task-space trajectory.In our previous work [4], an adaptive full-state feedback quaternion based controller developed in [5] was utilized and a general sub-task controller was designed. In [4], the sub-task controller was systematically integrated into the stability analysis and specific sub-task objectives (such as singularity avoidance, joint limit avoidance, bounding the impact forces and bounding the potential energy) were introduced to make use of the kinematic redundancy. In [6], configuration control of redundant robot manipulators was investigated. The proposed controller achieved taskspace tracking and the redundancy was utilized to impose kinematic and dynamic constraints or posture control. In [7], Hsu et al. proposed a dynamic feedback linearizing control law that guarantees asymptotic tracking of a desired task-space trajectory. However, the controller in [7] required

ROMANSY 21 - Robot Design, Dynamics and Control

“…In this work, utilizing (7) to formulate the objective function as shown in (8), impact force sub-task objective is defined to limit the impact force with the environment at the lowest level as used by Tatlicioglu et al (2009).…”

Adaptive operational space control of redundant robot manipulators

“…To apply joint force τ according to (10), an estimateĴ of the dynamically consistent generalized inverseJ, is required. However,J is also nonlinearly parameterized as follows:…”

“…In the previous section, two groups of nonlinearly parameterized uncertainties have been described, one appearing in the generalized inverseJ in the applied torque (10), and another in the left hand side of the operational space dynamics (11). We tackle the former by using a modified quadratic control Lyapunov function to directly handle the nonlinear parametrization ofJ.…”

“…To improve control performance, multi-rate operational control [9] has been proposed, in which joint command is computed using the operational space formulation in an outer loop, and the joint space robot dynamics is feedback linearized in an inner loop. Other methods of adaptive task space control for redundant robots, but which depart from the operational space control formulation [5], can be found in [10], [11], [12]. These methods employ some forms of pseudo-inverse for kinematic resolution of the desired joint trajectories, followed by control of robot dynamics to track the desired joint trajectories.…”

Redundantly actuated 3-RRR spherical parallel manipulator used as a haptic device: improving dexterity and eliminating singularity

“…In singular configurations a manipulator loses one or more of its degrees of freedom (d.o.f.s). Redundancy can be used for both force control 6 and motion control 7,8 in order to improve the kinematic and dynamic performances of both serial and parallel manipulators. 3,4 However, by improving the kinematic behavior, the parallel robot structure becomes larger and a problem of interference is generated.…”