Whenrobots physically interact with the environment, compliant behaviors should be imposed to prevent damages to all entities involved in the interaction. Moreover, during physical interactions, appropriate pose controllers are usually based on the robot dynamics, in which the ill-conditioning of the joint-space inertia matrix may lead to poor performance or even instability. When the control is not precise, large interaction forces may appear due to disturbed end-effector poses, resulting in unsafe interactions. To overcome these problems, we propose a task-space admittance controller in which the inertia matrix conditioning is adapted online. To this end, the control architecture consists of an admittance controller in the outer loop, which changes the reference trajectory to the robot end-effector to achieve a desired compliant behavior; and an adaptive inertia matrix conditioning controller in the inner loop to track this trajectory and improve the closed-loop performance. We evaluated the proposed architecture on a KUKA LWR4+ robot and compared it, via rigorous statistical analyses, to an architecture in which the proposed inner motion controller was replaced by two widely used ones. The admittance controller with adaptive inertia conditioning presents better performance than with a controller based on the inverse dynamics with feedback linearization, and similar results when compared to the PID controller with gravity compensation in the inner loop.
The ill-conditioning of the inertia matrix of serial manipulators is a problem intrinsic to multilink open serial chains, which may potentially reduce the accuracy and performance of most motion control techniques based on the robot's dynamic model. In more extreme cases, the ill-conditioning can even result in unstable behavior. In order to solve this, an adaptive control law is applied to the robot to improve the matrix conditioning while ensuring that the well-conditioned inertia matrix is positive definite and hence continues to have physical meaning. Simulation results on a serial manipulator with seven degrees of freedom show that the proposed control law outperforms other commonly used techniques in terms of smoother behavior, smaller steady-state error, and smaller condition number of the inertia matrix.
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