Unfalsified direct adpative control of a two-link robot arm (Q2719857)

This paper introduces the paradigm of unfalsified control into robotics and uses the principle of unfalsified control to design an adaptive tracking controller for the model of rigid manipulator dynamics NEWLINE\[NEWLINEQ(\theta, q)\ddot q+ C(\theta, q,\dot q)\dot q+ D(\theta, q)= uNEWLINE\]NEWLINE depending on a vector \(\theta\in \mathbb{R}^m\) of unknown parameters. A collection of computed torque controllers parameterized by \(\theta\), NEWLINE\[NEWLINEK_\theta= Q(\theta, q)(\ddot q_d- 2\lambda(\dot q_d-\dot q)- \lambda^2(q_d- q))+ C(\theta, q,\dot q)\dot q+ D(\theta, q),NEWLINE\]NEWLINE where \(q_d(t)\) denotes a desirable joint trajectory, \(\lambda> 0\), is chosen as admissible control laws. Performance specification of the closed-loop system is made by reference to a parameterized loss function. Input-output data from the robot are gathered on subsequent time intervals. The control strategy is the following: a controller defined by a specific value of \(\theta\) is applied as long as it remains unfalsified by comparing input-output data with performance specification. At an instant of falsification, the parameter is updated in accordance with a rule determined from the maximal distance from the boundary of the current unfalsified parameter set. The performance of the unfalsified adaptive controller has been assessed in simulations accomplished on the model of a 2 degree-of-freedom planar manipulator with different actuator bandwidth. A superiority of this controller over the adaptive Slotine-Li controller has been observed.