Adaptive control of a robotic system undergoing a non-contact to contact transition with a viscoelastic environment

Neural Network Control of a Robot Interacting With an Uncertain Hunt-Crossley Viscoelastic Environment

“…From the choice of the virtual control input in (17), an expression for can be developed which is continuous and does not require acceleration measurements. This fact can be used to show that the input to the NN is continuous and known.…”

“…Since the mass is to be controlled in the direction normal to the tissue surface, it is only required that be chosen such that the robot impacts the tissue surface. The closed-loop error system for the mass can be developed by substituting (17) into (16) as (19) Adding and subtracting to (19), and then using the Taylor series approximation in (12), the following expression for the closed-loop mass error system can be obtained (20) where the notation and is introduced in (12), and is defined as 1 The initial weights are selected in some compact set, then new estimates are generated based on the weight update laws in (18). If the weights on the boundary of the set are found to be directed outside the compact set, they are projected back into the set using a smooth projection algorithm (see [27], [28] for details).…”

“…However, the development in [17] assumed knowledge of the local deformation of the material raised to the Hertzian compliance exponent, which is usually difficult to determine [24]. One reason that exact knowledge of the Hertzian compliance exponent is required in [17] is that this effect does not satisfy the linear-in-the-parameters (LP) assumption. This limitation is overcome in this brief by the use of neural networks (NNs), which can approximate non-LP dynamics.…”

“…Experiments were performed where the robot collided with a stiff aluminum surface. Motivated by applications where the robot will collide with a compliant/viscoelastic surface, our preliminary work in [17] used the more general Hunt-Crossley contact model to account for the energy dissipation at contact. However, the development in [17] assumed knowledge of the local deformation of the material raised to the Hertzian compliance exponent, which is usually difficult to determine [24].…”

“…Motivated by applications where the robot will collide with a compliant/viscoelastic surface, our preliminary work in [17] used the more general Hunt-Crossley contact model to account for the energy dissipation at contact. However, the development in [17] assumed knowledge of the local deformation of the material raised to the Hertzian compliance exponent, which is usually difficult to determine [24]. One reason that exact knowledge of the Hertzian compliance exponent is required in [17] is that this effect does not satisfy the linear-in-the-parameters (LP) assumption.…”