Transport manipulator in a viscous medium: energy-saving motion algorithms (Q1881937)

The authors consider an optimization problem for the transport manipulator motion in a viscous medium of Lagrange type. They use the simplest model of a manipulator in the form of a lumped mass for every link, which is assumed absolutely rigid. The equations of motion are represented using Christoffel symbols of the first kind. For the cost functional, the authors use a condition of minimal work to overcome the medium resistance. So in the corresponding Hamiltonian the resistance power of the viscous medium is included. The problem is solved by means of methods based on the maximum principle. Remarks: It is not clear why the term \({\partial S_k\over\partial q}\) is the Fréchet derivative.