Port-Hamiltonian control of a brachiating robot via generalized canonical transformations

This paper is devoted to the design of a port Hamiltonian controller for different scenarios of brachiation movement by a two-link bio-inspired robot called brachiating robot. A unified technique for trajectory tracking control problem of nonholonomic (drift-less) port Hamiltonian systems was introduced in the past, which exploits a generalized canonical transformation to form an error system in order to convert the trajectory tracking problem into a stabilization one. Although the method is novel and promising, only fully actuated systems are considered and success of the approach relies on the possibility of solving a set of partial differential equations (PDEs). Considering the fact that the brachiating robot is an underactuated system which suffers from lack of control input, the control problem is demanding and solving the PDEs remains the main stumbling block for an applicability of the aforementioned technique to our problem. By exploiting insight to the intrinsic properties of the underactuated system and using some math tricks, we solve the PDEs explicitly and shape the kinetic and potential energy of the brachiating robot within the port Hamiltonian framework so that the brachiating maneuver is performed efficiently and without any redundant backward movements. Furthermore, the trajectory tracking control is proved thanks to the passivity property of the system. This paper opens up the way to deal with underactuated control problems in a different and broader framework and the method demonstrates promising outcomes in the analysis and simulation as will be showed here.