Project is devoted to the research of the novel methods of the design of underactuated walking for mechanical walking-like systems using the recently introduced methodology based on the so-called collocated virtual holonomic constraints. Currently, the use of the noncollocated virtual holonomic constraints prevails while the collocated ones may have the potential to handle better complexity of the design. Key theoretical problém to be addressed in this respect is the so-called hybrid invariance of the collocated constraints. Designed algorithms for walking design will be further analyzed using Poincare sections method and subsequently testred both in simulatins and using existing laboraty model of the walking robot. To do so, both theoretical investigation and practical application of the new identification and estimation methods for the underactuated mechanical systems will be included as well.