  Despite the extensive presence of the legged locomotion in animals, it is
extremely challenging to be reproduced with robots. Legged locomotion is an
dynamic task which benefits from a planning that takes advantage of the
gravitational pull on the system. However, the computational cost of such
optimization rapidly increases with the complexity of kinematic structures,
rendering impossible real-time deployment in unstructured environments. This
paper proposes a simplified method that can generate desired centre of mass and
feet trajectory for quadrupeds. The model describes a quadruped as two bipeds
connected via their centres of mass, and it is based on the extension of an
algebraic bipedal model that uses the topology of the gravitational attractor
to describe bipedal locomotion strategies. The results show that the model
generates trajectories that agrees with previous studies. The model will be
deployed in the future as seed solution for whole-body trajectory optimization
in the attempt to reduce the computational cost and obtain real-time planning
of complex action in challenging environments.
