Kinematic and Dynamic Analysis of Quadruped Legged Robots: A New Formulation Approach

This paper presents a framework for efficient kinematic and dynamic modelling of a quadruped robot using the recursive Newton-Euler method. The robot features 12 actuators—three per leg—and is analysed under both static walking and dynamic trotting gaits. The formulation incorporates assumed ground reaction forces and system over-constraints, enabling the resolution of contact forces through a reduced set of six linear equations. Twelve generalized coordinates are used for static gait analysis, with an additional generalized coordinate introduced for dynamic trotting. Body attitude, velocity, and acceleration are derived from joint-space trajectories, and forward dynamics is computed by inverting the inverse dynamics equations by numerically evaluating the mass matrix and nonlinear torque vectors. By employing a reduced set of generalized coordinates and simplified constraint handling of ground reactions, the proposed framework streamlines rigid-body dynamic simulation for such a high-degree-of-freedom system.