Kinematics and Dynamics of a New 16 DOF Humanoid Biped Robot with Active Toe Joint

Humanoid biped robots are typically complex in design, having numerous Degrees-of-Freedom (DOF) due to the ambitious goal of mimicking the human gait. The paper proposes a new architecture for a biped robot with seven DOF per each leg and one DOF corresponding to the toe joint. Furthermore, this work presents close equations for the forward and inverse kinematics by dividing the walking gait into the Sagittal and Frontal planes. This paper explains the mathematical model of the dynamics equations for the legs into the Sagittal and Frontal planes by further applying the principle of Lagrangian dynamics. Finally, a control approach using a PD control law with gravity compensation was recurred in order to control the desired trajectories and finding the required torque by the joints. The paper contains several simulations and numerical examples to prove the analytical results, using SimMechanics of MATLAB toolbox and SolidWorks to verify the analytical results.