Dynamic Modeling and SDRE Control of Biped Robot Locomotion

These codes show the kinematics, gait locomotion, dynamics, and control of a biped system without impact modeling using the SDRE controller.

The codes are related to the published paper:

Ali Mohamad Shafei, Reza Fazel, and Saeed Rafee Nekoo, "Dynamic modeling and nonlinear finite-time optimal control of biped robot locomotion: asymptotic motion control removes impact modeling," International Journal of Dynamics and Control 13, 327 (2025).

DOI: https://doi.org/10.1007/s40435-025-01835-y

The dynamics of the biped locomotion systems are hybrid complex equations with several phases, including stance, impact, and swing, periodically in transition. The impact phase on the dynamic provides an initial condition of the next phase as a function of the velocity of the joints, right before the contact with the ground. This work aims to propose a method for modeling and controlling a biped locomotion system with zero-velocity switching to omit the complexity of impact modeling. The impact dissipates energy, and the application of this work is headed toward the smooth optimal robot locomotion; however, smooth locomotion might be slow, which would be a drawback. Conventional controllers show asymptotic convergence by infinite-time horizon designs. The finite-time state-dependent differential Riccati equation (SDDRE) is proposed for the asymptotic zero-velocity impact control of the biped system. The finite-time characteristic of the SDDRE regulates the state velocities in a short proper time for obtaining a natural switching between steps. The SDDRE and faster convergence make the proposed approach a good option for the application of bipedal systems without impact for the sake of energy consumption, precise locomotion, or places that require no jump, such as space without gravity in which a jump could lead to instability in the system. The simulation results have been done for a biped robotic system with a six-degree-of-freedom model: two legs and a trunk, for an arbitrary number of steps. The steps are defined by introducing the points for the trunk and the swing leg in a regulation (point-to-point) framework. Zero-moment point criterion is considered to guarantee the stability of walking in modeling and simulations.

Video link: https://www.youtube.com/watch?v=SBOYX63mK5Y