Research Topic: Advanced Modeling of Biped Locomotion (Humans and Humanoids) – Kinematic and Dynamic Models of Biped Locomotion

The R/D objectives concern with advanced modeling of human and humanoid biped locomotion, biped kinematics and dynamics, dynamic balance characteristics (Zero Moment Point), body performances, modeling of ground support compliance, etc. R/D activities resulted in design of the HRSP (Humanoid Robot Simulation Platform), software toolbox for Matlab/Simulink dedicated to the researchers in bio-mechanics and robotics.

Biped robots (humanoids), being the future of robotic science, are becoming more and more human-like in all aspects of their functioning. It is expected that they will replace humans in a variety of tasks. Thus, it is generally accepted that their shape and motion should be based on bio-mechanical principles – to be bio-inspired. Because of the complexity and high requirements imposed on such robots, their control system has to utilize kinematic and dynamic models. In that sense, the control, design, and simulation, strongly require accurate dynamic models that will make humanoid robots capable of handling the increasing diversity of expected tasks. As the result of this research/developing project, a user-friendly simulation software of human/humanoid kinematics and dynamics was developed. Modeling software was realized as a MATLAB/SIMULINK toolbox using all advances of the Matlab programming interface. Designed spatial, non-linear model concerns with structure of a biped mechanism with 38 d.o.f. (6 basis, 6 body trunk, 2 x 7 legs, 2 x 6 arms, see Fig. 1).

Kinematic scheme of a 38 d.o.f. biped locomotion mechanism (human or humanoid)
assumed for modeling and simulation.

Fig. 1. Kinematic scheme of a 38 d.o.f. biped locomotion mechanism (human or humanoid) assumed for modeling and simulation.

It includes complete kinematical and dynamic models as well as model of the foot impact dynamics (6 d.o.f. compliance model of the support layer) in all phases of biped gait: single support, double support and flyer phase (running with no contact with the environment). The assumed model represents the compromise between the numerical complexity to be run on the PC computer and accuracy concerning anthropomorphic characteristics of locomotion.

Human body, for its complex motion, uses synergy of more than 600 muscles. It has more then 300 degrees of freedom. Some of these particular motions are essential for the human activities (gait, work, sport, dancing, etc.) while the others give it a full mobility. A biped locomotion mechanism of the anthropomorphic structure (presented in Fig. 1) was considered as a mechanical representative of a human body. In that sense, an articulated system consisting of the basic kinematic chain and four side branch chains, was considered as a biped mechanism. In a mechanical sense, it represents a multi-body, large-scale dynamic system with a variable structure (Fig. 2).

a) Branched mechanism of a biped locomotion system, b) Decomposition of the complex mechanism structure into the set of the single chains.

Fig. 2. a) Branched mechanism of a biped locomotion system, b) Decomposition of the complex mechanism structure into the set of the single chains.

Developed modeling and simulation software interface enable calculation: Jacobians, Descartes coordinates of particular joint centers, corresponding velocities and accelerations of joint centers, feet positions/orientations relative to the supporting surface, whole mechanism inertia matrix, vector of centrifugal, Coriolis and gravitational forces/torques, contact/impact forces (ground reaction forces/torques), driving torques acting into the robot joints and Zero Moment Point (ZMP) location with respect to the supporting polygon defined by biped feet. For more details about modeling and simulation of biped locomotion systems please refer to the HRSP modeling software.

Samples of the biped robot locomotion – simulation of kinematics and dynamics

Fig. 3. Samples of the biped robot locomotion – simulation of kinematics and dynamics.