A novel method to compute the contact force in forward dynamics simulation of rigid bodies based on contact volume is proposed. The conventional methods are based on contact vertices, where the normal and tangential directions are estimated with respect to each pair of facets or facet and vertex of colliding bodies. However, the normal direction is intrinsically determined based on the solid deformation. This paper proposes a novel method that combines the constraint-based method and the volumetric intersection computation. Since the method estimates a 6-axis resultant force directly, there are two problems that are how to predict the preferred deformation of the volume and how to confirm the friction limit. The idea is to apply the least-square method for the former and to check if the computed force can be resolved into each stress within the friction limit. The proposed method checks the condition with linear programming method through a pyramidal approximation.

An efficient method to compute the joint friction torques as well as the external contact forces in forward dynamics simulation of a robot manipulator is proposed. The existence of friction inside mechanical gears substantially affects behaviors of the robot, and hence, should be taken into account. The strict form of the equation of motion disables distinguishing the internal friction torques from the external forces, which causes an increase of the degree of indeterminacy and the computation cost. A semi-implicit approach in which the internal friction torques and the external contact forces are alternatively computed is proposed based on an assumption that the net joint actuation torque does not much vary in a short interval. It significantly reduces the computation cost at a comparative accuracy with a completely implicit method.

This paper proposed a novel forward dynamics computation method which complexity is O(n) where n is the number of bodies. In this method, contact constraints based on the macroscopic method are relaxed by regularization technique, thereby the numerical stability is improved. The relaxation causes larger penetrations at contact points, which are compensated the penetrations at the momentum-level by low computation cost. In addition, a novel friction model was proposed. This model enables to compute the static friction more stably. The performance of the proposed method was evaluated by comparing with the microscopic and macroscopic methods with simulation of 6DOF pendulum's motion.