This paper presents a general method for generating walking primitives for anthropomorphic 3D–bipeds. Corresponding control torques allowing straight ahead walking with pre–swing, swing, and heel–contact are derived by dynamic optimization using a direct collocation approach. The computed torques minimize an energy based, mixed performance index. Zero moment point (ZMP) and friction conditions ...

Biped locomotion created by a controller based on Zero-Moment Point [ZMP] known as reliable control method looks different from human’s walking on the view point that ZMP-based walking does not include falling state. However, the walking control that does not depend on ZMP is vulnerable to turnover. Therefore, keeping the walking of dynamical motion stable is inevitable issue for realization of...

The control of a biped humanoid is a difficult task due to the hard-to-stabilize dynamics. Walking reference trajectory generation is a key problem. Reference generation techniques with the so-called Linear Inverted Pendulum Model (LIPM) are reported. Improved versions of the LIPM based reference generation are obtained by applying the Zero Moment Point (ZMP) Criterion, widely employed in the s...

The integrated dynamic control of humanoid locomotion mechanisms based on the spatial dynamic model of humanoid mechanism is presented in this paper. The control scheme was synthesized using the centralized model with proposed structure of dynamic controller that involves two feedback loops: position-velocity feedback of the robotic mechanism joints and reinforcement learning feedback around Ze...

This paper gives numerical examples showing that non-self-similar collapse can occur in the motion of four point vortices on a sphere. It is found when the four-vortex problem is integrable, in which the moment of vorticity vector is zero. The non-self-similar collapse has significant properties. It is partial in the sense that three of the four point vortices collapse to one point in finite ti...

There are several ways of proving Central Limit Theorems: 1. Use characteristic or moment generating functions or some distributional transform, or 2. Use moment method to show that the k-th moment converges to the k-th moment of standard Normal for all k > 1, or 3. Use Fixed Point method (e.g., maximizing entropy given fixed mean and variance, zero bias transformation etc.) or 4. Replacement o...

We describe the finite volume effects of CP-odd quantities, such as the neutron electric dipole moment and the anapole moment in the θ-vacuum, under different topological sectors. We evaluate the three-point Green’s functions for the electromagnetic current in a fixed non-trivial topological sector in order to extract these CP-odd observables. We discuss the role of zero modes in the CP-odd Gre...