Real-time crowd simulation is a challenging task that demands a careful consideration of the classic trade-off between accuracy and efficiency. Existing particle-based methods have seen success in simulating crowd scenarios for various applications in the architecture, military, urban planning, robotics, and entertainment (film and gaming) industries. In this paper we focus on local dynamics an...

In the paper, by establishing the monotonicity of some functions involving the sine and cosine functions, the authors provide a unified and concise proof of some known inequalities and find some new sharp inequalities involving the Seiffert, contra-harmonic, centroidal, arithmetic, geometric, harmonic, and root-square means of two positive real numbers a and b with a = b . Mathematics subject c...

In this paper we propose distributed algorithms to automatically deploy a group of robotic agents and provide coverage of a discretized environment represented by a graph. We present a discrete coverage algorithm which converges to a centroidal Voronoi partition while requiring only pairwise “gossip” communication between the agents. Our theoretical analysis is based on a dynamical system on pa...

The zero moment point (ZMP), foot rotation indicator (FRI) and centroidal moment pivot (CMP) are important ground reference points used for motion identification and control in biomechanics and legged robotics. In this paper, we study these reference points for normal human walking, and discuss their applicability in legged machine control. Since the FRI was proposed as an indicator of foot rot...

It is well known that the complexity, i.e. the number of vertices, edges and faces, of the 3-dimensional Voronoi diagram of n points can be as bad as (n2). It is also known that if the points are chosen Independently Identically Distributed uniformly from a 3-dimensional region such as a cube or sphere, then the expected complexity falls to O(n). In this paper we introduce the problem of analyz...