On singular values decomposition and patterns for human motion analysis and simulation

We are interested in human motion characterization and automatic motion simulation. The apparent redun- dancy of the humanoid w.r.t its explicit tasks lead to the problem of choosing a plausible movement in the framework of redun- dant kinematics. This work explores the intrinsic relationships between singular value decomposition at kinematic level and optimization principles at task level and joint level. Two task- based schemes devoted to simulation of human motion are then proposed and analyzed. These results are illustrated by motion captures, analyses and task-based simulations. Pattern of singular values serve as a basis for a discussion concerning the similarity of simulated and real motions

On least-cost path for realistic simulation of human motion

We are interested in "human-like" automatic motion simulation with applications in ergonomics. The apparent redundancy of the humanoid wrt its explicit tasks leads to the problem of choosing a plausible movement in the framework of redundant kinematics. Some results have been obtained in the human motion literature for reach motion that involves the position of the hands. We discuss these results and a motion generation scheme associated. When orientation is also explicitly required, very few works are available and even the methods for analysis are not defined. We discuss the choice for metrics adapted to the orientation, and also the problems encountered in defining a proper metric in both position and orientation. Motion capture and simulations are provided in both cases. The main goals of this paper are: to provide a survey on human motion features at task level for both position and orientation, to propose a kinematic control scheme based on these features, to define properly the error between motion capture and automatic motion simulation

On geodesic paths and least-cost motions for human-like tasks

We are interested in ”human-like” automatic mo- tion generation. The apparent redundancy of the humanoid wrt its explicit tasks lead to the problem of choosing a plausible movement in the framework of redundant kinematics. Some results have been obtained in the human motion literature for reach motion that involves the position of the hands. We discuss these results and a motion generation scheme associated. When orientation is also explicitly required, very few works are available and even the methods for analysis are not defined. We discuss the choice for metrics adapted to the orientation, and also the problems encountered in defining a proper metric in both position and orientation. Motion capture and simulations are provided in both cases. The main goals of this paper are : - to provide a survey on human motion features at task level for both position and orientation, - to propose a kinematic control scheme based on these features - to define properly the error between motion capture and automatic motion simulation

Strength Guided Motion

A methodology and algorithm is presented that generates motions imitating the way humans complete a lifting task under various loading conditions. The path taken depends on natural parameters: the figure geometry, the given load, the final destination, and especially, the strength model of the agent. Additional user controllable parameters of the motion are the comfort of the action and the perceived exertion of the agent. The algorithm uses this information to incrementally compute a motion path of the end effector moving the load. It is therefore instantaneously adaptable to changing force, loading, and strength conditions. Various strategies are used to model human behavior (such as pull back, add additional joints, and jerk) that compute the driving torques as the situation changes. The strength model dictates acceptable kinematic postures. The resulting algorithm offers torque control without the tedious user expression of driving forces under a dynamics model. The algorithm runs in near-realtime and offers an agent-dependent toolkit for fast path prediction. Examples are presented for various lifting tasks, including one- and two-handed lifts, and raising the body from a seated posture

Analysis and synthesis of bipedal humanoid movement : a physical simulation approach

textAdvances in graphics and robotics have increased the importance of tools for synthesizing humanoid movements to control animated characters and physical robots. There is also an increasing need for analyzing human movements for clinical diagnosis and rehabilitation. Existing tools can be expensive, inefficient, or difficult to use. Using simulated physics and motion capture to develop an interactive virtual reality environment, we capture natural human movements in response to controlled stimuli. This research then applies insights into the mathematics underlying physics simulation to adapt the physics solver to support many important tasks involved in analyzing and synthesizing humanoid movement. These tasks include fitting an articulated physical model to motion capture data, modifying the model pose to achieve a desired configuration (inverse kinematics), inferring internal torques consistent with changing pose data (inverse dynamics), and transferring a movement from one model to another model (retargeting). The result is a powerful and intuitive process for analyzing and synthesizing movement in a single unified framework.Computer Science

Inverse Kinematics with Dual-Quaternions, Exponential-Maps, and Joint Limits

We present a novel approach for solving articulated inverse kinematic problems (e.g., character structures) by means of an iterative dual-quaternion and exponentialmapping approach. As dual-quaternions are a break from the norm and offer a straightforward and computationally efficient technique for representing kinematic transforms (i.e., position and translation). Dual-quaternions are capable of represent both translation and rotation in a unified state space variable with its own set of algebraic equations for concatenation and manipulation. Hence, an articulated structure can be represented by a set of dual-quaternion transforms, which we can manipulate using inverse kinematics (IK) to accomplish specific goals (e.g., moving end-effectors towards targets). We use the projected Gauss-Seidel iterative method to solve the IK problem with joint limits. Our approach is flexible and robust enough for use in interactive applications, such as games. We use numerical examples to demonstrate our approach, which performed successfully in all our test cases and produced pleasing visual results.Comment: arXiv admin note: substantial text overlap with arXiv:2211.0033

The Reasonable Effectiveness of Mathematics in the Natural Sciences

One of the most unsettling problems in the history of philosophy examines how mathematics can be used to adequately represent the world. An influential thesis, stated by Eugene Wigner in his paper entitled The Unreasonable Effectiveness of Mathematics in the Natural Sciences, claims that the miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. Contrary to this view, this thesis delineates and implements a strategy to show that the applicability of mathematics is very reasonable indeed. I distinguish three forms of the problem of the applicability of mathematics, and focus on one I call the problem of uncanny accuracy: Given that the construction and manipulation of mathematical representations is pervaded by uncertainty, error, approximation, and idealization, how can their apparently uncanny accuracy be explained? I argue that this question has found no satisfactory answer because our rational reconstruction of scientific practice has not involved tools rich enough to capture the logic of mathematical modelling. Thus, I characterize a general schema of mathematical analysis of real systems, focusing on the selection of modelling assumptions, on the construction of model equations, and on the extraction of information, in order to address contextually determinate questions on some behaviour of interest. A concept of selective accuracy is developed to explain the way in which qualitative and quantitative solutions should be utilized to understand systems. The qualitative methods rely on asymptotic methods and on sensitivity analysis, whereas the quantitative methods are best understood using backward error analysis. The basic underpinning of this perspective is readily understandable across scientific fields, and it thereby provides a view of mathematical tractability readily interpretable in the broader context of mathematical modelling. In addition, this perspective is used to discuss the nature of theories, the role of scaling, and the epistemological and semantic aspects of experimentation. In conclusion, we argue for a method of local and global conceptual analysis that goes beyond the reach of the tools standardly used to capture the logic of science; on their basis, the applicability of mathematics finds itself demystified

Computational methods and software systems for dynamics and control of large space structures

Two key areas of crucial importance to the computer-based simulation of large space structures are discussed. The first area involves multibody dynamics (MBD) of flexible space structures, with applications directed to deployment, construction, and maneuvering. The second area deals with advanced software systems, with emphasis on parallel processing. The latest research thrust in the second area involves massively parallel computers