Movimientos simétrico lineales esféricos segmentados para interpolación de orientaciones en planificación de trayectorias de herramienta en CNC de 5 Ejes

RESUMEN: Este artículo emplea biarcos cuaterniónicos para interpolar un conjunto de orientaciones con restricciones de velocidad angular. La curva cuaterniónica resultante representa un movimiento simétrico lineal esférico segmentado con continuidad C1 . El propósito de este esfuerzo es poner en uso los movimientos simétrico lineales desde el punto de vista de aproximación e interpolación de movimiento y presentar su potencial aplicación en la simulación de mecanizado por Control Numérico Computarizado (CNC) y planeación de trayectorias de herramienta. Los biarcos cuaterniónicos pueden ser usados para aproximar curvas B-spline cuaterniónicas que representan movimientos esféricos racionales, los cuales tienen aplicaciones en planeación de trayectorias de robots, en CAD/CAM y en gráficas por computador.ABSTRACT: This paper employs quaternion biarcs to interpolate a set of orientations with angular velocity constraints. The resulting quaternion curve represents a piecewise line-symmetric spherical motion with C1 continuity. The purpose of this effort is to put line-symmetric motions into use from the viewpoint of motion approximation and interpolation, and to present their potential applications in Computerized Numerical Control (CNC) machining simulation and tool path planning. Quaternion biarcs may be used to approximate B-spline quaternion curves that represent rational spherical motions that have applications in robot path planning, CAD/CAM and computer graphics

Online Motion Generation for Mirroring Human Arm Motion

Motion planning in robotics is a very large field of research. Many different approaches have been developed to create smooth trajectories for robot movement. For example there are optimization algorithms, which optimize kinematic or dynamic properties of a trajectory. Furthermore, nonlinear programming methods like e.g. optimal control, or polynomial based methods are widely used for trajectory generation. Most of these techniques are used to calculate a trajectory in advance, or they are limited to create point-to-point motions, where the robot needs to stop when switching to the next target point, especially, when interpolating in rotational space. In this paper, we combine a low-pass filter and spherical linear interpolation to realize a velocity-limited online trajectory generator for robot orientations in quaternion space. We use the developed motion generator for mirroring a human arm motion with a robot, recorded by a low frequency visual tracking. Using the proposed method, we can replicate the motion of the operator’s arm with very little delay and thereby achieve an easy-to-use interface. Furthermore, as we can strictly limit the velocity of the generated motion, the approach can safely be used in human robot collaboration applications

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

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

A novel kinematics analysis method using quaternion interpolation – a case study in frog jumping

Spherical Linear Interpolation (SLERP) has long been used in computer animation to interpolate movements between two 3D orientations. We developed a forward kinematics (FK) approach using quaternions and SLERP to predict how frogs modulate jump kinematics between start posture and takeoff. Frog limb kinematics have been studied during various activities, yet the causal link between differences in joint kinematics and locomotor variation remains unknown. We varied 1) takeoff angle from 8 to 60 degrees; 2) turn angle from 0 to 18 degrees; and 3) initial body pitch from 0 to 70 degrees. Simulations were similar to experimentally observed frog kinematics. Findings suggest a fundamental mechanism whereby limb elevation is modulated by thigh and shank adduction. Forward thrust is produced by thigh and proximal foot retraction with little contribution from the shank except to induce asymmetries for turning. Kinematic shifts causing turns were subtle, marked only by slight counter-rotation of the left versus right shank as well as a 10% timing offset in proximal foot adduction. Additionally, inclining initial body tilt influenced the centre of mass trajectory to determine direction of travel at takeoff. Most importantly, our theory suggests firstly that the convergence of leg segment rotation axes toward a common orientation is crucial both for limb extension and for coordinating jump direction; and, secondly, the challenge of simulating 3D kinematics is simplified using SLERP because frog limbs approximately follow linear paths in unit quaternion space. Our methodology can be applied more broadly to study living and fossil frog taxa as well as to inspire new control algorithms for robotic limbs

Constraint Jacobians for constant-time inverse kinematics and assembly optimization

technical reportAn algorithm for the constant-time solution of systems of geometric constraint equations is presented in this work. constraint equations and their Jacobians may be used in conjunction with other numerical methods to solve for a variety of kinematics, dynamics, and assembly optimization problems. The use of constraint equations for these purpose is an under-utilized method in this area. The use of quaternions for coordinates in these constraint equations is shown to be a key choice in the optimization problem for avoiding local minima

Multi-temporal time-dependent terrain visualization through localized spatial correspondence parameterization

Visualizing quantitative time-dependent changes in the topography requires relying on a series of discrete given multi-temporal topographic datasets that were acquired on a given time-line. The reality of physical phenomenon occurring during the acquisition times is complex when trying to mutually model the datasets; thus, different levels of spatial inter-relations and geometric inconsistencies among the datasets exist. Any straight forward simulation will result in a truncated, ill-correct and un-smooth visualization. A desired quantitative and qualitative modelling is presumed to describe morphologic changes that occurred, so it can be utilized to carry out more precise and true-to-nature visualization tasks, while trying to best describe the reality transition as it occurred. This research paper suggests adopting a fully automatic hierarchical modelling mechanism, hence implementing several levels of spatial correspondence between the topographic datasets. This quantification is then utilized for the datasets morphing and blending tasks required for intermediate scene visualization. The establishment of a digital model that stores the local spatial transformation parameterization correspondences between the topographic datasets is realized. Along with designated interpolation concepts, this complete process ensures that the visualized transition from one topographic dataset to the other via the quantified correspondences is smooth and continuous, while maintaining morphological and topological relations. © 2013 by the authors; licensee MDPI, Basel, Switzerland