Алгоритм определения внутренней геометрии манипулятора змеевидного типа при движении лидирующего звена по наращиваемой траектории

In the paper, we have formulated the invariant description form for geometry of a spatial, kinematically redundant manipulator with the orthogonal non-coplanar axes of rotation of the joints. We have obtained the explicit equations for determining the angular coordinates from the condition that points of joints belong to the smooth parametrically given curve. Inequality constraints on the relative position of neighboring parts of the manipulator have been formulated. We have proposed an algorithm for solving equations and the method of planning changes for hinge coordinates for the movement of joints points along the spatial curve that is formed by incremental addition of target points for the head link positions of the manipulator. The method has been applied for planning movements of a hyper-redundant manipulator with a fixed root link and a snakelike robot when moving along the path built on the basis of current and forecasted positions of joints in the Cartesian space.Сформулированы инвариантная к системе внешних координат форма задания геометрии пространственного кинематически избыточного манипулятора с последовательно ортогональными некомпланарными осями шарниров вращения. Получены аналитические выражения для определения угловых шарнирных координат из условий принадлежности точек шарниров параметрически заданной гладкой кривой, уравнение для координат положения точек на кривой и неравенства-ограничения на взаимное положение смежных звеньев манипулятора. Предложен алгоритм решения уравнения и метод планирования законов изменения шарнирных координат, обеспечивающий перемещения точек шарниров по пространственной траектории, наращиваемой добавлением целевых точек для головного звена манипулятора. Метод применен для планирования движения гиперизбыточного манипулятора с неподвижным основанием и змеевидного робота при перемещении по траектории, выстраиваемой на основе текущих и прогнозируемых положений шарниров в декартовом пространств

Mechanical Stability Margin for Scouting Poses in Modular Snake Robots

This paper presents an algorithm to calculate mechanical stability margins of a Modular Snake Robot (MSR) during scouting poses. Scouting poses are defined as robot configurations in which one or two of the end modules of the robot are raised up to increase the range of perception of sensors that might be placed in its distal parts. The robot center of mass (CoM) and each of the module's contact pad positions are calculated by computing the robot kinematics. Then, this kinematic model is placed in an environment that consist of a height map (the terrain), built on a 2D grid base of defined size and resolution. Due the hyper-stability of the MSR structure, as it features many static contact points with the terrain, we approximate by weighting the distribution of forces to ensure an iso-static simplified problem. Using this information as input, the algorithm calculates a representation of the supporting surface (not necessarily horizontal), and then, it computes the minimum distance of the CoM projection into this surface to one of its edges to define a mechanical stability margin. The effectiveness and robustness of the method is demonstrated by comparisons of simulation and the real robot results. Moreover, a sequence of quasi-static motions bounded by a threshold in the stability margin, keeps the robot stable as it rises. Thus, demonstrating qualitatively the convenience of the method