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Motion planning for haptic guidance

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Rosell, Jan
Vázquez, Carlos
Iñiguez, Pedro
Pérez Ruiz, Alexander
Abstract (Spanish)
Los dispositivos hápticos permiten al usuario sentir fuerzas de reacción procedentes de interacciones virtuales o fuerzas de reacción reflejadas desde un lugar remoto durante una tarea de teleoperación bilateral. Además, pueden ejercerse fuerzas de guiado para entrenar al usuario en la realización de una tarea virtual, o para ayudarle a teleoperar con seguridad un robot. La generación de fuerzas de guiado depende de la existencia de un plan de movimiento que proporcione la dirección a seguir para alcanzar el objetivo desde cualquier configuración libre del espacio de configuración (espacio C). Este trabajo propone un método para obtener dicho plan que intercala una exploración del espacio C basada en muestreos con un cálculo eficiente de funciones armónicas. Se utiliza una secuencia de muestreo determinista (con un sesgo basado en los valores de la función armónica) para obtener un modelo de descomposición jerárquica de celdas del espacio C. Se itera una función armónica. Se calcula iterativamente una función armónica sobre el modelo parcialmente conocido utilizando un enfoque novedoso. La función armónica es la función de navegación utilizada como plan de movimiento. El enfoque se ha implementado en un planificador (denominado planificador Kautham) que, dadas una configuración inicial y una configuración objetivo, proporciona: a) un canal de celdas que conecta la celda que contiene la configuración inicial con la celda que contiene la configuración objetivo; b) dos funciones armónicas sobre todo el espacio C: una que guía los movimientos hacia el canal y otra que guía los movimientos dentro del canal hacia el objetivo; c) una trayectoria calculada sobre una hoja de ruta construida con las muestras libres del canal. A continuación, las funciones armónicas y la trayectoria de solución se utilizan para generar las fuerzas de guiado del dispositivo háptico. El método de planificación se ilustra con ejemplos en espacios de trabajo 2D y 3D.
Abstract (English)
Haptic devices allow a user to feel either reaction forces from virtual interactions, or reaction forces reflected from a remote site during a bilateral teleoperation task. Also, guiding forces can be exerted to train the user in the performance of a virtual task, or to assist him to safely teleoperate a robot. The generation of guiding forces rely on the existence of a motion plan that provides the direction to be followed to reach the goal from any free configuration of the configuration space (C-space). This paper proposes a method to obtain such a plan that interleaves a sampling-based exploration of C-space with an efficient computation of harmonic functions. A deterministic sampling sequence (with a bias based on harmonic function values) is used to obtain a hierarchical cell decomposition model of C-space. An harmonic function is iteratively computed over the partially known model using a novel approach. The harmonic function is the navigation function used as motion plan. The approach has been implemented in a planner (called Kautham planner) that, given an initial and a goal configuration, it provides: a) a channel of cells connecting the cell that contains the initial configuration with the cell that contains the goal configuration; b) two harmonic functions over the whole C-space: one that guides motions towards the channel and the other that guides motions within the channel towards the goal; c) a path computed over a roadmap built with the free samples of the channel. The harmonic functions and the solution path are then used to generate the guiding forces for the haptic device. The planning approach is illustrated with examples on 2D and 3D workspaces.
Extent
15 páginas
URI: https://repositorio.escuelaing.edu.co/handle/001/2361
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