A Geodesics-Based Model for Obstacle Avoidance

by

Jason Olmstead Muhs

Virtual Soldier Research Program

Center for Computer-Aided Design

The University of Iowa

116 Engineering Research Facility

Iowa City, IA 52242-1000

Tel: (319) 353-2249

Fax: (319) 384-0542

www.digital-humans.org

E-mail: jolmstea@engineering.uiowa.edu

Abstract

This paper presents a motion prediction model for obstacle avoidance. A geodesics model is used to obtain the desired path in Cartesian space. The model numerically determines a minimum distance curve between two points on an obstacle surface, defined by the initial and final points of the hand, and offsets it in the normal direction to form a motion path around the obstacle. An algorithm that minimizes the distance between a point and a parametrically defined surface in Cartesian space determines the initial and final points. The discrete points on the curve serve as control points for the motion path. The data is combined with a motion prediction algorithm to optimize joint motion for the upper body.

Key Words: Obstacle avoidance, geodesics, offset, normalize

Introduction

Trajectory planning of human upper body movement is one of the most challenging problems in digital human simulation. Many tasks require the arm to move from its initial position to a specified target position without any constraints, or via a point for a curved path in case of obstacle avoidance.

The case of obstacle avoidance is very important for trajectory planning in virtual environments. A lot of research has gone into obstacle avoidance, especially in robotics. However, applying obstacle avoidance to real-time virtual simulations is an area that hasn’t been looked into as much. Flash and Hogan (1985) presented a mathematical model for obstacle avoidance that used a via-point to control the path of an end-effector around an obstacle between an initial point, A, and a destination point, B.

Figure 1: The via point is located above the obstacle and the path of the end-effecter moves from point A to point B through the via-point.

The path of the motion was optimized using a minimum-jerk model, which minimized the third derivative of position in all three directions of Cartesian space.

(1)

This model was applied to motion in a virtual environment by Mi (2003). The downside to using this model in a virtual environment is that the user had to input the via-point for the end-effector (hand) to move through. This necessitated some simple trial and error and was very tedious. The need for user input also made it impossible for any simulations to be done in real-time. Inst