## Statistical Motion Planning for Mobile Robots

### Introduction

In real environments motion planning for mobile robots generally has to take into account the presence of moving obstacles. Two types of approaches coping with this problem prevail: 1. Obstacle motions are presumed to be known exactly; then, a collision-free robot trajectory can be planned, e.g., in configuration-time space. 2. Obstacles are ignored until they are close to the robot; during its motion the robot reacts by performing evasive movements.
Both approaches have some drawbacks due to making presumptions which do not properly reflect reality: Usually, obstacle motions cannot be predicted precisely, yet some information about average behavior of obstacles can be obtained easily. Thus, the former approach is mainly of theoretical interest, while the latter may be quite inefficient as it uses local information only.
Consequently, we have developed a new concept which incorporates statistical data in order to respect obstacle behaviors: statistical motion planning. It yields efficient robot paths which are adapted to the prevailing motions of obstacles. Furthermore, this approach realizes a fundamental issue in robotics: The robot is adapted to its environment, (and not vice versa), the environment is minimally disturbed by the robot.

### Theoretical Basis

Even in simple situations, the selection of optimal robot paths depends on many factors (e.g. obstacle density, direction of motion, velocities). Mathematical models are thus a crucial foundation for statistical motion planning. To describe obstacle motions, two models -- differing in precision and complexity -- have been developed: Stochastic trajectories permit a precise evaluation of robot paths with respect to collision probability and expected driving time (which takes into account that the time to reach the goal also depends on the costs for non-deterministic evading maneuvers). The stochastic grid is a simpler representation, which is used in order to plan robot trajectories with minimum collision probability.

### Experimental System

The concepts of statistical motion planning have been tested in a real environment by an integration into the MONAMOVE-system. Statistical data about obstacle motions is gathered automatically with a global camera system. Obstacles are detected (based on difference image analysis) and their trajectories are recorded over long time intervals. Finally, this raw data is transformed into statistical models.

### Results

The paths generated by the statistical methods have been evaluated and compared to results obtained with a conventional planner, which minimizes the path length. Naturally, the statistically planned paths are longer as they purposely incorporate detours. In dynamic environments, however, the detours allow to significantly decrease collision probabilities and the expected driving time compared to the conventional trajectories.

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