Path Design and Control Algorithms for Articulated Mobile Robots Ulf Andersson, Kent Mrozek Q Navigator AB Aurorum 21B SE-977 75 Luleå, Sweden Kalevi Hyyppä Div. of Industrial Electronics Luleå University of Technology SE-971 87 Luleå, Sweden Kalle Åström Dept. of Mathematics Lund Institute of Technology Box 118 SE-221 00 Lund, Sweden Abstract Experiments have shown that continuity of curvature of a reference path and of its derivative with respect to distance are particularly important for articulated mobile robots. The X4Y4 curve and a control algorithm for an articulated mobile robot following an X4Y4 curve are presented. Experiments with a 55 ton LHD vehicle in an underground mine have shown that the sideways repeatability when driving through a 106° curve at 2.8 m/s is within ± 100 mm, and when driving through a 10° curve at 5.1 m/s is within ± 50 mm. 1 Introduction Path design is an important issue for real-world mobile robots. Ill-designed curves on a path can cause large guidance errors, and also result in high stress on servos, motors, bearings etc. in the robot. Traditionally reference paths have been designed from lines and arcs, laid out to make the heading along the path continuous. However it has been shown [Nelson and Cox, 1988] that it is not possible for most mobile robots to follow this kind of paths without errors. The cause of errors is the discontinuity in curvature at the junctions between the lines and the arcs. A step-wise change of curvature demands infinite acceleration of the actuator controlling the curvature taken by the robot guide point. (The only exception is a tricycle-type mobile robot with the guide point placed under the steering wheel. This placement should however be avoided because of the resulting complex control of the orientation of the robot, and the wide swept area. The common placement of guide point is at the mid-point between the non-steered wheels for a tricycle-type mobile robot, and at the mid-point between the rear or front wheels of an articulated mobile robot.) The importance of continuous curvature has been discussed extensively in [Nelson, 1989] where quintic polynomial paths are proposed, and in [Kanayama and. Hartman, 1989] where cubic spiral paths are proposed. In the second paper a smoothness cost function is introduced which makes it possible to find the optimally smooth path. In [Graettinger and Krogh, 1989] time-scaling has been proposed to fulfill the dynamic constraints of a path. In none of these papers has continuity of derivative of curvature with respect to distance along the path been discussed. A step change of the curvature derivative results in a step in actuator torque in the steering mechanism of the mobile robot. This might be acceptable for non-articulated types but our experiments have shown that it is not acceptable for an articulated vehicle driving at high speed. A rather different approach has been taken in [Steer, 1989] where the author proposes a gaussian shape of the steer angle versus time function of a tricycle-type mobile robot when driving in a curve. The gaussian function is infinitely differentiable, solving the problem with steps in actuator torque, but the path is complicated to find. In [Pin and Vasseur, 1990] a simple algorithm is presented to find the shortest path between two postures. Limitations of the steering rate is discussed. In this paper we present and discuss the X4Y4 curve. It consists of two or three parts depending on the total heading change along the curve. The first part is called the closing part and the last part (second or third) is called the opening part. They are both characterized by (1) where x and y are the coordinates of the path in a global coordinate system and c is a positive scaling constant which