A new continuous-curvature line/path-tracking method for car-like vehicles

Abstract

In this paper, we first investigate the problem of finding an algorithm for the movement of a car-like vehicle to track a given directed straight line. Car-like vehicles' motions possess 2 d.o.f., speed v and path curvature κ. We compute the 'derivative of path curvature', λ = dκ/ds, rather than the path curvature κ itself, to enforce continuous-curvature vehicle motions. Specifically, we compute λ as a linear function of the current path curvature, orientation and positional difference of the vehicle against the given line. We call this function λ the steering function. The uniform asymptotic stability of the feedback rule is proved through linearization and a Lyapunov function. Next, this basic line-tracking result is applied to the problem of path tracking where a path consists of directed straight lines. The main advantages and features of the results are summarized as follows. (i) Since the derivative dκ/ds of path curvature is obtained, the path curvature is always continuous while a vehicle converges to the line. (ii) By assuming the critical damping condition, the steering function contains one parameter σ that controls the smoothness (or equivalently, sharpness) of vehicle motions. (iii) This theory can be applied to a vehicle with any wheel architecture, i.e. this theory is vehicle independent. (iv) The theory can easily be extended to the more general problem of tracking a path consisting of any number of directed lines with a new principle of neutral switching. (v) The simplicity and machine independence of this theory makes implementation of this theory on vehicles easy. We present numerous simulation results of line/path-tracking motions. These results verify the effectiveness of this continuous-curvature motion control method. Some successful results obtained on the autonomous robot Yamabico at the Naval Postgraduate School are also included.