Driving on the Highway Driving on the Highway

| This paper deals with a particular kinodynamic 4] trajectory planning problem that we call thèhighway problem'. It consists in planning a time-optimal trajectory for a vehicle which is travelling in a structured workspace amidst other vehicles and is subject to constraints on its velocity and acceleration. By structured workspace, we mean that there exists lanes within which the vehicles are able to move. A lane is characterized by its`spine', i.e. a one-dimensional curve. A vehicle has to follow a predetermined lane but it may also shift from its lane to an adjacent one. This paper presents an eecient method which determines an approximate time-optimal solution to the highway problem. The approach consists in discretizing time and selecting the accelerations applied to the robot among a discrete set. These hypotheses make it possible to deene a grid in the robot's time-state space, i.e. the robot's state (or phase) space augmented of the time dimension. This grid is then searched in order to nd a solution. Accordingly trajectory planning is reduced to graph search. The choice of the time-step determines the size of the grid which, in turn, determines the running time of the algorithm as well as how close the approximate solution is to the exact time-optimal solution. Thus it is possible to trade oo the computation speed against the quality of the solution. Abstract This paper deals with a particular kinodynamic 4] trajectory planning problem that we call thèhighway problem'. It consists in planning a time-optimal trajectory for a vehicle which is travelling in a structured workspace amidst other vehicles and is subject to constraints on its velocity and acceleration. By structured workspace, we mean that there exists lanes within which the vehicles are able to move. A lane is characterized by its`spine', i.e. a one-dimensional curve. A vehicle has to follow a predetermined lane but it may also shift from its lane to an adjacent one. This paper presents an eecient method which determines an approximate time-optimal solution to the highway problem. The approach consists in discretizing time and selecting the accelerations applied to the robot among a discrete set. These hypotheses make it possible to deene a grid in the robot's time-state space, i.e. the robot's state (or phase) space augmented of the time dimension. This grid is then searched in order to nd a solution. Accordingly trajectory planning is reduced to graph search. The choice of …