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Most obstacle avoidance techniques do not take into account vehicle shape and kinematic constraints. They assume a punctual and omnidirectional vehicle and thus they are doomed to rely on approximations when used on real vehicles. Our main contribution is a framework to consider shape and kinematics together in an exact manner in the obstacle avoidance process, by abstracting these constraints from the avoidance method usage. Our approach can be applied to many non-holonomic vehicles with arbitrary shape.For these vehicles, the configuration space is three-dimensional, while the control space is two-dimensional. The main idea is to construct (centred on the robot at any time) the two-dimensional manifold of the configuration space that is defined by elementary circular paths. This manifold contains all the configurations that can be attained at each step of the obstacle avoidance and is thus general for all methods. Another important contribution of the paper is the exact calculus of the obstacle representation in this manifold for any robot shape (i.e. the configuration regions in collision). Finally, we propose a change of coordinates of this manifold so that the elementary paths become straight lines. Therefore, the three-dimensional obstacle avoidance problem with kinematic constraints is transformed into the simple obstacle avoidance problem for a point moving in a two-dimensional space without any kinematic restriction (the usual approximation in obstacle avoidance). Thus, existing avoidance techniques become applicable.The relevance of this proposal is to improve the domain of applicability of a wide range of obstacle avoidance methods. We validated the technique by integrating two avoidance methods in our framework and performing tests in the real robot.