This paper presents a new approach for geometrically constrained path planning applied to the field of robotic grasping. The method proposed in this paper is based on the Fast Marching Square (FM $\, ^2$ ) and a path calculation approach based on an optimization evolutionary filter named Differential Evolution (DE). The geometric restrictions caused by the link lengths of the kinematic chain composed by the robot arm and hand are introduced in the path calculation phase. This phase uses both the funnel potential of the surroundings created with FM $\, ^2$ and the kinematic constraints of the robot as cost functions to be minimized by the evolutionary filter. The use of an optimization filter allows for a near-optimal solution that satisfies the kinematic restrictions, while preserving the characteristics of a path computed with FM $\, ^2$ . The proposed method is tested in a simulation using a robot composed by a mobile base with two arms.

The proposed algorithm integrates in a single planner the global motion planning and local obstacle avoidance capabilities. It efficiently guides the robot in a dynamic environment. This eliminates some of the traditional problems of planned architectures (model-plan-act scheme) while obtaining many of the qualities of behavior-based architectures. The computational efficiency of the method allows the planner to operate at high-rate sensor frequencies. This avoids the need for using both a collision-avoidance algorithm and a global motion planner for navigation in a cluttered environment. The method combines map-based and sensor-based planning operations to provide a smooth and reliable motion plan. Operating on a simple grid-based world model, the method uses a fast marching technique to determine a motion plan on a Voronoi extended transform extracted from the environment model. In addition to this real-time response ability, the method produces smooth and safe robot trajectories.