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In this paper, a new method is introduced for computing energy-minimizing motions in twodimensional environments cluttered with a priori known static and moving obstacles. The proposed method is based on a new four-dimensional motion-planning space represented by a Bump- Surface embedded in ℜ4. The energy-minimizing motion-design problem is expressed by a variational curve-design problem on the introduced Bump-Surface. The optimal motion is determined by a new algorithm for computing a B-spline curve on the Bump-Surface which is conformal to the motion-planning constrains. The proposed method is applied for designing the motion of nonholonomic robots in the presence of moving obstacles and its performance is tested in simulated 2D dynamic environments with car-like robots.

Energy-Minimizing Motion Design for Nonholonomic Robots Amidst Moving Obstacles