1st scientific advances report on WP3

1st scientific advances report: state of the art, research organisation, and first results. Task 3.1 Control structures for motion design (ESR7): State of the art and performance comparisons of known approaches, possibly new approaches, if sufficiently developed, in motion design. Task 3.2 Skeleton-based design of surfaces (ESR6): Formulation and experimentation of topologically accurate convolution surfaces for skeletons made of arcs of circles and line segments. Task 3.3 Singularities and syzygies of parameterisations (ESR3): Familiarity with methods already known to compute invariants of parameterisations by exploiting syzygies and singularities, and implementations to use these ideas in an efficient and fast way. Task 3.4 Distance to NURBS curves and surfaces (ESR4): New method based on matrix representations for determining all the closest points to a single Bezier patch. Task 3.5 Path planning and workspace modelling (ESR2): Design of adaptive algebraic algorithms to model the workspace of mechanisms.