Additive manufacturing by layerwise photopolymerization, commonly called stereolithography (SLA), is attractive due to its high resolution and diversity of materials chemistry. However, traditional SLA methods are restricted to planar substrates and planar layers that are perpendicular to a single-axis build direction. Here, we present a robotic system that is capable of maskless layerwise photopolymerization on curved surfaces, enabling production of large-area conformal patterns and the construction of conformal freeform objects. The system comprises an industrial six-axis robot and a custom-built maskless projector end effector. Use of the system involves creating a mesh representation of the freeform substrate, generation of a triangulated toolpath with curved layers that represents the target object to be printed, precision mounting of the substrate in the robot workspace, and robotic photopatterning of the target object by coordinated motion of the robot and substrate. We demonstrate printing of conformal photopatterns on spheres of various sizes, and construction of miniature three-dimensional objects on spheres without requiring support features. Improvement of the motion accuracy and development of freeform toolpaths would enable construction of polymer objects that surpass the size and support structure constraints imparted by traditional SLA systems.