The goal of this thesis is to develop a methodology for designing 3D target shapes for accurate LIDAR pose estimation. Scanned from a range of views, this shape can be attached to the surface of a spacecraft and deliver accurate pose scanned. It would act as an LIDAR- based analogue to fiducial markers placed on the surface and viewed by CCD camera(s). Continuum Shape Constraint Analysis (CSCA) which assesses shapes for pose estimation and measures the performance of the Iterative Closest Point (ICP) Algorithm is used as a shape design tool. CSCA directly assesses the sensitivity of pose error to variation in viewing direction. Three of the CSCA measures, Noise Amplification Index, Minimal Eigen-value and Expectivity Index, were compared, and Expectivity Index was shown to be the best index to use as shape design tool. Using CSCA and numerical simulations, a Cuboctahedron was shown to be an optimal shape which delivers an accurate pose when viewed from all angles and the initial pose guess is close to the true poses. Separate from Constraint Analysis, the problem of shape ambiguity was addressed using numerical tools. The Cuboctahedron was modified in order to resolve shape ambiguity - the tendency of the ICP algorithm to converge with low registration error on a pose configuration geometrically identical, but actually different from a “true pose”. The numerical characteristics of geometrical ambiguity were studied, and a heuristic design methodology to reduce shape ambiguity was developed and is presented in this thesis. A Reduced Ambiguity Cuboctahedron is the resultant shape that delivers an accurate pose from all views and does not suffer from shape ambiguity. The shapes were subjected to simulation and experimental validation. They were manufactured using 3D Rapid Prototyper, and a NEPTEC Design Group TriDAR Scanner was used to obtain experimental data for three shapes: the Tetrahedron, Cuboctahedron, and reduced Ambiguity Cuboctahedron. The Tetrahedron, which has poorly constrained views, was included in the testing process as a comparison shape. The simulation and experimental results were congruent, and validated the design methodology and the designed shapes.