  The collision avoidance constraints are prominent as non-convex,
non-differentiable, and challenging when defined in optimization-based motion
planning problems. To overcome these issues, this paper presents a novel
non-conservative collision avoidance technique using the notion of convex
optimization to establish the distance between robotic spacecraft and space
structures for autonomous on-orbit assembly operations. The proposed technique
defines each ellipsoidal- and polyhedral-shaped object as the union of convex
compact sets, each represented non-conservatively by a real-valued convex
function. Then, the functions are introduced as a set of constraints to a
convex optimization problem to produce a new set of differentiable constraints
resulting from the optimality conditions. These new constraints are later fed
into an optimal control problem to enforce collision avoidance where the motion
planning for the autonomous on-orbit assembly takes place. Numerical
experiments for two assembly scenarios in tight environments are presented to
demonstrate the capability and effectiveness of the proposed technique. The
results show that this framework leads to optimal non-conservative trajectories
for robotic spacecraft in tight environments. Although developed for autonomous
on-orbit assembly, this technique could be used for any generic motion planning
problem where collision avoidance is crucial.
