  In this paper, we propose a novel trajectory optimization algorithm for
mobile manipulators under end-effector path, collision avoidance and various
kinematic constraints. Our key contribution lies in showing how this highly
non-linear and non-convex problem can be solved as a sequence of convex
unconstrained quadratic programs (QPs). This is achieved by reformulating the
non-linear constraints that arise out of manipulator kinematics and its
coupling with the mobile base in a multi-affine form. We then use techniques
from Alternating Direction Method of Multipliers (ADMM) to formulate and solve
the trajectory optimization problem. The proposed ADMM has two similar
non-convex steps. Importantly, a convex surrogate can be derived for each of
them. We show how large parts of our optimization can be solved in parallel
providing the possibility of exploiting multi-core CPUs/GPUs. We validate our
trajectory optimization on different benchmark examples. Specifically, we
highlight how it solves the cyclicity bottleneck and provides a holistic
approach where diverse set of trajectories can be obtained by trading-off
different aspects of manipulator and mobile base motion.
