Achieving high accuracy motion while ensuring real-time collision avoidance in cluttered and dynamic environments is a dual challenge often requiring a compromise. Here, we address this problem by proposing AIKIDO (Accordant Inverse Kinematics through Inferential Dynamics), a novel approach to local motion synthesis that combines closed-loop inverse kinematics, constrained rigid-body dynamics, and optimal control. AIKIDO leverages a receding horizon control scheme to compute physically plausible, collision-free future states, which are then tracked by an acceleration optimal controller. The main advantage of this approach is in the precise enforcement of non-compenetration constraints. We assessed the performance of our method both in simulation and real world experiments. AIKIDO outperforms the state of the art planners in terms of all metrics considered, even under challenging conditions with tight clearances, cluttered and dynamic environments.