Target reaching is one of the most important problems in robotics - object interaction, manipulation and grasping tasks require reaching of specific targets. We avoid the complexity of calculating the inverse kinematics and doing motion planning, and instead we use a combination of motor primitives. We propose a bio-inspired architecture that performs target reaching with a robot arm without planning. A spiking neural network represents motions in a hierarchy of motor primitives. Different correction primitives are combined using an error signal. We present experiments with a simulation of a robot arm to extensively cover the working space by going to different points and returning to the start point, and experiments to test extreme targets and random points in sequence. Robotics applications - like target reaching - can provide benchmarking tasks and realistic scenarios for validation of neuroscience models. Robotics can take advantage of the capabilities of spiking neural networks and the advantages of neuromorphic hardware to run them.