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To enable a robotic assistant to autonomously reach for and transport objects while avoiding obstacles we have generalized the attractor dynamics approach established for vehicles to trajectory formation in robot arms. This approach is able to deal with the time-varying environments that occur when a human operator moves in a shared workspace. Stable fixed points (attractors) for the heading direction of the end-effector shift during movement and are being tracked by the system. This enables the attractor dynamics approach to avoid the spurious states that hamper potential field methods. Separating planning and control computationally, the approach is also simpler to implement. The stability properties of the movement plan make it possible to deal with fluctuating and imprecise sensory information. We implement this approach on a seven degree of freedom anthropomorphic arm reaching for objects on a working surface. We use an exact solution of the inverse kinematics, which enables us to steer the spatial position of the elbow clear of obstacles. The straight-line trajectories of the end-effector that emerge as long as the arm is far from obstacles make the movement goals of the robotic assistant predictable for the human operator, improving man-machine interaction.