Dynamical systems can generate movement trajectories that are robust against perturbations. This article presents an improved modification of the original dynamic movement primitive (DMP) framework by Ijspeert et al [1], [2]. The new equations can generalize movements to new targets without singularities and large accelerations. Furthermore, the new equations can represent a movement in 3D task space without depending on the choice of coordinate system (invariance under invertible affine transformations). Our modified DMP is motivated from biological data (spinal-cord stimulation in frogs) and human behavioral experiments. We further extend the formalism to obstacle avoidance by exploiting the robustness against perturbations: an additional term is added to the differential equations to make the robot steer around an obstacle. This additional term empirically describes human obstacle avoidance. We demonstrate the feasibility of our approach using the Sarcos Slave robot arm: after learning a single placing movement, the robot placed a cup between two arbitrarily given positions and avoided approaching obstacles.