We introduced a method to design topological mechanical metamaterials that are not constrained by Newtonian dynamics. The unit cells in a mechanical lattice are subjected to active feedback forces that are processed through autonomous controllers, pre-programmed to generate the desired local response in real-time. As an example, we focused on the quantum Haldane model, a two-band topological system supporting the anomalous quantum Hall effect. This model breaks time-reversal symmetry via nonreciprocal coupling terms, the implementation of which in mechanical systems required violating Newton’s third law. We demonstrated that the required topological phase, characterized by chiral edge modes, can be achieved in an analogous mechanical system only with closed-loop control. We demonstrated that the resulting system has all the properties of the quantum model, supporting unidirectional, topologically-protected wave propagation along the metamaterial edges.