Motor brain-machine interfaces (BMIs) transform neural activities recorded directly from the brain into motor commands to control the movements of an external object by establishing an interface between the central nervous system (CNS) and the device. Bidirectional BMIs are closed-loop systems that add a sensory channel to provide the brain with an artificial feedback signal produced by the interaction between the device and the external world. Taking inspiration from the functioning of the spinal cord in mammalians, in our previous works we designed and developed a bidirectional BMI that uses the neural signals recorded form rats' motor cortex to control the movement of an external object. We implemented a decoding interface based on the approximation of a predefined force field with a central attractor point. Now we consider a non-linear transformation that allows to design a decoder approximating force fields with arbitrary attractors. We describe here the non-linear mapping algorithm and preliminary results of its use with behaving rats.