Systems and methods for learning and generating movement policies for a dynamical system

A system for generating a trajectory of a dynamical system, comprising:

• a recurrent mixture density network (RMDN) configured to model a policy from demonstration data, wherein the policy is a distribution of a plurality of system actions conditioned on a plurality of system states and outcomes;
• and
• a processor and a memory operably connected to the processor, wherein the memory has computer-executable instructions stored thereon that, when executed by the processor, cause the processor to:
• generate a first set of action particles by sampling from the policy, wherein each of the action particles in the first set includes a respective system action;
• predict a respective outcome of the dynamical system in response to each of the action particles in the first set;
• weight each of the action particles in the first set according to a respective probability of achieving a desired outcome of the dynamical system, wherein the respective probabilities of achieving the desired outcome are determined using the respective outcome of the dynamical system in response to each of the action particles in the first set;
• generate a second set of action particles by sampling from the weighted action particles, wherein each of the action particles in the second set includes a respective system action;
• and
• select a next system action in the trajectory of the dynamical system from the action particles in the second set.