Model-based control with uncertain motion model

A method for controlling a system, wherein the method uses a processor coupled to a memory storing a particle filter configured to estimate weights of a set of particles based on fitting of the particles into a measurement model, wherein a particle includes a motion model of the system having an uncertainty modeled as a Gaussian process over possible motion models of the system and a state of the system determined with the uncertainty of the motion model of the particle, wherein a distribution of the Gaussian process of the motion model of one particle is different from a distribution of the Gaussian process of the motion model of another particle, wherein each execution of the particle filter updates the state of the particle according to a control input to the system and the motion model of the particle with the uncertainty, and determines the weight of the particle by fitting the state of the particle in the measurement model subject to measurement noise, wherein the Gaussian process of each particle is parameterized as a weighted combination of a set of basis functions, wherein the distribution of the Gaussian process is a Student-t distribution having a mean defining weights of the weighted combination and a scale defining the uncertainty of the motion model of the particle, wherein the weights of the basis functions are modeled as a weight matrix, wherein the weight matrix is Matrix-Normal distributed, wherein the processor is coupled with stored instructions implementing the method, wherein the instructions, when executed by the processor carry out steps of the method, comprising:

• executing the particle filter to produce the weight of each particle and the state of each particle determined with the uncertainty of the motion model of each particle;
• updating the distribution of the Gaussian process of a particle based on a difference between the state of the particle determined with the uncertainty of the motion model of the particle and a state of the particle determined without the uncertainty of the motion model of the particle;
• determining a current estimate of the motion model as a weighted combination of the motion models of the particles weighted according to the weights of the particles;
• determining a current estimate of the state of the system as a weighted combination of the states of the particles weighted according to the weights of the particles;
• and
• executing a controller configured to generate a value of the control input based on the current estimate of the motion model and the current estimate of the state of the system and control the system using the value of the control input.

A non-transitory computer readable storage medium embodied thereon a program executable by a processor for performing a method, the medium stores a particle filter configured to estimate weights of a set of particles based on fitting of the particles into a measurement model, wherein a particle includes a motion model of the system having an uncertainty modeled as a Gaussian process over possible motion models of the system and a state of the system determined with the uncertainty of the motion model of the particle, wherein a distribution of the Gaussian process of the motion model of one particle is different from a distribution of the Gaussian process of the motion model of another particle, wherein each execution of the particle filter updates the state of the particle according to a control input to the system and the motion model of the particle with the uncertainty, and determines the weight of the particle by fitting the state of the particle in the measurement model subject to measurement noise, wherein the Gaussian process of each particle is parameterized as a weighted combination of a set of basis functions, wherein the distribution of the Gaussian process is a Student-t distribution having a mean defining weights of the weighted combination and a scale defining the uncertainty of the motion model of the particle, wherein the weights of the basis functions are modeled as a weight matrix, wherein the weight matrix is Matrix-Normal distributed, the method comprising:

• executing the particle filter to produce the weight of each particle and the state of each particle determined with the uncertainty of the motion model of each particle;
• updating the distribution of the Gaussian process of a particle based on a difference between the state of the particle determined with the uncertainty of the motion model of the particle and a state of the particle determined without the uncertainty of the motion model of the particle;
• determining a current estimate of the motion model as a weighted combination of the motion models of the particles weighted according to the weights of the particles;
• determining a current estimate of the state of the system as a weighted combination of the states of the particles weighted according to the weights of the particles;
• and
• executing a controller configured to generate a value of the control input based on the current estimate of the motion model and the current estimate of the state of the system and control the system using the value of the control input.