System and method for controlling an operation of a manipulation system

A method for controlling an operation of a manipulation system, wherein the manipulation system includes a robotic arm for performing a manipulation task of manipulating an object, the method comprising:

• formulating a particle based optimization problem for covariance control of the manipulation system, based on a Stochastic Discrete-time Linear Complementarity Model (SDLCM) of the manipulation task, and a sample average approximation;
• solving the formulated particle based optimization problem using an important-particle algorithm to compute an optimal state trajectory, an optimal feedforward control trajectory, an optimal complementarity variable trajectory, a state feedback gain, and a complementarity feedback gain;
• collecting, from one or more sensors associated with the manipulation system, measurements indicative of a current state trajectory and a current complementarity variable trajectory;
• computing a deviation of the current state trajectory from the optimal state trajectory and a deviation of the current complementarity variable trajectory from the optimal complementarity variable trajectory;
• determining an online control input based on the optimal feedforward control trajectory and a feedback control to control a covariance of states and complementarity variables of the manipulation system, wherein the feedback control is based on the deviation of the current state trajectory from the optimal state trajectory, the deviation of the current complementarity variable trajectory from the optimal complementarity variable trajectory, the state feedback gain, and the complementarity feedback gain;
• and
• producing control commands for actuators of the robotic arm based on the determined online control input;
• and
• operating the actuators of the robotic arm according to the determined online control input by transmitting control signals of the control commands to the robotic arm.

A non-transitory computer-readable storage medium embodied thereon a program executable by a processor for performing a method for controlling an operation of a manipulation system, wherein the manipulation system includes a robotic arm for performing a manipulation task of manipulating an object, the method comprising:

• formulating a particle based optimization problem for covariance control of the manipulation system, based on a Stochastic Discrete-time Linear Complementarity Model (SDLCM) of the manipulation task, and a sample average approximation;
• solving the formulated particle based optimization problem using an important-particle algorithm to compute an optimal state trajectory, an optimal feedforward control trajectory, an optimal complementarity variable trajectory, a state feedback gain, and a complementarity feedback gain;
• collecting, from one or more sensors associated with the manipulation system, measurements indicative of a current state trajectory and a current complementarity variable trajectory;
• computing a deviation of the current state trajectory from the optimal state trajectory and a deviation of the current complementarity variable trajectory from the optimal complementarity variable trajectory;
• determining an online control input based on the optimal feedforward control trajectory and a feedback control to control a covariance of states and complementarity variables of the manipulation system, wherein the feedback control is based on the deviation of the current state trajectory from the optimal state trajectory, the deviation of the current complementarity variable trajectory from the optimal complementarity variable trajectory, the state feedback gain, and the complementarity feedback gain;
• and
• producing control commands for actuators of the robotic arm based on the determined online control input;
• and
• operating the actuators of the robotic arm according to the determined online control input by transmitting control signals of the control commands to the robotic arm.

A control system for controlling an operation of a manipulation system, wherein the manipulation system includes a robotic arm for performing a manipulation task of manipulating an object, the control system comprising:

• at least one processor;
• and a memory having instructions stored thereon that cause the at least one processor to:
• collect, from one or more sensors associated with the manipulation system, measurements indicative of a current state trajectory and a current complementarity variable trajectory;
• compute a deviation of the current state trajectory from an optimal state trajectory and a deviation of the current complementarity variable trajectory from an optimal complementarity variable trajectory;
• wherein a particle based optimization problem is solved using an important-particle algorithm to obtain the optimal state trajectory, the optimal complementarity variable trajectory, an optimal feedforward control trajectory, a state feedback gain, and a complementarity feedback gain, and wherein the particle based optimization problem is based on a Stochastic Discrete-time Linear Complementarity Model (SDLCM) of the manipulation task and a sample average approximation;
• determine an online control input based on the optimal feedforward control trajectory and a feedback control to control a covariance of states and complementarity variables of the manipulation system, wherein the feedback control is based on the deviation of the current state trajectory from the optimal state trajectory, the deviation of the current complementarity variable trajectory from the optimal complementarity variable trajectory, the state feedback gain, and the complementarity feedback gain;
• and
• produce control commands for actuators of the robotic arm based on the determined online control input;
• and
• operate the actuators of the robotic arm according to the determined online control input by transmitting control signals of the control commands to the robotic arm.