System and method for controlling a robot using constrained dynamic movement primitives

A controller for controlling an operation of a robot to execute a task, the controller comprising:

• a memory configured to:
• store a set of dynamic movement primitives (DMPs) parameterized for the task, wherein the set of DMPs comprise a set of at least two dynamical systems, the set of the at least two dynamical systems comprising at least:
• a function representing point attractor dynamics associated with the task;
• and
• a learned forcing function encoding motion characteristics from a demonstration of the task;
• a processor configured to:
• transform, the set of DMPs to a set of constrained DMPs (CDMPs) by determining a perturbation function that modifies the learned forcing function based on a set of operational constraints that need to be satisfied for the execution of the task;
• solve, a non-linear optimization problem to determine the perturbation function for the set of CDMPs such that the learned forcing function is adjusted minimally while satisfying the set of operational constraints;
• and
• generate, a control input causing the robot to execute the task, wherein the control input is computed based on the modified forcing function incorporating the perturbation function determined by the optimization problem;
• and
• an output interface configured to command the robot to execute the generated control input to execute the task.

A non-transitory computer-readable medium storing computer-executable instructions for executing a task by a robot, the computer-executable instructions configured for:

• obtaining a set of dynamic DMPs parameterized for the task, wherein the obtained set of DMPs comprises a set of at least two dynamical systems, the set of the at least two dynamical systems comprising at least:
• a function representing point attractor dynamics associated with the task, and a learned forcing function a encoding motion characteristics from a learned demonstration of the task;
• transforming, the obtained set of DMPs to a set of constrained DMPs (CDMPs) by defining a perturbation function that modifies the learned forcing function based on a set of operational constraints that need to be satisfied for performance of the task;
• solving, a non-linear optimization problem to determine the perturbation function for the set of CDMPs such that the learned forcing function is adjusted minimally while satisfying the set of operational constraints;
• and
• generating, a control input causing the robot to execute the task, wherein the control input is computed based on the modified forcing function incorporating the perturbation function determined by the optimization problem.