US 10,065,312 B1Granted

Unscented optimization and control allocation

AssigneeThe United States of America as represented by the Secretary of the Navy

InventorsIsaac Michael Ross, Mark Karpenko, Ronald J. Proulx

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Abstract

The disclosure provides a robotic arm controller which determines a control parameter for at least one actuator comprising the robotic arm using a control equation having the general form Ax=b, where A is a transformation matrix A based on the geometry and Jacobian of the robotic arm, x is the control parameter x such as a torque vector at a specific joint, and b is the end effector parameter b which specifies a desired corrective state of the end effector. The methodology, by way of constructing and solving an unscented optimization problem, provides a solution to the Ax=b problem by perturbing at least one joint angle appearing in the Jacobian to generate a plurality of distributed joint angles, determining a control parameter x which minimizes an error function. In a particular embodiment, the error function is sum of residual squares, and the appropriate control parameter x is determined by minimizing the error function subject to a series of constraints Aix−b−zi=0, where each constraint arises by virtue of the error generated through use of a given joint angle in the plurality of distributed joint angles selected.

Claims20

Dependent claims

A control system for a robotic arm comprising:

a robotic arm comprising at least one link and comprising an end effector;
a group of sensors attached to the robotic arm where the group of sensors comprises one or more sensors and where the group of sensors provides one or more signals describing at least one joint angle established by the robotic arm;
a group of actuators attached to the robotic arm where the group of actuators comprises one or more actuators and where the group of actuators is configured to generate motion of the at least one link comprising the robotic arm;
and
a processor in communication with the group of sensors and the group of actuators and configured to perform steps comprising:
communicating with the group of sensors and determining an actual position, where the actual position is a position of the end effector at a given time t;
determining a desired position, where the desired position is a prescribed position of the end effector at the given time t;
evaluating a feedback equation for the end effector, where the feedback equation comprises the desired position and the actual position of the end effector and determining an end effector parameter b using the feedback equation, where the end effector parameter b describes a condition at the end effector of the robotic arm;
determining a prospective control parameter x for at least one actuator in the group of actuators by using a transformation matrix Ao and the end effector parameter b, where the transformation matrix Ao comprises at least one parameter having a value dependent on the value of the at least one joint angle established by the robotic arm, by performing steps comprising:
selecting a plurality of distributed joint angles;
and
minimizing an error function, where the error function comprises a plurality of errors, and where a quantity of errors in the plurality of errors is equal to a quantity of joint angles in the plurality of distributed joint angles, and where each error in the plurality of errors corresponds to a specific joint angle in the plurality of distributed joint angles, where the each error comprises a specific transformation matrix Ai, the prospective control parameter x, and the end effector parameter b, where the specific transformation matrix A, is the transformation matrix Ao when the specific joint angle is utilized as the at least one joint angle, thereby determining the prospective control parameter x;
and
communicating the prospective control parameter x to the at least one actuator in the group of actuators;
and controlling the at least one actuator in the group of actuators using the prospective control parameter x.

12 more elements

A computer implemented method of controlling a robotic arm comprising:

receiving in a processor one or more signals describing at least one joint angle established by a robotic arm, where the robotic arm comprises at least one link and comprises an end effector, and where the robotic arm comprises a group of actuators attached to the robotic arm where the group of actuators comprises one or more actuators and where the group of actuators is configured to generate motion of the at least one link comprising the robotic arm;
utilizing the one or more signals to determine an actual position of the end effector, where the actual position is a position of the end effector at a given time t;
determining a desired position, where the desired position is a prescribed position of the end effector at the given time t;
evaluating a feedback equation, where the feedback equation comprises the desired position and the actual position of the end effector and determining an end effector parameter b using the feedback equation, where the end effector parameter b describes a condition at the end effector of the robotic arm;
determining a prospective control parameter x for at least one actuator in the group of actuators by using a transformation matrix Ao and the end effector parameter b, where the transformation matrix Ao comprises at least one parameter having a value dependent on the value of the at least one joint angle established by the robotic arm, by performing steps comprising:
selecting a plurality of distributed joint angles;
and
minimizing an error function, where the error function comprises a plurality of errors, and where a quantity of errors in the plurality of errors is equal to a quantity of joint angles in the plurality of distributed joint angles, and where each error in the plurality of errors corresponds to a specific joint angle in the plurality of distributed joint angles, where the each error comprises a specific transformation matrix Ai, the prospective control parameter x, and the end effector parameter b, where the specific transformation matrix Ai, is the transformation matrix Ao when the specific joint angle is utilized as the at least one joint angle, thereby determining the prospective control parameter x;
and
communicating the prospective control parameter x to the at least one actuator in the group of actuators;
and controlling the at least one actuator inthe group of actuators using the prospective control parameter x.

8 more elements

A control system for a robotic arm comprising:

a robotic arm comprising at least one link and comprising an end effector;
a group of sensors attached to the robotic arm where the group of sensors comprises one or more sensors and where the group of sensors provides one or more signals describing at least one joint angle established by the robotic arm, where the one or more signals is referenced to a coordinate system in a joint space;
a group of actuators attached to the robotic arm where the group of actuators comprises one or more actuators and where the group of actuators is configured to generate motion of the at least one link comprising the robotic arm;
and
a processor in communication with the group of sensors and the group of actuators and configured to perform steps comprising:
communicating with the group of sensors and determining an actual position, where the actual position is a position of the end effector at a given time t;
determining a desired position, where the desired position is a prescribed position of the end effector at the given time t, where the desired position of the end effector is referenced to a coordinate system in a task space;
evaluating a feedback equation for the end effector, where the feedback equation comprises the desired position and the actual position of the end effector and determining an end effector parameter b using the feedback equation, where the end effector parameter b describes a condition at the end effector of the robotic arm;
determining a prospective control parameter x in the task space for at least one actuator in the group of actuators by using a transformation matrix Ao and the end effector parameter b, where the transformation matrix Ao comprises a manipulator Jacobian comprising the at least one joint angle in the j oint space, by performing steps comprising:
communicating with the group of sensors and determining an actual joint angle, where the actual joint angle is the at least one joint angle established by the robotic arm at the given time t;
defining a probability function (μ, σ2), where the μ is the actual joint angle and the σ is less than or equal to 10 degrees;
selecting a plurality of distributed joint angles where each specific joint angle in the plurality of distributed joint angles satisfies a relationship 0.8≤θ/θM≤1.2, where the θ is the each specific joint angle in the plurality of distributed joint angles and the θM is an angle on the probability function (μ, σ2);
and
minimizing an error function, where the error function comprises a plurality of errors, and where a quantity of errors in the plurality of errors is equal to a quantity of joint angles in the plurality of distributed joint angles, and where each error in the plurality of errors corresponds to a specific joint angle in the plurality of distributed joint angles, where the each error comprises a specific transformation matrix Ai, the prospective control parameter x, and the end effector parameter b, where the specific transformation matrix Ai, is the transformation matrix Ao when the specific joint angle is utilized as the at least one joint angle, where an absolute value of the error function decreases as a summation of the each individual errors in the plurality of errors comprising the error function decreases, and where the end effector parameter b is referenced in the task space, thereby determining the prospective control parameter x in the task space;
and
communicating the prospective control parameter x to the at least one actuator in the group of actuators;
and controlling the at least one actuator in the group of actuators using the prospective control parameter x.

14 more elements

Dependencies are inferred from the claim text.