Tool position determination in a robotic appendage
System and techniques for tool position determination in a robotic appendage are described herein. A robotic appendage is put through a rotational movement to induce acceleration in a tool mounted to the appendage. A model for acceleration is created from positional kinematics of the appendage. A measurement of acceleration is taken at the tool and fit to the model to determine distance from the axis of rotation to the tool. The distance is provided for use in control or modeling of the robotic appendage.
1 . A device for determining a position of a tool affixed to a robotic appendage, the device comprising:
an interface configured to communicate with the robotic appendage;
processing circuitry configured to:
communicate an instruction, via the interface, to perform a rotational movement of a portion of the robotic appendage to determine the position of the tool, the rotational movement being defined by rotational positions about an axis;
generate a model of tool acceleration for the tool along the rotational movement that predicts acceleration of the tool at a variety of distances from the axis;
obtain acceleration measurements from a sensor affixed to the tool, the acceleration measurements being taken during the rotational movement; and
fit the acceleration measurements to the model of tool acceleration to determine a distance from the axis to the tool.
2 . The device of claim 1 , wherein the rotational positions are less than a complete revolution about the axis.
3 . The device of claim 1 , wherein the rotational positions are a quarter or a third of a complete revolution about the axis.
4 . The device of claim 1 , wherein the rotational movement repeats the rotational positions multiple times.
5 . The device of claim 1 , wherein the robotic appendage includes multiple portions, and
wherein each portion of the multiple portions is defined by a rotating member and a support member.
6 . The device of claim 5 , wherein additional rotational movements are respectively performed for the multiple portions to determine a distance between the tool and respective rotating member of the multiple portions.
7 . The device of claim 1 , wherein multiple portions of the robotic appendage other than the portion of the robotic appendage are placed into a predefined position as the acceleration measurements are obtained from the sensor affixed to the tool.
8 . The device of claim 1 , wherein the processing circuitry is configured to determine an orientation of the tool with respect to the portion of the robotic appendage based on the model of tool acceleration and the acceleration measurements.
9 . The device of claim 8 , wherein the acceleration measurements include acceleration in multiple axes, and
wherein the orientation of the tool is determined based on a distribution of tool acceleration between at least two of the multiple axes.
10 . The device of claim 1 , wherein the processing circuitry is configured to generate the model of the tool acceleration by generating a kinematic model of tool positioning based on the rotational movement.
11 . The device of claim 10 , wherein the processing circuitry is configured to generate the model of the tool acceleration by deriving tool acceleration from the kinematic model to generate a differential kinematic model of tool acceleration.
12 . The device of claim 1 , wherein the processing circuitry is configured to determine the distance from the axis to the tool by minimizing an error between the acceleration measurements and the model of tool acceleration.
13 . The device of claim 1 , wherein the instruction comprises an instruction to perform the rotational movement of the portion of the robotic appendage to determine the position of the tool as part of a calibration operation, and
wherein the distance from the axis to the tool is determined in accordance with the calibration operation.
14 . The device of claim 1 , wherein the model of tool acceleration is generated using differential kinematics in conformal geometric algebra to compute linear acceleration of the tool as a function of joint accelerations.
15 . A non-transitory machine-readable medium including instructions for determining a position of a tool affixed to a robotic appendage, the instructions, when executed by processing circuitry, cause the processing circuitry to:
communicate an instruction to perform a rotational movement of a portion of the robotic appendage to determine the position of the tool, the rotational movement being defined by rotational positions about an axis;
generate a model of tool acceleration for the tool along the rotational movement that predicts acceleration of the tool at a variety of distances from the axis;
obtain acceleration measurements from a sensor affixed to the tool, the acceleration measurements being taken during the rotational movement; and
fit the acceleration measurements to the model of tool acceleration to determine a distance from the axis to the tool.
16 . The non-transitory machine-readable medium of claim 15 , wherein the rotational positions are less than a complete revolution about the axis.
17 . The non-transitory machine-readable medium of claim 15 , wherein the rotational positions are a quarter or a third of a complete revolution about the axis.
18 . The non-transitory machine-readable medium of claim 15 , wherein the robotic appendage includes multiple portions, and
wherein each portion of the multiple portions is defined by a rotating member and a support member.
19 . The non-transitory machine-readable medium of claim 18 , wherein additional rotational movements are respectively performed for the multiple portions to determine a distance between the tool and respective rotating member of the multiple portions.
20 . The non-transitory machine-readable medium of claim 15 , wherein multiple portions of the robotic appendage other than the portion of the robotic appendage are placed into a predefined position as the acceleration measurements are obtained from the sensor affixed to the tool.
21 . The non-transitory machine-readable medium of claim 15 , wherein an orientation of the tool with respect to the portion of the robotic appendage is determined based on the model of tool acceleration and the acceleration measurements.
22 . The non-transitory machine-readable medium of claim 21 , wherein the acceleration measurements include acceleration in multiple axes, and
wherein the orientation of the tool is determined based on a distribution of tool acceleration between at least two of the multiple axes.
23 . The non-transitory machine-readable medium of claim 15 , wherein generating the model of the tool acceleration includes generating a kinematic model of tool positioning based on the rotational movement.
24 . The non-transitory machine-readable medium of claim 23 , wherein the model of the tool acceleration is generated by deriving tool acceleration from the kinematic model to generate a differential kinematic model of tool acceleration.
25 . The non-transitory machine-readable medium of claim 15 , wherein the distance from the axis to the tool is determined based on minimizing error between the acceleration measurements and the model of tool acceleration.