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1. (WO2018226673) ROBOTIC SYSTEM AND METHOD FOR PRODUCING REACTIVE FORCES TO IMPLEMENT VIRTUAL BOUNDARIES
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CLAIMS

1. A robotic system comprising:

a tool;

a manipulator comprising a plurality of links and configured to move the tool; and a controller coupled to the manipulator and configured to implement a virtual simulation wherein the tool is represented as a virtual volume being adapted to interact relative to a virtual boundary defined by a mesh of polygonal elements, and wherein the controller is configured to:

compute a reactive force in response to penetration of one of the polygonal elements by the virtual volume in the virtual simulation, wherein the reactive force is computed based on a penetration factor being a function of a geometry of the virtual volume bound relative to a geometry of the polygonal element;

apply the reactive force to the virtual volume in the virtual simulation to reduce penetration of the polygonal element by the virtual volume; and

command the manipulator to move the tool in accordance with application of the reactive force to the virtual volume in the virtual simulation to constrain movement of the tool relative to the virtual boundary.

2. The robotic system of claim 1, wherein the penetration factor is functionally independent of a linear depth of penetration of the polygonal element by the virtual volume.

3. The robotic system of any preceding claim, further comprising a navigation system configured to track states of the tool and being coupled to the controller and wherein the virtual volume is positioned based on tracked states of the tool.

4. The robotic system of claim 3, wherein the tool is configured to interact with a target site and wherein the navigation system is configured to track states of the target site and wherein the virtual boundary is associated with the target site.

5. The robotic system of any one of claims 3 and 4, wherein the navigation system is configured to track states of an object to be avoided by the tool and wherein the virtual boundary is associated with the object to be avoided.

6. The robotic system of any one of claims 3-5, wherein, for subsequent changes of state of the tool, the controller is further configured to iteratively compute the reactive force, iteratively apply the reactive force, and iteratively command the manipulator to move the tool in accordance with application of the reactive force to the virtual volume in the virtual simulation.

7. The robotic system of any preceding claim, wherein the polygonal elements are triangles.

8. The robotic system of any preceding claim, wherein the virtual volume comprises a single face, zero vertices, and zero edges.

9. The robotic system of any preceding claim, wherein the virtual volume is spherical.

10. The robotic system of any preceding claim, wherein the reactive force is further defined as an impulse force.

11. The robotic system of any preceding claim, wherein the controller is further configured to compute multiple reactive forces in response to simultaneous penetration of multiple polygonal elements by the virtual volume in the virtual simulation, wherein each reactive force is computed based on the penetration factor being a function of the geometry of the virtual volume bound relative to the geometry of each polygonal element.

12. The robotic system of claim 11, wherein the controller is further configured to: simultaneously apply the multiple reactive forces to the virtual volume in the virtual simulation; and

command positioning of the manipulator in accordance with application of the multiple reactive forces to the virtual volume in the virtual simulation.

13. The robotic system of claim 11, wherein the controller is further configured to: combine the multiple reactive forces to generate a combined reactive force;

apply the combined reactive force to the virtual volume in the virtual simulation; and command positioning of the manipulator in accordance with application of the combined reactive force to the virtual volume in the virtual simulation.

14. The robotic system of claim 13, wherein the controller is further configured to apply a weighting factor to each of the reactive forces such that the combined reactive force is constant for any given simultaneous penetration of multiple polygonal elements by the virtual volume.

15. The robotic system of any preceding claim further comprising a force-torque sensor being configured to sense an input force applied to the tool and wherein the input force is applied to the virtual volume in the virtual simulation to cause penetration of one of the polygonal elements by the virtual volume.

16. The robotic system of any preceding claim wherein the penetration factor is a projected area defined by intersection of the virtual volume with the polygonal element and wherein the projected area is bound by the geometry of the polygonal element.

17. The robotic system of any preceding claim wherein the penetration factor is a projected arc defined by a combination of any arcs of a cross-sectional area of the virtual volume being bound by the geometry of the polygonal element during intersection of the virtual volume with the polygonal element.

18. The robotic system of any preceding claim wherein the penetration factor is a displaced volume defined by a volume of the virtual volume that penetrates the polygonal element and wherein the volume is bound by the geometry of the polygonal element.

19. A method of controlling a robotic system comprising a tool, a manipulator comprising a plurality of links and configured to move the tool, and a controller coupled to the manipulator and configured to implement a virtual simulation wherein the tool is represented as a virtual volume being configured to interact relative to a virtual boundary defined by a mesh of polygonal elements, the method comprising the controller:

computing a reactive force in response to penetration of one of the polygonal elements by the virtual volume in the virtual simulation, wherein the reactive force is computed based on a penetration factor being a function of a geometry of the virtual volume bound relative to a geometry of the polygonal element;

applying the reactive force to the virtual volume in the virtual simulation for reducing penetration of the polygonal element by the virtual volume; and

commanding the manipulator for moving the tool in accordance with application of the reactive force to the virtual volume in the virtual simulation for constraining movement of the tool relative to the virtual boundary.

20. The method of claim 19, wherein the penetration factor is functionally independent of a linear depth of penetration of the polygonal element by the virtual volume.

21. The method of any one of claims 20 and 21, further comprising:

receiving, from a navigation system, tracked states of the tool; and

positioning the virtual volume based on tracked states of the tool.

22. The method of claim 21, further comprising:

commanding the manipulator for moving the tool in relation to a target site;

receiving, from the navigation system, tracked states of the target site; and

associating the virtual boundary with the target site.

23. The method of any one of claims 21 and 22, further comprising:

receiving, from the navigation system, tracked states of an object to be avoided by the tool; and

associating the virtual boundary with the object to be avoided.

24. The method of any one of claims 21-23, further comprising iteratively computing the reactive force, iteratively applying the reactive force, and iteratively commanding the manipulator for moving the tool in accordance with application of the reactive force to the virtual volume in the virtual simulation, for subsequent changes of state of the tool.

25. The method of any one of claims 19-24, further comprising computing multiple reactive forces in response to simultaneous penetration of multiple polygonal elements by the virtual volume in the virtual simulation, wherein each reactive force is computed based on the penetration factor being a function of the geometry of the virtual volume bound relative to the geometry of each polygonal element.

26. The method of claim 25, further comprising:

simultaneously applying the multiple reactive forces to the virtual volume in the virtual simulation; and

commanding positioning of the manipulator in accordance with application of the multiple reactive forces to the virtual volume in the virtual simulation.

27. The method of claim 25, further comprising:

combining the multiple reactive forces for generating a combined reactive force;

applying the combined reactive force to the virtual volume in the virtual simulation; and commanding positioning of the manipulator in accordance with application of the combined reactive force to the virtual volume in the virtual simulation.

28. The method of claim 27, further comprising applying a weighting factor to each of the reactive forces such that the combined reactive force is constant for any given simultaneous penetration of multiple polygonal elements by the virtual volume.

29. The method of any one of claims 19-28, further comprising:

determining an input force applied to the tool based on measurements from a force-torque sensor;

applying the input force to the virtual volume in the virtual simulation for causing penetration of one of the polygonal elements by the virtual volume.

30. The method of any one of claims 19-29, wherein computing the reactive force is based on the penetration factor being a projected area defined by intersection of the virtual volume with the polygonal element and wherein the projected area is bound by the geometry of the polygonal element.

31. The method of any one of claims 19-30, wherein computing the reactive force is based on the penetration factor being a projected arc defined by a combination of any arcs of a cross-sectional area of the virtual volume being bound by the geometry of the polygonal element during intersection of the virtual volume with the polygonal element.

32. The method of any one of claims 19-31, wherein computing the reactive force is

based on the penetration factor being a displaced volume defined by a volume of the virtual volume penetrating the polygonal element and wherein the volume is bound by the geometry of the polygonal element.

33. A controller-implemented method of simulating dynamics of a tool of a robotic system, the method comprising:

simulating the tool as a virtual volume;

simulating a virtual boundary comprising a mesh of polygonal elements;

simulating movement of the virtual volume to penetrate multiple polygonal elements simultaneously;

computing multiple reactive forces in response to simultaneous penetration of the multiple polygonal elements, wherein each reactive force is computed based on a penetration factor being a function of a geometry of the virtual volume bound relative to a geometry of each polygonal element;

combining the multiple reactive forces for generating a combined reactive force;

applying a weighting factor to each of the reactive forces such that the combined reactive force is constant for any given simultaneous penetration of multiple polygonal elements by the virtual volume; and

simulating application of the combined reactive force to the virtual volume.