System and method for planning support removal in hybrid manufacturing with the aid of a digital computer

Abstract

Parameters of a set of tools are stored on a storage device. The tools are part of a manufacturing assembly usable for removing one or more support structures from a part. The support structures are formed with the part to facilitate additive manufacturing of the part. A near-net shape is modeled which includes the part combined with the support structures. A process plan is developed that includes subtractive manufacturing operations by the manufacturing assembly that remove the support structures. The process plan repeatedly updates the near-net shape as each one of the support structures is incrementally removed.

Claims

1. A method comprising: storing parameters of a set of tools of a manufacturing assembly usable for removing one or more support structures from a part, the support structures formed with the part to facilitate additive manufacturing of the part; modeling a near-net shape comprising the part combined with the support structures; and developing a process plan comprising subtractive manufacturing operations by the manufacturing assembly that remove the support structures, wherein the process plan repeatedly updates the near-net shape as each one of the support structures is incrementally removed.

2. The method of claim 1, wherein the process plan removes only those parts of the support structures that are in contact with the part.

3. The method of claim 1, wherein developing the process plan comprises: representing a set of states, each state identifying an orientation of the manufacturing assembly and describing the near-net shape with selected ones of the support structures that remain at the state, with one of the states representing an initial state; representing a set of actions, each action describing one of the orientations of the manufacturing assembly and describing removal of at least one of the support structures from the near-net shape; starting at the initial state, repetitively transitioning from one of the states to another of the states by choosing one of the actions as guided by a cost constraint function until a goal condition is satisfied; and using the chosen actions to form the process plan.

4. The method of claim 3, wherein each of the orientations of the set of states is selected from a limited set of total orientations, the limited set of total orientations reducing a deviation of the tools from a surface normal of the part.

5. The method of claim 4, wherein the reducing the deviation of the tools from the surface normal of the part minimizes scalloping of the part.

6. The method of claim 1, wherein a greedy algorithm is used to plan the incremental removal of the support structures from the near-net shape.

7. A system comprising: a storage device that stores a model of a part and parameters of a set of tools of a manufacturing assembly usable for removing one or more support structures from the part, the support structures formed with the part to facilitate additive manufacturing of the part; and a processor and memory coupled to the storage device and operable to perform steps comprising: modeling a near-net shape comprising the part combined with the support structures; and developing a process plan comprising subtractive manufacturing operations by the manufacturing assembly that remove the support structures, wherein the process plan repeatedly updates the near-net shape as each one of the support structures is incrementally removed.

8. The system of claim 7, wherein the process plan removes only those parts of the support structures that are in contact with the part.

9. The system of claim 7, wherein developing the process plan comprises: representing a set of states, each state identifying an orientation of the manufacturing assembly and describing the near-net shape with selected ones of the support structures that remain at the state, with one of the states representing an initial state; representing a set of actions, each action describing one of the orientations of the manufacturing assembly and describing removal of at least one of the support structures from the near-net shape; starting at the initial state, repetitively transitioning from one of the states to another of the states by choosing one of the actions as guided by a cost constraint function until a goal condition is satisfied; and using the chosen actions to form the process plan.

10. The system of claim 9, wherein each of the orientations of the set of states is selected from a limited set of total orientations, the limited set of total orientations reducing a deviation of the tools from a surface normal of the part.

11. The system of claim 10, wherein the reducing the deviation of the tools from the surface normal of the part minimizes scalloping of the part.

12. The system of claim 7, wherein a greedy algorithm is used to plan the incremental removal of the support structures from the near-net shape.

13. A method comprising: storing parameters of a machining tool assembly usable for removing one or more support structures from a part, the support structures formed with the part to facilitate additive manufacturing of the part; representing a set of states, each state identifying an orientation of the machining tool assembly and describing a near-net shape comprising the part combined with selected ones of the support structures that remain at the state, with one of the states representing an initial state; representing a set of actions, each action describing one of the orientations of the machining tool assembly and describing removal of at least one of the support structures from the near-net shape; starting at the initial state, repetitively transitioning from one of the states to another of the states by choosing one of the actions as guided by a cost constraint function until a goal condition is satisfied; and using the chosen actions to form a process plan comprising subtractive manufacturing operations used by the machining tool assembly to remove the support structures.

14. The method of claim 13, wherein each of the orientations of the set of states is selected from a limited set of total orientations, the limited set of total orientations reducing a deviation of the machining tool assembly from a surface normal of the part.

15. The method of claim 14, wherein the reducing the deviation of the machining tool assembly from the surface normal of the part minimizes scalloping of the part.

16. The method of claim 13, wherein the cost constraint function minimizes a time to perform to perform the operations by the machining tool assembly.

17. The method of claim 13, wherein the cost constraint function maximizes a surface finish of the part.

18. The method of claim 13, wherein choosing one of the actions as guided by the cost constraint function comprises using an A* algorithm.

19. The method of claim 13, wherein a greedy algorithm is used to plan the removal of the at least one of the support structures from the near-net shape.

20. The method of claim 13, wherein each action removes only those parts of the support structures that are in contact with the part.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 is a side view showing, by way of example, a near-net shape as fabricated through AM processes.

(2) FIG. 2 is a functional block diagram showing a system for planning support removal in hybrid manufacturing with the aid of a digital computer in accordance with one embodiment.

(3) FIG. 3 is a flow diagram showing a method for planning support removal in hybrid manufacturing with the aid of a digital computer in accordance with one embodiment.

(4) FIG. 4 is a flow diagram showing a routine for performing a greedy algorithm to plan the removal of the support beams from the near-net shape for use in the method of FIG. 3.

(5) FIG. 5 is a flow diagram showing a recursive routine for evaluating manufacturability of a part being fabricated for use in the routine of FIG. 4.

DETAILED DESCRIPTION

(6) Planning SM processes for removing scaffolding from an AM-produced near-net shape requires analysis of feasible non-colliding cutting tool configurations in a dynamically-changing space. As each support is removed from the near-net shape, the space available to the cutting tool for collision-free motion around the near-net shape changes, usually by increasing the amount of free space within which a cutting tool assembly can move. For each type of cutting tool to be used, a tool's configuration includes a position and orientation. Thus, the combination of the part and scaffolding, which constitute the near-net shape, and tool assembly configuration geometries together creates a complex problem space for determining support removability through SM processes.

(7) A support removal process plan for SM processes includes sequences of support beams to be removed. FIG. 1 is a side view showing, by way of example, a near-net shape 10 as fabricated through AM processes. Support structures or scaffolding, often in the form of support beams 12, have been added during AM to support the part being fabricated 11. The scaffolding is often organized in tree-like shapes to save material, which is eventually discarded or potentially reused for other purposes. For convenience, “support structure,” “scaffolding,” and “support beam” will be used interchangeably to refer to the support material that has been added to a part being fabricated by AM processes.

(8) For each support removal sequence generated, a tool path planner, such as a computer-aided manufacturing (CAM) system, or a system using motion planning algorithms, for instance, the Open Motion Planning Library (OMPL), generates a tool path to be used in a process plan. FIG. 2 is a functional block diagram showing a system 20 for planning support removal in hybrid manufacturing with the aid of a digital computer in accordance with one embodiment. A tool path planner 21 is provided through a centralized server 22. The server 22 can be remotely accessed via the Web over a wide area public data communications network, such as the Internet, using wired or wireless connections. Users can interface with the server 22 through a Web browser 28 executing on a personal computer 27, mobile “smart” phone, or similar device. Alternatively, the tool path planner 21 can be provided locally on the personal computer 27 or similar device. The server 22 is operatively coupled to a storage device 24, within which is stored models of designed parts 25 that define surfaces and the interior of the part, such as represented using some CAD representation such as STEP, STL, voxels or some other solid model representation, a library of cutting or machining tools 26, and, in one embodiment, a library of motion planning algorithms, such as the Open Motion Planning Library (OMPL). Both the server 22 and personal computer 27 include components conventionally found in general purpose programmable computing devices, such as a central processing unit, memory, input/output ports, network interfaces, and non-volatile storage, although other components are possible. In addition, other computational components are possible.

(9) In one embodiment, through the tool path planner 21, the Web-based service 23 generates process plans 30 that each contain support removal sequences. Each sequence includes CNC machining instructions that have been generated by the tool path planner 21 by modeling the inherent capabilities of a hybrid manufacturing setup 29. The hybrid manufacturing setup 29 includes a cutting or machining tool assembly 31 for performing SM operations. The machining tool assembly 29 can be programmed with the machining instructions in the process plans 30 generated by the tool path planner 21 and operated to remove supporting beams 12 from the near-net shape 10.

(10) The tool path planner 21 implements a geometric engine that executes a set of spatial planning algorithms for automated manufacturability analysis of arbitrary geometric models, without making assumptions on the tool geometry and degrees of freedom, or the existence of surrounding tooling and fixtures, such as described in U.S. Pat. No. 9,292,626, issued Mar. 22, 2016, to Nelaturi et al., the disclosure of which is incorporated by reference. The manufacturing setup model corresponds to the library of cutting or machining tools 26 with specifications for each operable tool, and the tool path planner 21 connects the available capability of each tool to the uploaded geometric model of each part 25 to provide qualitatively distinct process plans, represented in the form of a JSON (“JavaScript Object Notation”) file or similar structured encoding or human-readable format, with detailed feedback for each individual plan.

(11) The geometric reasoning algorithms use tooling information from the library 26 to allow the tool path planner 21 to generate a collision-free path for the tool assembly to remove one support beam 12 at a time, as further described infra with reference to FIG. 3. As each support beam 12 is removed, the tool path planner 21 must reason about accessing the removal of the remaining support beams 12 in the context of the space just freed up by the removal of that support beam 12. In each successive iteration within the support removal sequence, the tool path planner 21 relies upon a solid model corresponding to the near-net shape 10 and all remaining support structure 12 that together constitute a physical obstacle that the machining tool assembly 31 must avoid. Thus, based upon the available space, the tool path planner 21 attempts to find the best way to remove the next support beam 12 in the support removal sequence, provided that the next support beam 12 is accessible to the machining tool assembly 31.

(12) In modeling an SM process plan problem space, begin by assuming that there are finitely many (say k) support beams 12 that contact the fabricated part 11. Each support beam 12 can be numbered and indexed, so as to generate all k! permutations of support structure removal sequences. Considering that a single part 11 being fabricated may consist of several hundred support beams 12, an enumeration of all k! permutations would result in an astronomically large set of possible support removal sequences. Generating and testing each possible sequence would be impracticable.

(13) On the other hand, human engineers may be able to visually inspect a near-net shape and recommend a candidate set of support beam removal sequences based on their own experience. Importantly, a human engineer may be able to quickly decide if a near-net shape 10 has support beams 12 that cannot be removed, for example, when supports support beams 12 are placed in internal voids 13, and that knowledge can be used to pare down the size of the problem space.

(14) Nevertheless, relying upon human expertise can present shortcomings due to the limitations inherent in the human reasoning of three-dimensional space and a fully automated process plan generate and test approach for candidate sequences of support removal is needed.

(15) Algorithmic reasoning about a cutting tool assembly's space of feasible configurations can be effectively harnessed by the tool path planner to construct a sequence of supports structures 12 that guarantees a collision-free path for the tool assembly to remove each support structure 12 in the sequence. FIG. 3 is a flow diagram showing a method 40 for planning support removal in hybrid manufacturing with the aid of a digital computer in accordance with one embodiment. The method 40 is performed as a series of process or method steps performed by, for instance, a general purpose programmed computer, such as the server 22 and personal computer 27, or other programmable computing device.

(16) Initially, a model of the manufacturing setup, including a library of the cutting tools 26 to be used to machine the near-net shape 12, as well as knowledge of the part 11 as designed and the scaffolding 12 (available through the stored models of designed parts 25), are respectively retrieved (steps 41 and 42). Note that initially, the near-net shape 10 is the combination of the part 11 and the scaffolding 12. The library 26 stores information on each type of milling tool, including the orientations and positions in which the milling tool can operate.

(17) Next, for process planning purposes, the tip of the machining tool assembly 29 is logically located (step 43) to coincide with the origin of a coordinate system in R.sup.3. The tool assembly's tip would ordinarily be the aspect of the machining tool 31 that makes actual physical contact with the near-net shape 10 to remove a support beam 12 from the part 11. This coordinate system is used to measure the relative positions and orientations of the tool assembly T with respect to the near-net shape N. Next, logically assume that there are finitely many support beams S={S.sub.1, . . . , S.sub.k} added on to the part P that is intended to be fabricated by the AM process (step 44). In general, k will represent the actual number of support beams 12. Therefore, N=P∪.sub.i=1.sup.kS.sub.i.

(18) Unlike traditional machining, the entire scaffolding 12 need not be completely machined off the near-net shape 10, though that is a feasible strategy. Rather, in SM processes, fracturing the region (or point) of contact between the support beam 12 and the part 11, so that the part 11 can be disengaged from the support beam 12, will suffice. Therefore, at a minimum, collision-free contacts between the cutting tool's tip and the region of a near-net shape 10 where a support beam 12 touches the part's surface must be found. A greedy algorithm to plan the removal of the support beams 12 from the near-net shape 10 is performed (step 45), as further described infra with reference to FIG. 4 (step 46), after which process plans are created (step 47) based upon the collection of tool assembly configurations that were generated and the method completes.

(19) The greedy algorithm models the motion of the tool assembly 31 through the free-spaces around the near-net shape 10 and the part 10 to determine feasible points of contact for the tool assembly 31. FIG. 4 is a flow diagram showing a routine 60 for performing a greedy algorithm to plan the removal of the support beams 12 from the near-net shape 10 for use in the method 40 of FIG. 3. First, a configuration space of rigid motions for the tool assembly 31 (geometric transformations) is set up (step 61) by assuming that the tool assembly T can operate with all six degrees of freedom available for a rigid body, that is, three translations and three rotations. Mathematically, this assumption can be expressed as the configuration space of rigid motions C=R.sup.3×SO(3), where SO(3) refers to the group of 3×3 orthogonal transformations that represent spatial rotations of the tool assembly T based upon the tool assembly's parameters, including orientations and positions along which the tool cuts away raw material. Define projections from C to R.sup.3 and to SO(3) as follows:
π.sub.1:C.fwdarw.R.sup.3  (1)
π.sub.2:C.fwdarw.SO(3)  (2)

(20) Now, define the free-space .sub.N around the near-net shape N as the set of all of tool assembly T's configurations that do not collide with the near-net shape N, that is, all non-colliding orthogonal transformations of the machining tool assembly within the configuration space C, and any workholding devices W that are used to fixture the part as scaffolding is removed:
.sub.N={g∈Cs.t.T.sub.g∩*{N∪W}=∅}  (3)
where the letter g emphasizing that C is also a Lie group called the Special Euclidean group SE(3). Here T.sub.g refers to the tool assembly T transformed by an element g∈C, and ∩* refers to regularized intersection. The complement of the free space .sub.N is called the obstacle space O that delineates configurations of the tool assembly T that cause collision with the near-net shape N. Therefore, the boundary shared by O and .sub.N delineates all of the tool configurations that cause contact, but no collision between the tool assembly T and the near-net shape N.

(21) Similarly, define the free-space .sub.P around the part P as the set of all of tool assembly configurations that do not collide with P∪W, which is the part P and any workholding devices W:
.sub.P={g∈Cs.t.T.sub.g∩*{P∪W}=∅}  (4)
Notice that after the AM processes complete and before the SM processes start, .sub.p⊃.sub.N, that is, the free-space .sub.P around the part P is a superset of the free-space .sub.N around the near-net shape N because the support beams 12 will prevent the tool assembly T from being able to reach the physical space otherwise available to access the part P. As the support beams 12 are removed, the near-net shape N will get smaller and converge in size towards the size of the part P, while the free-space .sub.N around the near-net shape N will get larger and converge towards the free-space .sub.p around the part P.

(22) Given a boundary feature F⊂∂P, where boundary of a set Y is denoted ∂Y, two sets of collision-free contact configurations of tool assembly Tat the boundary feature F can be defined as:
.sub.F.sup.P={g∈∂F.sub.P|π.sub.1(T.sub.g)∈F}  (5)
.sub.F.sup.N={g∈∂F.sub.N|π.sub.1(T.sub.g)∈F}  (6)
The intersection of each support beam S.sub.i∈S with the part P will be a boundary feature F.sub.i. For simplicity, assume that boundary feature F.sub.i is a point set, which is consistent with AM practice, where support beams S are often designed to have minimal contact with the boundary of the part ∂P to minimize surface roughness and enable easier fracture and removal of the support beams S by SM processes.

(23) Next, the manner of construction of the support beams 12 is determined (step 62) to provide boundary features at the intersection of the individual support beam S.sub.i and the part P. Preferably, support beams are constructed from a surface of ∂P to a stationary base plate or fixture. However, in some situations, the support beams 12 may have to be constructed from one location of ∂P to another location of ∂P. Also, an individual support beam S.sub.i may contact the part P at multiple locations when the contacting support beams are “branched” outwards from a main “trunk,” such as occurs when the scaffolding is organized in tree-like shapes. To accommodate these situations, a specific boundary feature F.sub.i=S.sub.i∩P can be a discrete point set, which is the intersection of the individual support beam S.sub.i and the part P. Therefore, if .sub.F.sub.i.sup.N≠∅, where .sub.F.sub.i.sup.N is the set of collision-free contact configurations of tool assembly Tat the boundary feature F.sub.i, then each f∈F.sub.i, such that π.sub.1(.sub.F.sub.i.sup.N)=f, is a feasible point of contact for the tool assembly T within the configuration space C to either partially or totally remove the individual support beam S.sub.i.

(24) The part 11 is then evaluated for manufacturability (step 63), as further described infra with reference to FIG. 5. If a part being fabricated 11 is non-manufacturable (step 64), no SM process plan to cut the support beams S from the near-net shape N so that the part P can be dislodged, exists and the greedy algorithm terminates.

(25) On the other hand, if a part being fabricated 11 is manufacturable (step 64), that is, boundary features F.sub.i have been found for all of the support beams S, a collection of tool assembly configurations that are guaranteed to be non-colliding but which can access all points in the boundary features F.sub.i can be generated (step 65) using the support removal sequence, after which the greedy algorithm terminates. In a further embodiment, human engineers can validate the process plans and, if desired, re-order the support removal sequence. The reordered support removal sequence is resubmitted to the greedy algorithm to attempt to re-plan the tool motions to remove the supports without collision, starting with determining the manner of construction of the support beams 12 (step 62) based upon the reordered support removal sequence.

(26) Hybrid manufacturability hinges upon the ability to remove the support beams 12 from a near-net shape 10 to yield the part 11. FIG. 5 is a flow diagram showing a recursive routine 80 for evaluating manufacturability of a part being fabricated 11 for use in the routine 60 of FIG. 4. The routine is recursive, although an iterative structure could be used instead. Assuming that there are still support beams S.sub.i remaining in the set of support beams S (step 81), all of those support beams S.sub.i are evaluated to find an individual support beam S.sub.i where π.sub.1(.sub.F.sub.i.sup.N)=F.sub.i (step 82), that is, F.sub.i is a feature along the boundary of the near-net shape 10 that constitutes a feasible point of contact for the tool assembly T to either partially or totally remove the individual support beam S.sub.i. If an individual support beam S.sub.i does not exist (step 83), the part P is found to be non-manufacturable (step 84) because no SM process plan to cut the support beams S from the near-net shape N, so that the part P can be dislodged exists. However, if such an individual support beam S.sub.i does exist (step 83), then by constructing .sub.F.sub.i.sup.N, which is the set of collision-free contact configurations of tool assembly T at the boundary feature F.sub.i, a collection of tool assembly configurations that are guaranteed to be non-colliding but which can access all points in F.sub.i can be extracted. The near-net shape 10 is continually updated as each support beam S.sub.i is incrementally removed. Thus, the near-net shape N is updated to become N−S.sub.i (step 85), the individual support beam S.sub.i is removed from the set of remaining support beams S (step 86), and individual support beam S.sub.i is added to the support removal sequence (step 87). The routine recurses (or iterates) until no support beams S remain in the set (step 81), or the part P is found to be non-manufacturable (step 84) for a given sequence of support beams to be removed.

(27) There may be multiple individual support beams S.sub.i that are eligible for removal at each recursion (or iteration), that is, multiple support beams S.sub.i may satisfy the condition that π.sub.1(.sub.F.sub.i.sup.N)=F.sub.i (step 82). The choice of a particular individual support beam S.sub.i then affects how the near-net shape N is updated, which in turn affects the subsequent collision-free contact configurations .sub.F.sup.N of tool assembly Tat the boundary feature F. A tool path planner 21 that uses motion planning algorithms, for instance, the OMPL, cited supra, may be used to choose a particular support beam 12 and plan the individual tool assembly trajectories from the chosen support beam 12 to the next support beam 12 in the support removal sequence. The challenge with this approach, though, is computing the collision-free contact configurations .sub.F.sub.i.sup.N of tool assembly Tat the boundary feature F.sub.i at each iteration of the support removal sequence, as the near-net shape N is updated as each support beam 12 is removed, which occurs in the six-dimensional configuration space C, as discussed in detail infra. Furthermore, limited accessibility may require complex tool paths to execute (if possible). Nevertheless, the greedy algorithm will always return a valid sequence of support removals if such a sequence exists.

(28) In practical situations, several collision-free support removal sequences may be possible and various combinations of collision-free contact configurations .sub.F.sub.i.sup.N may need to be explored to find optimal removal sequences. A “good” sequence could be determined by evaluating the candidate process plans based upon a manufacturing heuristic, optimization constraint, or cost constraint sought to be optimized, for instance, minimizing time, using as few orientations as possible for three-axis milling, or maximizing surface finish, such as described in U.S. Patent application Pub. No. US 2017/0220028, filed Jan. 29, 2016, pending, the disclosure of which is incorporated by reference. One or more qualitatively distinct process plans for machining a part through SM processes are created; the surfaces of the part are modeled and parameters for a plurality of cutting tools are obtained. The parameters include orientations and positions along which each cutting tool cuts away raw material. Each process plan includes a maximal set of translations for each cutting tool, where each translation includes a collision-free orientation of the cutting tool and a maximal machinable volume of material removable from the part in that orientation. A search engine navigates through a hierarchically-structured search space that starts at an initial state and transitions to successive states based on actions that satisfy a cost constraint function. One of the actions is chosen as guided by a heuristic that is based on aggregate cost and the negative volume that remains after subtracting the maximal sub-volume for the action chosen. Each state and each action includes a tool, orientation of the tool, and a maximal machinable volume. The search ends when a goal condition is satisfied and the actions that satisfy the cost constraint function constitute the process plan to be used.

(29) More generally, to optimize the sequencing of SM processes, a search space can be iteratively built where each search node stores distinct boundary features F.sub.N for the near-net shape N as obtained by calculating the free-space .sub.N around the near-net shape N resulting from subtracting a distinct support beam S.sub.i∈S from the near-net shape N. Several practical heuristics may be used to pick the support beams 12 that are good candidates for removal. For example, visibility analysis for manufacturing algorithms may be used to decide which of the F.sub.i have the most visibility because visibility can be used as a weak condition for accessibility. Furthermore, there may be practical considerations about how much deviation from the surface normal can be allowed for the tool contact orientations to minimize scalloping the part surface. Therefore, a limited set of cutting tool assembly orientations may be chosen a priori to minimize the number of cutting tool assembly orientations for which the free-spaces need to be computed.

(30) The six-dimensional configuration space of obstacles and free-space for complex cutting tool and fixture assemblies can be effectively modeled to compute the collision-free contact configurations .sub.F.sub.i.sup.N of tool assembly Tat the boundary feature F.sub.i at each iteration of a support removal sequence, such as described in S. Nelaturi, Configuration Modeling, Ph.D. Dissertation, Univ. of Wisconsin-Madison (2012), and U.S. Pat. No. 9,235,658, issued Jan. 12, 2016, to Nelaturi et al., and U.S. Pat. No. 9,566,697, issued Feb. 14, 2017, to Nelaturi et al., the disclosures of which are incorporated by reference. Given a collection of orientations sampled to a desired density, the six-dimensional spaces can be computed by calculating the three-dimensional translational free-space for each sampled orientation. In practice, computing the obstacle space, that is, the complement of the free-space, may be more convenient to compute since the obstacle space is a closed and bounded set. By computing the six-dimensional obstacle space, all of the contact configurations at a specific location can be retrieved by querying the boundary of the six-dimensional obstacle in time linear to the number of sampled orientations. The collision-free contact configurations .sub.F.sub.i.sup.N can be obtained by querying the contact configurations at each F.sub.i.

(31) More generally, given a collection of free-spaces obtained by iteratively reducing the number of support beams, standard search algorithms, such as A* (with an implemented cost function), can be used to find the best sequence of free-spaces that will provide a low-level tool path planner that uses motion planning algorithms, for instance, the OMPL, cited supra, all the available configurations to find a tool path from one support beam to the next support beam, and execute the support removal.

(32) While the invention has been particularly shown and described as referenced to the embodiments thereof, those skilled in the art will understand that the foregoing and other changes in form and detail may be made therein without departing from the spirit and scope of the invention.