Autonomous robotic execution of nonlinear toolpaths for geometry-matched osteotomy in tooth autotransplantation: an in vitro study

Abstract

Tooth autotransplantation requires recipient socket preparation that matches donor root morphology while preserving surrounding bone. We developed an autonomous multi-axis robotic system that executes nonlinear, surface-conforming milling trajectories to create a geometry-matched socket and compared it with a static tooth-supported guide in forty 3D-printed mandibular models representing single-rooted and double-rooted anatomies. Recipient sockets were planned by offsetting the donor root surface by 0.5 mm and eliminating insertion axis undercuts. The robot executed the planned milling path with a depth-stop Lindemann bur, whereas the guide workflow used guided pilot drilling followed by freehand refinement. Robot assistance reduced deep positional errors and improved agreement between planned and prepared socket geometry, with the most pronounced benefit in double-rooted models, while overall preparation time was comparable between approaches. These findings support further clinical validation to confirm that autonomous robotic, surface-conforming osteotomy can improve full-depth geometric fidelity and reduce unnecessary bone removal in technique-sensitive autotransplantation procedures.

Introduction

Autotransplantation of teeth (ATT), defined as the repositioning of a tooth from one site to another within the same individual, is an established treatment option for replacing missing teeth.^1,2 Compared with prosthetic restorations and dental implants, autotransplanted teeth preserve a functional periodontal ligament, allowing physiological proprioception and continued alveolar bone remodeling,^3,4 while also representing a cost-effective approach. When appropriate case selection and surgical conditions are met, long-term survival rates exceeding 80% have been consistently reported.^5–7

Despite these advantages, the clinical success of tooth autotransplantation remains highly technique-sensitive.⁸ Among the factors influencing treatment outcomes, the accuracy of recipient socket preparation and the duration of extra-alveolar time are considered particularly critical.^9,10 A recipient socket that closely replicates the donor root morphology is critical for primary stability and optimal periodontal healing. In contrast, extended extraoral exposure can reduce periodontal ligament cell viability.¹¹ Achieving a well-fitted socket within a limited time window, therefore, represents a considerable clinical challenge.

Conventional freehand techniques depend largely on surgical experience and tactile feedback and frequently involve repeated trial insertion of the donor tooth or replicas.^8,9,12 Inaccurate socket preparation may lead to excessive insertion pressure, inadequate stability, delayed healing, or injury to adjacent anatomical structures.¹¹ Although digital technologies such as cone beam computed tomography,¹³ 3D-printed replicas,¹² and static surgical guides have been introduced to improve predictability and reduce extra-alveolar time, static guides remain limited by their reliance on cylindrical drills and restricted ability to reproduce complex root geometries.^14,15 This often necessitates additional manual bone adjustment, particularly in multi-rooted cases, and may result in deviations from the planned geometry and unnecessary bone removal.

Robotic surgical systems have been proposed as a means to address these limitations.^16–18 In implant dentistry, robot-assisted workflows have shown high accuracy and repeatability, largely because implant osteotomy and implant insertion are predominantly axis-oriented, along a planned, near-linear trajectory, which fits well with the motion characteristics of current dental robotic platforms.^19,20 Similar strengths may also be advantageous for other procedures that rely on controlled, directionally constrained tool paths, such as apical surgery and the negotiation of calcified canals.^21–24

However, many oral and maxillofacial procedures require irregular, non-linear, multi-degree-of-freedom movements and continuous adaptation to complex anatomy and changing tactile conditions,^17,25 including tooth preparation,²⁶ crown-lengthening osteoplasty,²⁷ and removal of impacted teeth.²⁸ Within tooth autotransplantation, the limited quantitative evidence available for robot-assisted recipient site preparation has, to date, largely involved robots executing regular, axis-dominant motions in in vitro work and case-level reports.^29,30

This in vitro study provides the first evaluation of an autonomous, multi-axis robotic osteotomy that executes nonlinear, surface-conforming toolpaths to create a recipient socket geometrically matched to the donor tooth root in tooth autotransplantation. The accuracy and efficiency of a robot-assisted osteotomy protocol were compared with those of a static guide-assisted approach for recipient-site preparation, using 3D-printed mandibular models representing single-rooted and double-rooted donor tooth anatomies.

Results

Accuracy and efficiency outcomes are summarized in Table 1 and Fig. 1. Figures 1a, b depict the 3D distributions of platform and apex deviation components for robot-assisted and static guide-assisted preparations. In Fig. 1c, platform deviation was comparable between groups overall (0.79 mm ± 0.35 mm vs 0.78 mm ± 0.37 mm, P = 0.954) and within the single-rooted (0.96 mm ± 0.32 mm vs 0.75 mm ± 0.36 mm, P = 0.169) and double-rooted subgroups (0.62 mm ± 0.29 mm vs 0.82 mm ± 0.39 mm, P = 0.200). Figure 1d shows significantly lower apex deviation with robot assistance overall (0.94 mm ± 0.35 mm vs 1.96 mm ± 0.67 mm, P < 0.001), mainly driven by double-rooted teeth (0.85 mm ± 0.37 mm vs 2.38 mm ± 0.54 mm, P < 0.001), whereas the difference in single-rooted teeth did not reach significance (1.03 mm ± 0.31 mm vs 1.53 mm ± 0.50 mm, P = 0.055). Figure 1e demonstrates reduced angular deviation with robot assistance overall (1.86° ± 1.04° vs 7.32° ± 3.21°, P < 0.001), in both single-rooted (2.29° ± 0.96° vs 5.99° ± 2.69°, P < 0.01) and double-rooted teeth (1.43° ± 0.97° vs 8.64° ± 3.25°, P < 0.001).

Table 1.

Comparison of accuracy and efficiency outcomes between robot-assisted and static guide-assisted osteotomy

Accuracy measures	n	Robot-assisted		Static guide-assisted		P value
		Mean	SD	Mean	SD
Platform deviation/ mm	20	0.79	0.35	0.78	0.37	0.954
Single-rooted	10	0.96	0.32	0.75	0.36	0.169
Double-rooted	10	0.62	0.29	0.82	0.39	0.200
P value		0.051		0.647
Apex deviation/mm	20	0.94	0.35	1.96	0.67	<0.001
Single-rooted	10	1.03	0.31	1.53	0.50	0.055
Double-rooted	10	0.85	0.37	2.38	0.54	<0.001
P value		0.266		<0.001
Angular deviation/°	20	1.86	1.04	7.32	3.21	<0.001
Single-rooted	10	2.29	0.96	5.99	2.69	<0.01
Double-rooted	10	1.43	0.97	8.64	3.25	<0.001
P value		0.062		0.045
RMS surface deviation/ (mm)	20	0.20	0.05	0.33	0.06	<0.001
Single-rooted	10	0.21	0.05	0.28	0.03	<0.01
Double-rooted	10	0.18	0.04	0.39	0.02	<0.001
P value		0.172		<0.001
Dice similarity coefficient/%	20	88.00	3.69	63.31	6.58	<0.001
Single-rooted	10	87.33	3.56	60.88	7.65	<0.001
Double-rooted	10	88.68	3.89	65.75	4.43	<0.001
P value		0.431		0.103
Over-removal rate /%	20	7.89	2.89	95.99	28.14	<0.001
Single-rooted	10	8.15	2.60	99.05	36.86	<0.001
Double-rooted	10	7.62	3.27	92.94	17.09	<0.001
P value		0.695		0.643
Preparation time /s	20	759.38	173.22	832.82	440.59	0.494
Single-rooted	10	590.55	1.63	460.74	50.91	<0.001
Double-rooted	10	928.20	1.54	1 204.90	315.55	<0.01
P value		<0.001		<0.001

Fig. 1.

Outcome visualization and statistical comparisons. a, b 3D distribution of deviation components in the mesial–distal, buccal–lingual, and apico–coronal coordinate system. c Platform deviation. d Apex deviation. e Angular deviation. f RMS surface deviation. g Dice similarity coefficient. h Over-removal rate. i Preparation time

Surface matching metrics in Fig. 1f–h consistently favoured robot assistance, with lower RMS surface deviation (0.20 mm ± 0.05 mm vs 0.33 mm ± 0.06 mm, P < 0.001), higher Dice similarity (88.00% ± 3.69% vs 63.31% ± 6.58%, P < 0.001), and markedly lower over-removal rate (7.89% ± 2.89% vs 95.99% ± 28.14%, P < 0.001); these differences remained significant within both root-morphology subgroups. Figure 1i indicates no overall difference in preparation time (759.38 s ± 173.22 s vs 832.82 s ± 440.59 s, P = 0.494), while subgroup analysis showed longer time for robot assistance in single-rooted teeth (590.55 s ± 1.63 s vs 460.74 s ± 50.91 s, P < 0.001) but shorter time in double-rooted teeth (928.20 s ± 1.54 s vs 1 204.90 s ± 315.55 s, P < 0.01).

A two-way ANOVA revealed significant preparation-technique × anatomy interactions for apex deviation, angular deviation, RMS surface deviation, and preparation time, indicating that the relative benefit of robotic assistance became more pronounced as anatomical complexity increased (Table 2). By contrast, no significant interaction was observed for platform deviation, Dice similarity coefficient, or over-removal rate.

Table 2.

Two-way ANOVA (Technique × Anatomy) with interaction effects

Outcome	Effect	F	P value	Partial η²
Platform deviation/mm	Technique	<0.01	0.952	<0.001
	Anatomy	1.53	0.225	0.041
	Interaction	3.83	0.058	0.096
Apex deviation/mm	Technique	53.39	<0.001	0.597
	Anatomy	5.96	0.020	0.142
	Interaction	13.73	<0.001	0.276
Angular deviation/°	Technique	60.55	<0.001	0.627
	Anatomy	1.64	0.209	0.044
	Interaction	6.26	0.017	0.148
RMS surface deviation/mm	Technique	131.83	<0.001	0.785
	Anatomy	12.13	0.001	0.252
	Interaction	35.73	<0.001	0.498
Dice similarity coefficient/%	Technique	230.16	<0.001	0.865
	Anatomy	3.64	0.064	0.092
	Interaction	1.17	0.286	0.032
Over-removal rate/%	Technique	186.16	<0.001	0.838
	Anatomy	0.26	0.611	0.007
	Interaction	0.19	0.668	0.005
Preparation time/s	Technique	2.11	0.155	0.055
	Anatomy	114.55	<0.001	0.761
	Interaction	16.17	<0.001	0.310

Discussion

This in vitro study compared an autonomous, multi-axis robotic osteotomy that executes nonlinear, surface-conforming toolpaths with a static guide-assisted approach for recipient socket preparation in tooth autotransplantation. Comparable coronal entry point accuracy was achieved with both approaches, whereas the autonomous robotic execution markedly improved deep positional accuracy and more faithfully reproduced the planned socket morphology, without a significant increase in osteotomy time. Overall, these findings indicate that the principal advantage of autonomous robotic osteotomy lies in maintaining the planned geometry throughout the full preparation depth, rather than improving initial targeting alone.

From a clinical perspective, accuracy in recipient socket preparation is central to autotransplantation success because excessive mismatch between the donor root and the prepared socket can compromise primary stability and increase insertion trauma, while prolonged extra-alveolar time jeopardizes periodontal ligament viability.^11,12,14 These constraints make the procedure highly operator dependent, particularly for less experienced surgeons who must achieve a close root-shaped fit within a limited time window.^31,32 Over-preparation may not only reduce initial stability, but also increase the risk of iatrogenic injury to adjacent anatomical structures, especially in posterior sites. Digital workflows combining CBCT-based planning,¹³ three-dimensional printing,³³ and tooth-supported guides have been introduced to reduce trial insertion and shorten extra-alveolar time, but deviations from the planned socket geometry remain difficult to eliminate, particularly when extensive manual adjustment is required.^10,14 Against this background, a robotic system capable of conservative, geometry-matched osteotomy may address a key technical bottleneck in current digital-assisted autotransplantation workflows.²⁹

The comparable platform deviation is clinically meaningful because it suggests that when the coronal entry region is constrained by tooth-supported referencing, the initial access point can be reproduced predictably with either approach. In the robot-assisted workflow, optical registration relied on a tooth-supported positioning stent with fiducial markers, enabling autonomous alignment to the planned entry point.¹⁷ In the static guide-assisted workflow, a tooth-supported guide constrained pilot drilling via metal sleeves. Because both workflows impose rigid coronal constraints using stable dental references, coronal variability is likely minimized in both, explaining the similar platform discrepancies.

In contrast, robot assistance yielded comparable deviations at the platform and apex, whereas the static guide-assisted group showed substantially greater apical than platform deviation, indicating that directional errors became progressively amplified with increasing preparation depth. Even small angular deviations at entry can amplify into larger apical discrepancies, and deep preparation is further influenced by bur deflection, cumulative alignment error, and the extent of manual enlargement.^14,15,34 In the static guide-assisted workflow, constraint is strongest during guided pilot drilling but diminishes after guide removal, when connecting and enlarging pilot channels requires freehand refinement; small directional variations during this phase can accumulate along the osteotomy. By comparison, robot assistance executes preplanned multi-axis milling with sustained pose and toolpath control and terminates automatically at the predefined endpoint, thereby reducing opportunities for cumulative deviation.^19,28 The observed pattern, namely similar platform deviation but markedly lower apex and angular deviations, supports the interpretation that the robotic workflow primarily improves full-depth trajectory maintenance. Because the present study was designed to compare overall geometric performance rather than isolate individual error sources, a formal error-budget analysis will be needed in future work.

The magnitude and nature of benefit observed here should also be interpreted in light of differences in robotic strategy and kinematic capability. Earlier generations of dental robotic systems were largely optimized for target-point positioning followed by predominantly axis-aligned, linear osteotomy, which is well suited for implant site preparation but less compatible with recipient sockets that require continuous three-dimensional contouring.^{20,21,23,29,30,35} By contrast, the platform evaluated in this study supports continuous multi-axis, non-linear toolpaths that can conform to irregular root geometries and execute envelope-based milling to directly generate a patient-specific, shape-matched socket.¹⁷ This distinction is clinically relevant because it shifts the robotic contribution from “accurate localization” toward “accurate morphology reproduction.” Recent clinical reports and trials of robot-assisted tooth extraction further illustrate the expanding feasibility of non-linear, anatomically constrained robotic tasks in dentistry, supporting continued translation of these systems beyond implant osteotomy.^28,36

Socket morphology and over-preparation are particularly consequential in autotransplantation because the recipient site must accommodate the donor root while preserving surrounding bone to support primary stability and minimize insertion trauma.^8,11,32 In the static guide-assisted workflow, volumetric agreement with the plan was limited and over-removal was pronounced, suggesting that a substantial portion of removed material extended beyond the planned socket volume. This likely reflects a geometric mismatch: the guide defines discrete cylindrical pilot channels at the mesial, distal, buccal, and lingual aspects, whereas tooth roots are continuous, tapered, and often irregular; freehand connection and enlargement are therefore required to achieve seating, particularly in deeper or interradicular regions that are not directly constrained. By quantifying over-removal beyond the planned socket, the present study adds a clinically oriented measure that complements global overlap metrics and more directly reflects unnecessary bone sacrifice relevant to socket wall integrity and septal preservation.

The selection of evaluation metrics is also important when interpreting autotransplantation osteotomy accuracy. Many prior studies, including those extrapolating implant-style accuracy frameworks to transplantation, have focused primarily on positional deviations, such as entry-point, endpoint, and angular deviation.^10,14,29 While these measures are informative, they do not fully capture whether the prepared socket conserves bone and reproduces the intended root-shaped envelope. To address this gap, the present study introduced a multidimensional evaluation that integrates surface-based discrepancy (RMS), volumetric similarity (Dice similarity coefficient), and surgical conservativeness (over-removal rate, ORR). Considered together, these metrics link geometric fidelity to clinically meaningful goals: conserving socket walls and the interradicular septum, limiting unnecessary bone removal, and reducing the likelihood of excessive insertion force or repeated trial insertion that could threaten periodontal ligament preservation. This broader metric set may provide a useful framework for subsequent mechanistic and clinical studies, enabling more comprehensive comparisons across techniques and anatomies.

By contrast, robot-assisted preparation achieved high volumetric concordance with minimal over-removal, suggesting that the planned offset and insertion-axis undercut elimination were largely sufficient to permit seating without extensive compensatory enlargement. Mechanistically, closer reproduction of the planned root envelope may reduce repeated trial insertion and excessive insertion forces, while conservative preparation preserves socket wall integrity and may better support primary stability. Although these biological consequences cannot be confirmed in a resin model, the geometric findings provide a coherent explanation for how autonomous milling could improve procedural predictability in a technique-sensitive procedure. However, unlike implant surgery, which requires a certain degree of insertion resistance to achieve primary stability, tooth autotransplantation requires a passive, resistance-free fit between the recipient socket and the donor root to provide space for periodontal ligament healing; excessive resistance may increase the risk of root resorption. Therefore, insertion resistance was not instrumentally quantified in the present study, and the effect of fit-related differences on seating adaptation could not be objectively evaluated.

Root morphology further modified the benefit, with the most pronounced gains in double-rooted models. This is clinically relevant because autotransplantation is not limited to single-rooted teeth; multi-rooted donor teeth are frequently encountered, and they introduce bifurcation architecture and septal constraints that are difficult to reproduce with channel-based drilling strategies.^15,37,38 The present study therefore evaluated both single-rooted and double-rooted tooth anatomies to better reflect clinical variability and to clarify whether performance differences are anatomy dependent. For double-rooted teeth, the bifurcation region introduces concavities and transitions that are challenging to shape freehand after guide removal, and iterative enlargement can encroach on the septum or trade fit for space, amplifying deep positional error. Robot-assisted preparation is better suited to these constraints because boundary-constrained, multi-axis toolpaths can shape each root region while respecting the septal envelope. These observations highlight interradicular architecture and root-form complexity as key determinants of recipient-site preparation accuracy in autotransplantation and support focusing early clinical translation on anatomically complex cases.

Efficiency outcomes should be interpreted within the predefined timing framework because preparation time captured only the active preparation phase from drilling initiation to completion of an acceptable socket. The preparation times reported here were obtained under controlled laboratory conditions and may therefore underestimate operative duration in clinical practice. In actual intraoral procedures, freehand and guide-assisted workflows may be prolonged by soft tissue interference, bleeding, irrigation requirements, restricted visibility and access, patient-related constraints, and repeated verification of guide or replica seating; moreover, the speed of conventional preparation is likely to vary with operator experience. Under real clinical conditions, the robotic workflow may offer a more favorable efficiency profile, while also providing greater procedural consistency, predictability, and reduced dependence on manual skill. Taken together, these considerations highlight the need for future clinical time-motion studies to more comprehensively evaluate workflow efficiency, predictability, and practical feasibility under realistic operative conditions. Consistent with this interpretation, the significant preparation-technique × anatomy interaction indicated that the time profile differed according to anatomical complexity, with the robotic workflow appearing more favorable in the double-rooted condition. Because registration, calibration, and seating verification were not included in the timed interval, these findings should not be interpreted as equivalence in total chairside time. Comprehensive clinical time-motion studies are warranted for translation.

For methodological consistency, the same depth-stop Lindemann bur configuration was intentionally used in both groups because the static guide-assisted workflow required a bur compatible with the guide sleeve and depth-control design. However, this instrumentation does not fully represent the most common clinical approach to tooth autotransplantation, in which individualized recipient-site preparation is often performed with a high-speed handpiece and clinically conventional diamond or fissure burs. This should not be interpreted as an intrinsic limitation of the robotic workflow, because robot-assisted surgery can likewise be performed clinically using a high-speed angled handpiece with fissure burs for personalized osteotomy, as shown in recent clinical reports of robot-assisted impacted tooth extraction.²⁷

Several limitations warrant consideration. First, the present study should be interpreted as a standardized in vitro proof-of-concept of geometric accuracy rather than a direct simulation of intraoral surgery. The resin model did not reproduce soft tissues, bleeding, limited mouth opening, restricted intraoral visibility, or other clinical factors that may affect surgical accessibility, workflow feasibility, cutting behavior, and handling. Further validation in clinically representative settings will therefore be necessary to assess the real-world applicability of the robotic workflow.³⁹ The digitization pipeline, including impressions and intraoral scanning, can introduce distortion and reconstruction artifacts that may reduce measurement precision, although such effects should be similar across groups under standardized conditions.^40,41 In addition, the static guide workflow necessarily includes freehand refinement that depends on operator technique and seating tolerance, which reflects clinical reality but limits isolation of guide performance from operator behavior.¹⁵ Finally, robotic accuracy depends on registration and calibration fidelity, underscoring the need for robust clinical protocols for stent seating verification, marker visibility, and intraoperative error checking.¹⁷

Future studies should validate these findings in clinically representative settings and determine whether improved socket fidelity translates into fewer trial insertions, shorter extra-alveolar time, improved primary stability, and favorable periodontal healing. Workflow optimization should focus on streamlining registration and objectively confirming stent or guide seating, as well as refining trajectory planning across donor anatomies. Given the pronounced benefit in double-rooted models, clinical studies may preferentially target anatomically complex cases where bifurcation reproduction and septum preservation are most challenging. Because all osteotomies were performed by a single operator under standardized conditions, the present study does not permit evaluation of learning effects, inter-operator variability, or whether robotic assistance genuinely reduces dependence on surgical experience. Future studies should therefore recruit operators with different experience levels and characterize skill acquisition, performance stabilization, and reproducibility, ideally using an LC-CUSUM-based framework. In addition, operational events such as calibration failure, path deviation, procedural interruption, or safety override activation were not systematically recorded and should be incorporated as dedicated translational endpoints in future studies.

In this standardized in vitro model, an autonomous, multi-axis robotic osteotomy executing nonlinear, surface-conforming toolpaths achieved substantially better apical and angular accuracy and more faithfully reproduced the planned socket morphology than a static guide-assisted workflow, while maintaining a similar overall preparation time. The performance advantage was most evident in double-rooted scenarios, indicating that anatomical complexity modifies the benefit conferred by robotic trajectory control. Together with emerging in vitro evidence and early clinical reports of robot-assisted tooth autotransplantation, these findings support further clinical validation of autonomous robotic execution to improve precision and minimize unnecessary bone removal in technique-sensitive transplantation procedures.

Materials and methods

Group design

This in vitro study compared two recipient-site preparation techniques for tooth autotransplantation: robot-assisted osteotomy and static guide-assisted osteotomy. Models were allocated to either technique and were predefined as single-rooted or double-rooted scenarios. The primary comparison was between techniques, with prespecified subgroup analyses by root morphology. As this was an in vitro laboratory study using 3D-printed models, no ethics approval was required.

Sample-size calculation

The required sample size was calculated using G*Power software (version 3.1; Heinrich Heine University, Düsseldorf, Germany) based on pilot data. Apex deviation was defined a priori as the primary outcome. A two-group comparison between robot-assisted and static guide-assisted osteotomy was assumed for sample-size estimation. Using the pilot-estimated effect size, with a significance level of 0.05 and a power of 0.80, the minimum required sample size was 16 specimens (8 per group). To increase robustness and enable predefined subgroup analyses by root morphology, 20 specimens were included in each technique group, with 10 single-rooted and 10 double-rooted models per group (total n = 40).

System structure

The robotic system used in this study comprised an intraoperative navigation subsystem and a robotic arm subsystem (Fig. 2). The navigation subsystem was based on the FusionTrack 250 optical tracking system, which captured visual markers attached to the robotic end effector and the mandibular model to calculate their spatial relationship in real time. This enabled the robotic arm to move according to the preoperative plan, while surgical progress and force feedback were displayed on a high-definition monitor.

Fig. 2.

Overview of the robotic surgical system

The software platform was developed using an application development framework and the Visualization Toolkit (VTK), with a modular, dynamic loading architecture that allowed flexible adaptation to different experimental and clinical requirements. The system integrated an automatic segmentation module, a surgical planning module, a multi-view navigation module, a data management module, and modules for force sensor and optical tracker management, thereby jointly ensuring surgical accuracy and safety. The trajectory planning and execution strategy for personalized milling of complex geometries using this system has been described in detail in our previous study.¹⁷

Model design

The digitized mandibular arch model was imported into Geomagic Wrap software (version 2017; 3D Systems, Rock Hill, SC, USA). The model consisted of a fixed mandibular base and a removable alveolar segment. The removable segment included the right second premolar (#45), the right second molar (#47), and the intervening region corresponding to the missing right first molar (#46) (Fig. 3a–c).

Fig. 3.

Construction of the mandibular model with a removable alveolar segment. a 3D-printed mandibular arch model. b Removable alveolar segment. c Assembled model with the removable segment seated in the mandibular base

Preoperative planning

Virtual surgical planning was performed using DentalNavi software (version 3.0.0; Yakebot Technology Co., Ltd., Beijing, China). For both single-rooted and double-rooted donor conditions, the donor tooth models were imported and positioned at the recipient site (#46). Each donor tooth was adjusted to an optimal position based on the dental arch form and its relationship with the adjacent teeth (Fig. 4a–d).

Fig. 4.

Virtual donor tooth models and planned positioning at the recipient site. a Single-rooted donor tooth model. b Planned single-rooted donor tooth position in the mandibular model. c Double-rooted donor tooth model. d Planned double-rooted donor tooth position in the mandibular model

For single-rooted donor teeth, the donor root surface was first uniformly offset outward by 0.5 mm to preserve periodontal ligament space and facilitate atraumatic insertion. The enlarged donor tooth model was then positioned at the recipient site in the planned donor tooth position (Fig. 5a). Based on the planned insertion axis, undercuts were eliminated using a reverse undercut-filling procedure along the direction opposite to insertion, thereby generating a socket geometry compatible with single-path insertion (Fig. 5b, c). After the final socket geometry had been established, a Dentium SuperLine II Lindemann guided bur with a depth stop (1.65 mm diameter; Dentium, South Korea) was selected, and the corresponding milling trajectory was generated (Fig. 5d).

Fig. 5.

Robot-assisted workflow for single-rooted socket design and trajectory planning. a Planned donor tooth position at the recipient site. b Direction of undercut elimination along the planned insertion axis. c Final socket geometry after undercut removal. d Corresponding planned milling path and visualization of the planned milling trajectory with the Lindemann bur relative to the seated donor tooth position

For double-rooted donor teeth, the donor root surface was also offset outward by 0.5 mm. The enlarged donor tooth model was subsequently placed at the planned donor tooth position within the recipient site (Fig. 6a). Undercuts were then removed by applying a reverse undercut-filling procedure along the planned insertion axis, thereby producing a final socket geometry compatible with the planned insertion path (Fig. 6b, c). Once the socket design was finalized, the donor root was divided into distal and mesial root regions, and a Dentium SuperLine II Lindemann guided bur with a depth stop was selected to generate separate planned milling trajectories for preparation of the distal root region (Fig. 6d, e) and the mesial root region (Fig. 6f, g). The same tooth-supported registration stent was used in both the single-rooted and double-rooted groups. These accessories included a support structure for connecting the surgical markers and registration holes required for intraoperative registration, and were fabricated by 3D printing (Pro S95; SprintRay Co., Los Angeles, CA).

Fig. 6.

Robot-assisted workflow for double-rooted socket design and trajectory planning. a Planned donor tooth position at the recipient site. b Direction of undercut elimination along the planned insertion axis. c Final socket geometry after undercut removal. d, e Corresponding planned milling path and visualization of the planned milling trajectory for preparation of the distal root region after tooth positioning. f, g Corresponding planned milling path and visualization of the planned milling trajectory for preparation of the mesial root region after tooth positioning

For the static guide-assisted workflow, patient-specific tooth-supported surgical guides were designed in the DentalNavi software (Fig. 7). The enlarged donor tooth model was positioned at the recipient site in the same planned donor tooth position as that used in the robot-assisted group. Based on this identical donor tooth position, four guided pilot-drilling channels were arranged around the perimeter of the planned socket at the mesial, distal, buccal, and lingual aspects for both the single-rooted (Fig. 7a, b) and double-rooted (Fig. 7c, d) conditions. These channels were designed to guide pilot drilling to the planned depth, after which socket preparation was completed by freehand refinement. Metal sleeves were incorporated to control drill angulation and depth.

Fig. 7.

Static guide design workflow. a, b Guide design for the single-rooted condition, illustrating the planned pilot drilling channels and guide configuration. c, d Guide design for the double-rooted condition, illustrating the planned pilot drilling channels and guide configuration

All guides were manufactured by 3D printing using surgical guide resin (Pro S95; SprintRay Co., Los Angeles, CA) and were verified on the models for passive fit and stable seating before experimentation.

Experimental procedure

Models were randomly allocated to the robot-assisted or static guide group, with equal numbers in each root-morphology subgroup. All osteotomies were performed by a single operator, whereas postoperative scanning and digital analyses were conducted by a separate investigator who was not involved in the surgical procedures. All procedures were performed on bench-mounted mandibular models secured within a mannequin head to simulate clinical positioning.

The planned surgical file was imported into the control software. In the robot-assisted groups, the tooth-supported registration stent was seated and used for optical registration (Fig. 8). The workflow consisted of robotic arm calibration (Fig. 8a), calibration of the reference disc (Fig. 8b), and intraoral registration (Fig. 8c). After registration, a Lindemann bur corresponding to the virtual plan was mounted on the robotic handpiece. The robot then aligned to the planned entry point and executed the preplanned osteotomy trajectories under continuous irrigation (Fig. 8d). Single-rooted cases were prepared using a single continuous path, whereas double-rooted cases were prepared using sequential distal and mesial trajectories. Milling automatically terminated at the predefined endpoint, and the robotic arm retracted along a safe exit path. All drilling was initiated via foot-pedal control without manual drilling.

Fig. 8.

Experimental operative procedures. a Robotic arm calibration. b Calibration of the reference disc. c Intraoral registration. d Robot-assisted milling/osteotomy execution. e Static guide-assisted socket preparation, including guided pilot drilling and subsequent freehand refinement

In the static guide groups, the corresponding surgical guide was seated on the model and verified for complete seating through the inspection windows. Using the same depth-stop Lindemann bur as in the robot-assisted group, guided pilot drilling was manually performed through the four metal sleeves to achieve the planned depth and angulation. After guide removal, the same depth-stop Lindemann bur was used for the subsequent freehand connection, enlargement, and refinement of the pilot channels. Socket refinement was then performed using repeated trial insertion of a 3D-printed donor tooth replica until the replica could be seated reproducibly in a position consistent with the planned placement, rather than until frictional engagement or a press-fit was achieved (Fig. 8e).

For both groups, preparation time was recorded from initiation of drilling to completion of an acceptable socket. After osteotomy, the models were removed and thoroughly irrigated to eliminate residual debris.

Data acquisition and accuracy assessment

A donor-tooth reference model was created by adding virtual spherical markers to define the coronal reference point and apical endpoint(s) (Fig. 9a). The planned donor-tooth position within the mandibular model was then established and exported for subsequent analysis (Fig. 9b).

Fig. 9.

Postoperative digitization and accuracy assessment workflow. a Donor tooth reference model with spherical markers defining the coronal reference point and apical endpoint(s). b Planned donor tooth position in the mandibular model. c Postoperative intraoral scan representing the achieved replica position. d Registration and analysis pipeline for extracting planned and achieved coordinates and comparing socket geometries. e RMS surface deviation analysis between planned and prepared socket surfaces in the robot-assisted group. f RMS surface deviation analysis between planned and prepared socket surfaces in the static guide-assisted group. g Planned preparation volume in the robot-assisted group. h Actual preparation volume in the robot-assisted group after plane filling. i Over-removal volume in the robot-assisted group. j Intersected volume in the robot-assisted group. k Planned preparation volume in the static guide-assisted group. l Actual preparation volume in the static guide-assisted group. m Over-removal volume in the static guide-assisted group. n Intersected volume in the static guide-assisted group

After osteotomy, a 3D-printed donor tooth replica was seated in the prepared socket, and postoperative intraoral scanning was performed to capture the achieved replica position relative to the surrounding dentition (Fig. 9c). To reconstruct the internal socket surface, a silicone impression of the prepared socket was obtained and subsequently digitized with the intraoral scanner. Thus, two postoperative datasets were generated: an impression-derived socket model and a scan of the seated replica for positional analysis.

The postoperative scan was registered to the planned model using initial alignment followed by best-fit registration based on the crown surfaces of teeth #45 and #47. The reference donor-tooth model was then aligned to the seated replica to extract planned and achieved coordinates for deviation calculations (Fig. 9d). For double-rooted cases, the apical endpoint was defined as the midpoint between the mesial and distal apical marker centers. Morphological accuracy was assessed by the RMS surface deviation between the planned and prepared socket surfaces in the robot-assisted and static guide-assisted groups (Fig. 9e, f). The over-removal rate was calculated based on the Boolean volumetric analysis, in which the planned preparation volume, actual preparation volume, over-preparation volume, and intersected volume were derived for both the robot-assisted (Fig. 9g–j) and static guide-assisted groups (Fig. 9k–n). Volumetric overlap was quantified using the Dice similarity coefficient. Positional accuracy metrics included platform deviation, apex deviation, and angular deviation. Preparation time was recorded from drilling initiation to completion of an acceptable socket. Detailed definitions and computational procedures are provided in the Supplementary Material.

Statistical analysis

Statistical analyses were conducted using IBM SPSS Statistics (version 25; IBM Corp., Armonk, NY, USA). Data are reported as mean ± standard deviation. Normality and homogeneity of variance were assessed using the Shapiro–Wilk test and Levene’s test, respectively. To evaluate the effects of preparation technique and root anatomy, as well as their interaction, a two-way ANOVA was performed for each outcome variable. When significant interaction effects were identified, simple between-technique comparisons within each anatomy subgroup were subsequently performed using an independent-samples t-test or the Mann–Whitney U test, as appropriate. Statistical significance was set at α = 0.05 (two-sided).

Author contributions

Chen Liu contributed to data acquisition, analysis and interpretation, drafted the manuscript, and critically revised the manuscript. Guangwei Chen and Libin Zhou contributed to data analysis and drafting of the manuscript. Jun Qiu, Dongmei Li, Yuchen Liu, Zhiwen Li, and Shizhu Bai contributed to the investigation. Shizhu Bai and Yimin Zhao contributed to the conception and design of the study, contributed to interpretation of the findings, and critically revised the manuscript. All authors approved the final version and accept responsibility for the integrity of the work in all its aspects.

Data availability

The data supporting the findings of this study are available from the corresponding authors upon reasonable request.

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at 10.1038/s41368-026-00446-3.