Combined Control for Precise Film Tasks

• The paper introduces an adaptive sliding mode and iterative learning framework that compensates for nonlinear uncertainties and minimizes chattering in multi‐axis film control.
• It employs multi‐modal sensor fusion and hierarchical reinforcement learning to achieve sub‐millimeter precision and robust real-time control in robotic and cinematographic applications.
• It further integrates physics-informed neural networks and PDE-constrained optimal control to enhance film deposition and video synthesis, paving the way for adaptive thin-film processing.

Combined control for precise film tasks refers to the integration of advanced control methodologies—often incorporating model-free adaptive strategies, sensor fusion, reinforcement learning, and physics-informed modeling—to achieve rigorous precision in film-related operations. These operations span robotic manipulation in manufacturing (such as lithography, inspection, deposition), precision motion for cinematography, and optimization tasks in thin-film physics. Key challenges include nonlinear uncertain dynamics, sensor noise, multi-axis coupling, and the need for real-time adaptability. The following sections synthesize established techniques, mathematical frameworks, and machine learning approaches as detailed in the linked research, encapsulating both theory and application.

1. Adaptive Sliding Mode and Iterative Learning for Multi-Axis Film Control

Contouring tasks in industrial film processing, lithography, and inspection systems commonly deploy multi-axis gantry mechanisms subject to strong nonlinear coupling, friction, and uncertainty. The global iterative sliding mode control framework (Wang et al., 2021) addresses this by:

• Modeling all unknown dynamics (coupling, friction, disturbances) as generalized uncertainties.
• Implementing an adaptive sliding mode controller per axis, with the control law $u = -\Gamma \cdot \text{sigm}_a(s)$, where $s$ is the sliding variable grouping error and its derivative, and $\Gamma$ is an online-updated gain vector.
• Updating gain via $$\dot{\Gamma} = \bar{\Gamma} \cdot \text{diag}(|s_1|, |s_2|, |s_y|)$$, ensuring minimal gain near the sliding surface and suppressing overcompensation-induced chattering.
• Employing an iterative learning component across cycles: $y_{r,i+1} = r + w_{i+1}$, $w_{i+1} = w_i + l e_{i+1}$, allowing repetitive error patterns to be corrected progressively.

In experimental scenarios such as tracking cardioid or circular contours (common in advanced film shaping), the method achieved superior root-mean-square contouring accuracy and reduced chattering, even in absence of boundary knowledge for uncertainties or precise system ID. This approach is essential for applications requiring extremely accurate film motion without excessive vibration or mechanical wear.

2. Multi-Modal Sensor Fusion and Hierarchical Policy Learning

Complex film tasks, particularly those involving contact-rich robotic manipulation, benefit from multi-modal data integration and hierarchical control architectures (Jin et al., 2022). Components include:

• Fusion of force/torque signals (pre-filtered for noise attenuation), vision, and proprioceptive readings within a neural network policy. Filtered F/T readings are inserted in later neural layers (late fusion) to mitigate early-layer state corruption.
• Local model-based RL controllers (e.g., iLQG for operational space force control) trained per-task phase, projecting force commands to joint torques while handling environmental compliance.
• Distillation of these controllers into a global policy via guided policy search (MDGPS), enforcing compatibility via KL divergence minimization between policy networks and local controllers.

This architecture achieves sub-millimeter precision in assembly (e.g., robotic gear insertion with $<0.25$ mm clearance), successfully generalizes to wide configuration and shape variation, and enables direct transfer to reality without fine-tuning. Applications to film tasks include precision camera motion, adaptive control on dynamic sets, and multi-modal stabilization for moving rigs, all requiring generalization and sensor synergy.

3. Vision-Based End-to-End Pixel-to-Torque Control

Film production increasingly relies on autonomous or semi-autonomous manipulation and motion control driven by visual feedback. End-to-end pixel-to-torque approaches (Bleher et al., 2022):

• Map raw image pixels directly to torque commands via DNNs, bypassing separate state estimation and classical feedback control.
• Employ separation of the control policy (learned via RL [PPO]) and the state estimator (a convnet regressing trigonometric pose features), trained under high-speed constraints (>100 Hz) and robust to noise and lighting variation.
• Assess precision requirements by injecting Gaussian noise into state and measuring controller tolerance, then ranking feature importance and estimator fidelity accordingly.

In experimental platforms such as the Furuta pendulum (unstable, underactuated), this approach demonstrated update rates $>$100 Hz and reliably performed fast, unstable tasks previously not achievable by vision-only feedback. A plausible implication is the extension of such pipelines to film domain camera arms, lighting rigs, or dynamic set elements where environmental variability and responsiveness are paramount.

4. Data-Driven and Trajectory-Oriented Control for Cinematographic Video Synthesis

Recent advancements in generative AI for video asset creation in film and animation have introduced control networks capable of disentangling cinematic components (Li et al., 21 Jun 2024). The Image Conductor framework features:

• Decoupled camera and object motion via independently trained LoRA weights. Camera LoRA is optimized on camera transition-only sequences; object LoRA is trained on mixed-motion datasets, with an orthogonalization penalty ensuring independence.
• Camera-free guidance at inference, enabling selective enhancement or suppression of either motion species by tuning output compositions.
• Data curation pipelines: Video segments are cropped, motion is scored using optical flow, and dense trajectory extraction is undertaken to ensure high quality for both training and evaluation, supporting 130k+ annotated examples.

Quantitative metrics (FID, FVD, CamMC, ObjMC) and human evaluation confirm high fidelity in following user-specified motion trajectories. This modular separation enables interactive storyboarding, post-production refinement, and trajectory-based scene design in film, allowing granular specification of elementary camera/object movements.

5. PDE-Constrained Optimal Control for Thin-Film Flow

Controlling physical film profiles in manufacturing, coating, or advanced surface patterning is governed by nonlinear PDEs reflecting fluid mechanics and substrate elasticity. The optimal control approach for thin-film flows on flexible topography (Alrashidy et al., 18 Jun 2025):

• Couples a fourth-order nonlinear lubrication equation for film thickness $h(x,t)$ and a substrate PDE for $s(x,t)$ via the total surface $𝓗(x,t) = h(x,t) + s(x,t)$.
• Embeds an energy-dissipation law expressed as

$$\frac{d\mathcal{E}}{dt} = -\left[\frac{1}{3}\int h^3 (\mu_x)^2 \, dx + \frac{1}{\gamma}\int (s_t)^2 dx\right] + \frac{1}{\gamma}\int f s_t dx$$

where $f(x,t)$ is a distributed control force and $\gamma$ is a damping parameter.

• States an optimal control problem with the objective

$$\mathcal{J}(h,s,f) = \frac{1}{2} \Vert(h + \beta s)(\cdot, T) - \bar{h}(\cdot)\Vert^2_{L^2(\Omega)} + \frac{\alpha}{2} \int_0^T \Vert f(\cdot, t) \Vert^2_{L^2(\Omega)} dt$$

solved via reduced gradient descent and first-order IMEX time-stepping, preserving energy stability and efficiently handling singularities (rupture, dewetting).

Simulations demonstrate accurate shaping and stabilization of films—both suppressing unwanted rupture and promoting uniform target profiles at accelerated rates compared to uncontrolled evolution. This framework provides a rigorous pathway to real-time adaptable control for film profile engineering.

6. Physics-Informed Neural Networks for Semiconductor Film Deposition

Integrating domain knowledge and physical laws in learning-based controllers is essential for high-precision film deposition technical domains. Physics-Informed Neural Networks (PINNs) (Han et al., 15 Jul 2025):

• Embed governing PDEs (conservation, reaction-diffusion, transport) directly within the network training objective:

$$\mathcal{L} = w_{f} \mathcal{L}_{f}(\theta) + w_B \mathcal{L}_B(\theta) + w_d \mathcal{L}_d(\theta)$$

and, for inverse/design problems,

$$\mathcal{L} = J + w_{f} \mathcal{L}_{f} + w_{B} \mathcal{L}_B + w_{h} \mathcal{L}_h$$

• Enable real-time adaptive control of deposition processes (CVD, PVD, ALD) even in sparse or variable-data regimes, predicting film evolution and facilitating operational corrections.
• Can be merged with advanced optimizers (Bayesian optimization, Ant Colony, RL) for runtime controller adjustment, improving uniformity and defect rates.

A plausible implication is enhanced closed-loop precision control in semiconductor fabs by integrating PINN-driven controllers, optimizing both yield and process robustness. The approach is extensible to multi-modal fusion (e.g., with GNN/CGNN architectures) for further scalability and operational efficiency.

7. Cross-Domain Impact and Prospective Research Directions

Combined control frameworks for precise film tasks manifest across industrial manufacturing, robotic manipulation, cinematography, and thin-film physics. Emerging trends highlight:

• Model-free adaptive controllers and sensor fusion networks as robust strategies in settings with high uncertainty and limited system identification.
• Hierarchical reinforcement learning and policy distillation for generalization over variable environments and task specifications.
• Data-driven decoupling of complex motion phenomena, particularly in AI-driven video synthesis pipelines, supporting fine-grained scene and motion design.
• PDE-constrained optimization and PINNs for physically grounded, process-integrated control, strengthening precision and scalability in manufacturing.

Future research directions include enhanced fusion of physical modeling with data-driven learning, adaptive online reweighting to target high-error domains, closed-loop deployment of PINNs, and modular architectures balancing real-time computation and expressive control for advanced film tasks across disciplines.