APEX-RBD: Mixed-Precision Exploration Framework for Hardware-Efficient Robot Dynamics Accelerator Design

• RBD computations can consume up to 90% of controller runtime, motivating dedicated accelerators and quantization for higher throughput.Quantization shrinks MAC units, allowing more parallel units within a fixed hardware footprint.Source: §1 · p. 1
• RBD quantization is more challenging than perception quantization because feedback-loop errors compound through nonlinear dynamics, causing trajectory drift and instability.Small torque errors alter the physical trajectory and feed erroneous states back into the controller.Source: §1 · pp. 1–2
• Mixed-precision assignments can reduce resource waste, but their combinatorial search space and costly closed-loop evaluation make exploration intractable.More than 50 variables with 12 bit-width choices yield a space exceeding 12^50, while verifying 100 candidates takes 8.5 hours even with 8-thread parallelization.Source: §1 · p. 2
• APEX-RBD combines physics-based grouping and sensitivity analysis, a prior-informed surrogate model, and a hybrid Bayesian/local optimizer for efficient exploration.The surrogate predicts trajectory error in milliseconds, while hardware cost estimation guides optimization under user-defined constraints.Source: §1 · pp. 2–3
• APEX-RBD discovers designs with up to 1.9× area reduction and 1.8× power savings over uniform-precision baselines under identical accuracy constraints.Source: §1 · p. 3

• RBD algorithms such as RNEA and Minv operate on robot kinematic trees and use bidirectional traversal through forward and backward passes.Source: §2.1 · p. 3
• RBD accelerator performance depends on parallel MAC units that implement the algorithms’ bidirectional dataflow.Source: §2.1 · p. 3, §2.2 · p. 3
• Performance is a hard control-frequency constraint that fixes the required accelerator parallelism and high-level architecture.Source: §2.2 · p. 3
• The design problem minimizes MAC area and power by optimizing fixed-point bit-widths while satisfying motion-accuracy and performance requirements.Fixed-point arithmetic supports efficient integer hardware implementation.Source: §2.2 · p. 3
• Uniform precision is simple but inefficient because RBD variables have widely varying quantization sensitivities, motivating mixed-precision assignments.Mixed precision allocates precision where needed but makes brute-force, simulation-based exploration computationally intractable.Source: §2.3 · p. 3

• The profiling dataset combines representative motion workloads with stress tests such as high-velocity maneuvers.Source: §3.1 · p. 3
• The tailored workload benchmark drives sensitivity analysis and surrogate training for hardware optimized to the target robot and application.This exploration is performed offline as a one-time process for each new deployment scenario.Source: §3.1 · p. 3

Initial grouping

• Stage 1 groups RBD variables by physical and algorithmic roles to reduce the number of quantized entities.The initial grouping is performed offline using principles considered fundamental to RBD.Source: §3.2 · p. 3, §3.2.1 · p. 3
• Initial grouping reduces the search space from over 12^50 to 12^27 by replacing individual variables with grouped entities.Source: §3.2.1 · p. 4

Sensitivity analysis

• Sensitivity analysis evaluates how each group’s bit-width affects the robot’s final motion trajectory and uses module-level output error to avoid full closed-loop evaluation.Source: §3.2.2 · p. 4
• Targeted fractional-width sweeps are repeated across Latin-Hypercube-sampled background configurations to account for sensitivity coupling among groups.Source: §3.2.2 · p. 4
• The stage produces sensitivity curves, module-level error data for surrogate priors, and integer bit-widths required to prevent overflow.Source: §3.2.2 · p. 4

Group merging

• Groups with similar sensitivity profiles are merged only when the resulting module-level error remains below an empirical threshold.Merging reduces search dimensionality but can introduce slight precision degradation.Source: §3.2.3 · p. 4

Motivation

• Closed-loop simulation is computationally expensive, motivating a surrogate that predicts final trajectory error directly from grouped bit-width configurations.The model is intended to replace costly physical simulations with rapid algorithmic predictions during exploration.Source: §3.3 · p. 4, §3.3.1 · p. 5
• A universal surrogate is impractical because error propagation and dynamic responses vary across robotic platforms and application scenarios.The framework therefore targets scenario-specific models rather than one model for all robots and workloads.Source: §3.3.1 · p. 5

Hierarchical Framework

• The hierarchical framework decomposes prediction into module-level error characterization followed by system-level trajectory-error prediction.Lightweight Random Forest models first predict localized RBD output errors, which then support the final predictor.Source: §3.3.2 · p. 5

System-Level Error Prediction

• System-level features combine module-error priors, derived error ratios and imbalances, robotics dependencies, bit-widths, and pairwise interactions.These features represent intermediate quantization effects and structural dependencies that raw bit-widths alone may not capture.Source: §3.3.2 · p. 5

Local Refinement

• The search implementation includes cost-driven greedy refinement that reduces bit-widths in hardware-impact order and compensates when predicted error exceeds 1.1·εmax.The algorithm updates the candidate pool when refined configurations improve the hardware objective.Source: §3.3.2 · p. 6

Feature Selection

• Random Forest feature importance selects the top 20 salient features to reduce overfitting in the high-dimensional feature space.The approach uses the model’s intrinsic feature-importance mechanism rather than isolated preprocessing filters.Source: §3.3.2 · pp. 5–6

Search Objective

• The search minimizes estimated hardware cost while satisfying a user-defined trajectory-error tolerance.The framework uses a fast analytical cost estimator together with the surrogate error predictor.Source: §3.4 · p. 6, §3.4.2 · p. 6

Analytical Hardware Cost Estimator

• The analytical estimator maps each quantization configuration to area and power by counting unique arithmetic-operator instances and summing their cell-library costs.The model primarily captures arithmetic logic; secondary effects such as FIFOs, control, and routing are treated as negligible based on post-layout analysis.Source: §3.4.1 · p. 6

Bayesian Optimization

• Bayesian Optimization performs global exploration using the analytical cost estimator and surrogate trajectory-error predictor.The search relaxes the error boundary by 10% and retains the top 30 configurations satisfying the relaxed constraint.Source: §3.4.2 · p. 6

Local Refinements

• Cost-driven refinement reduces bit-widths of high-impact groups, while sensitivity-guided tuning trades precision from low-sensitivity groups toward high-sensitivity groups.These complementary heuristics target local improvements after Bayesian Optimization identifies promising regions.Source: §3.4.3 · p. 6

Final Validation

• The framework validates 30 candidate configurations with end-to-end simulation and selects the feasible candidate with minimum hardware cost.Final selection uses true trajectory error rather than only surrogate predictions.Source: §3.4.3 · p. 7, §3.4.4 · p. 7

Evaluation Setup

• APEX-RBD evaluates iiwa, HyQ, and Atlas using domain-specific workloads containing 40 representative trajectories per robot.The platforms span 7, 12, and 29 DoF, respectively.Source: §4.1 · p. 7

Surrogate Model

• Using 100 training samples, the surrogate achieves R^2=0.937, RMSE=0.307, Spearman correlation=0.95, and Kendall’s Tau=0.81.The evaluation uses an additional 80-sample test set and closed-loop simulation labels.Source: §4.2 · p. 7

Search Strategy

• APEX-RBD finds lower-cost configurations than competing search methods for a given trajectory error threshold, including near the 1.0 mm threshold versus pure Bayesian Optimization.The comparison uses a shared surrogate model and hardware cost estimator across algorithms.Source: §4.3 · p. 7

End-to-End Hardware Gains

• APEX-RBD achieves up to 1.9× area reduction and 1.8× power savings versus the uniform 24-bit baseline while maintaining the same motion accuracy.Mixed-precision configurations are generated to RTL and evaluated using post-layout hardware costs.Source: §4.4 · p. 8
• Against Pure BO, APEX-RBD achieves up to 1.5× area and 1.3× power savings, while the 32-bit comparison reaches up to 3.1× savings in both metrics.The reported gains are attributed to local refinement heuristics that improve the searched configurations.Source: §4.4 · p. 8

Framework Runtime

• The iiwa exploration completes in 10.8 hours, with simulation-based data collection accounting for 78.95% of runtime.The framework uses 100 samples; group merging takes 1.09% of runtime, while a DNN alternative requires over 300 samples for comparable accuracy.Source: §4.5 · p. 8

Conclusion

• APEX-RBD integrates physics-aware search-space pruning with a surrogate-guided hybrid optimizer for automated mixed-precision RBD quantization.The framework searches configurations that satisfy accuracy constraints.Source: §5 · p. 8
• Up to 1.9× area and 1.8× power reductions are achieved over uniform-precision baselines while satisfying accuracy constraints.Source: §5 · p. 8