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APEX-RBD: Mixed-Precision Exploration Framework for Hardware-Efficient Robot Dynamics Accelerator Design
Xingyu Liu, Hanwei Fan, Chaofang Ma, Jiawei Liang, Guangyu Hu, Jiang Xu, Wei Zhang
TL;DR
RBD accelerator design must reduce hardware cost without violating motion-accuracy and performance requirements, but mixed-precision exploration is hindered by a vast search space and expensive closed-loop simulation. APEX-RBD combines physics-aware pruning, a prior-informed surrogate, and hybrid optimization to make this search tractable. It finds designs with up to 1.9× area reduction and 1.8× power savings over uniform-precision baselines while satisfying accuracy constraints.
Problem
Mixed-precision RBD design is difficult because variable sensitivities differ, the search space is combinatorial, and closed-loop trajectory evaluation is prohibitively expensive.
Method
APEX-RBD prunes the search with physics-driven grouping and sensitivity analysis, predicts trajectory error with a data-efficient prior-informed surrogate, and uses a hardware-aware hybrid optimizer.
Results
1.9× area reduction and 1.8× power savings are achieved over uniform-precision baselines while satisfying accuracy constraints.
Takeaways & Limitations
APEX-RBD enables hardware-efficient mixed-precision RBD configurations tailored to deployment workloads and user-defined constraints.
Takeaways & Limitations
The framework requires scenario-specific workload characterization and does not use a universal surrogate across robots and tasks.
Abstract
from arXiv · showhide
Rigid Body Dynamics (RBD) forms the computational core of real-time robotic control, but its immense computational complexity creates a performance bottleneck that necessitates dedicated hardware accelerators. However, the substantial hardware resource and power costs of these accelerators make their deployment on resource-constrained edge platforms highly challenging. While quantization offers a promising path to optimize RBD hardware for edge computing, existing uniform-precision approaches remain inefficient by ignoring the diverse quantization sensitivities of different variables. Although mixed-precision offers a superior alternative, its exploration is intractable due to a vast search space and the prohibitive cost of closed-loop simulation for motion accuracy evaluation. To address these challenges, we introduce APEX-RBD, an automated framework that makes mixed-precision exploration computationally tractable while effectively identifying hardware-efficient configurations. Specifically, it performs physics-driven search space pruning via variable grouping and sensitivity analysis, and employs a data-efficient, prior-informed surrogate model to enable rapid trajectory error prediction. This formulation guides a hybrid optimizer to identify area- and power-efficient designs under user-defined accuracy and performance constraints. Experimental results demonstrate that APEX-RBD discovers designs achieving up to 1.9$\times$ area reduction and 1.8$\times$ power savings compared to uniform-precision baselines across diverse robotic platforms.
1 Introduction
APEX-RBD addresses the inefficiency and intractability of mixed-precision RBD accelerator design by pruning the search space, predicting trajectory error efficiently, and guiding hardware-aware optimization. It targets area- and power-efficient configurations under accuracy and performance constraints.
- 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.
- 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.
- 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.
- 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.
- APEX-RBD discovers designs with up to 1.9× area reduction and 1.8× power savings over uniform-precision baselines under identical accuracy constraints.
2 Preliminaries
RBD algorithms operate over kinematic trees with bidirectional dataflow that maps naturally to pipelined accelerators. Quantization therefore becomes a constrained hardware-cost problem balancing bit-width, accuracy, and required performance.
- RBD algorithms such as RNEA and Minv operate on robot kinematic trees and use bidirectional traversal through forward and backward passes.
- RBD accelerator performance depends on parallel MAC units that implement the algorithms’ bidirectional dataflow.
- Performance is a hard control-frequency constraint that fixes the required accelerator parallelism and high-level architecture.
- 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.
- 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.
3.1 Application Workload Characterization
APEX-RBD characterizes each deployment with an application-specific profiling dataset so downstream sensitivity analysis and surrogate training match intended operating conditions.
- The profiling dataset combines representative motion workloads with stress tests such as high-velocity maneuvers.
- 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.
3.2 Variable Grouping and Sensitivity Analysis
Stage 1 reduces mixed-precision complexity by grouping variables, measuring workload-specific sensitivity, determining integer widths, and pruning fractional-width choices. These analyses also provide priors and heuristics for later optimization.
- 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.
- Initial grouping: Initial grouping reduces the search space from over 12^50 to 12^27 by replacing individual variables with grouped entities.
- 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.
- Sensitivity analysis: Targeted fractional-width sweeps are repeated across Latin-Hypercube-sampled background configurations to account for sensitivity coupling among groups.
- Sensitivity analysis: The stage produces sensitivity curves, module-level error data for surrogate priors, and integer bit-widths required to prevent overflow.
- 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.
3.3 Surrogate Model for Trajectory Error Prediction
APEX-RBD uses a hierarchical, prior-informed surrogate to predict trajectory error efficiently from mixed-precision configurations. It combines module-level error models, physically grounded features, and feature selection to address data scarcity and complex error propagation.
- 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.
- Motivation: 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.
- 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.
- 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.
- 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.
- 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.
3.4 Hardware-Aware Searching
APEX-RBD searches mixed-precision configurations with an analytical hardware-cost estimator, Bayesian Optimization, and two domain-guided local refinements. It validates the resulting candidate pool with end-to-end simulation before selecting the lowest-cost feasible design.
- 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.
- 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.
- 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.
- 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.
- 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.
4 Evaluation
Across robotic platforms and search strategies, APEX-RBD evaluates surrogate accuracy, optimization quality, hardware gains, and exploration runtime. Its mixed-precision designs reduce hardware cost while maintaining the 24-bit baseline’s motion accuracy.
- 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.
- 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.
- 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.
- 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.
- End-to-End Hardware Gains: 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.
- 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.
5 Conclusion
APEX-RBD automates mixed-precision quantization exploration for RBD by combining physics-aware pruning with surrogate-guided hybrid optimization. It discovers hardware-efficient designs under accuracy constraints, achieving substantial area and power reductions over uniform-precision baselines.
- 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.
- Conclusion: Up to 1.9× area and 1.8× power reductions are achieved over uniform-precision baselines while satisfying accuracy constraints.