FPGA Accelerator for MPPI Control

• Hardware Accelerator for MPPI control is a specialized engine implemented on FPGAs that speeds up stochastic trajectory sampling and cost evaluation in nonlinear control loops.
• The architecture splits tasks between a host CPU for tasks like noise generation and reduction, and an FPGA for parallel pipelined rollout pipelines, optimizing energy usage and resource allocation.
• Comparative results show that this accelerator achieves smoother control trajectories and improved energy efficiency over GPU-based implementations in embedded robotic applications.

A hardware accelerator for Model Predictive Path Integral (MPPI) control is a domain-specific computation engine, most notably implemented on Field-Programmable Gate Arrays (FPGAs), designed to expedite the stochastic trajectory sampling and cost evaluation core to MPPI algorithms. Such accelerators are motivated by the demands of real-time feedback control in autonomous robotic systems, where energy efficiency and deterministic throughput are required but general-purpose hardware such as GPUs may be inadequate due to excessive power consumption or unpredictable latency. Hardware MPPI accelerators provide tailored parallel and pipelined datapaths for the dominant computational kernels of MPPI, enabling fine-grained trade-offs between resource usage, power, and control fidelity (Tanguy-Legac et al., 17 Jan 2026).

1. Model Predictive Path Integral Control Fundamentals

MPPI is a stochastic, sampling-based variant of Model Predictive Control (MPC), particularly effective for highly nonlinear systems where gradient-based optimization is intractable. The controller synthesizes optimal actions by:

• Sampling $N$ control sequences $\{u_t^{(i)}\}$ over horizon $H$ from a zero-mean Gaussian perturbation about a nominal sequence.
• Rolling out each trajectory via the (potentially nonlinear) dynamics $x_{t+1}^{(i)} = F(x_t^{(i)},u_t^{(i)})$, while accumulating costs $S^{(i)}$ from a running cost $\mathcal{L}$ and terminal cost $\phi$.
• Computing soft-min weights $$w^{(i)} = \exp(-h\,(S^{(i)}-S_{\min})/(S_{\max}-S_{\min}))$$ to bias toward low-cost samples.
• Yielding the next control as the importance-weighted mean $u_0^* = \sum_i w^{(i)}u_0^{(i)} / \sum_i w^{(i)}$.

The complete control loop includes resampling, control application, horizon shifting, and repetition at subsequent steps. The performance and real-time viability of MPPI is predominantly constrained by the computational load of trajectory rollout and cost evaluation (Tanguy-Legac et al., 17 Jan 2026).

2. Hardware Architecture and Partitioning

The MPPI accelerator architecture divides the overall control computation between a host CPU and a parallel, pipelined FPGA engine:

• Host CPU:
  • Generates $N \times H$ Gaussian noise samples and uploads them, along with state, references, and nominal controls, to FPGA-local memory (on-chip BRAM).
  • Handles post-rollout reductions: weight calculations, normalization, and final nominal control update.
• FPGA Accelerator:
  • Implements $N_{\text{pipelines}}$ independent "rollout pipelines" for parallel evaluation of sampled trajectories.
  • Each pipeline comprises $H+1$ stages, unrolling the temporal horizon loop for temporal parallelism, so that after pipeline fill-up, one cost result emerges every cycle.
  • Computes plant dynamics, per-step and terminal costs, and aggregates total trajectory costs for each sample.

No random number generation or exponential/logarithmic operations are performed on-chip; only arithmetic for system evolution and cost is instantiated on the FPGA. The architecture exploits both spatial (by pipeline replication) and deep temporal (by horizon unrolling) parallelism (Tanguy-Legac et al., 17 Jan 2026).

3. FPGA Implementation and Resource Utilization

The accelerator is synthesized for a Xilinx Alveo U55C FPGA, utilizing Vivado 2023.1 and employing 32-bit IEEE-754 floating point arithmetic throughout:

Pipelines	Stages/pipeline	Stage size*	LUT use (%)
1	25	1	12.58
2	5	5	66.30
5	25	1	83.28
10	1	25	69.22
14	1	25	96.56

(*Stage size is the number of rollout steps folded into one pipeline stage.)

• Increase in pipeline count and temporal unrolling directly impacts LUT consumption, as each simultaneous trajectory requires dedicated logic and memory buffers.
• No DSP slice, BRAM, or precise clock frequency figures are reported, but per-pipeline BRAM stores each trajectory’s local variables and inputs.
• All exponentials and reductions required for control updates remain CPU-resident.
• Floating-point arithmetic in LUT-based FPGAs, as on the U55C, constraints maximum pipeline replication; fixed-point arithmetic is proposed for future area/power optimization.
• Direct power or throughput measurements are absent, but qualitative analysis suggests significantly lower power than GPU-based implementations (Tanguy-Legac et al., 17 Jan 2026).

4. Performance Characteristics and Comparative Results

Performance evaluation is conducted via behavioral simulation on a nonlinear quadrotor plant, with a 25-step horizon at 20 ms per step (0.5 s look-ahead):

• GPU Reference: 2,000 simultaneous rollouts in a single launch.
• FPGA Accelerator: 200 pipelines with 25-stage pipelines (10× fewer trajectories in parallel, but tightly pipelined execution).
• In the no-obstacle scenario, the FPGA implementation yields noticeably smoother position and input trajectories than the GPU, attributed to the reduced "jitter" from consistent pipelined update cadence.
• In the static obstacle scenario, the GPU implementation cannot find a feasible collision-free path, whereas the FPGA-based accelerator successfully reroutes, demonstrating improved solution quality in closed-loop operation.

Key missing metrics include cycle-accurate latency, energy per control update, and absolute error/tracking scores. Nonetheless, the simulation results establish feasibility and indicate that—despite omitting on-chip reductions and weightings—the FPGA MPPI pipeline can yield more robust (and in some cases unique) solutions at a substantially lower energy cost compared to high-throughput GPUs (Tanguy-Legac et al., 17 Jan 2026).

5. Design Trade-offs and Implementation Limitations

Design choices in the reported accelerator impose several trade-offs:

• Spatial/Temporal Parallelism: Folding multiple rollout steps into a single logic block ("stage size" parameter) enables more pipelines per chip area, but raises per-stage logic complexity and may impact clock speed.
• Numerical Precision: Exclusive use of floating-point arithmetic drastically inflates LUT usage on FPGAs without hard FPUs. Fixed-point or mixed-precision logic is proposed to improve frequency and area.
• Offloaded vs. On-Chip Computation: Only dynamic- and cost-rollout is accelerated; sampling, nonlinear weighting, and reduction remain CPU-bound, introducing host–FPGA latency and reducing single-chip autonomy.
• Resource Constraints: Maximum parallelism is limited by LUT/BRAM availability; more aggressive resource sharing or memory-mapped rolling-window structures may improve scalability.
• Lack of Direct Measurements: No physical power, throughput, or silicon utilization measurements are provided, only synthesis and functional simulation (Tanguy-Legac et al., 17 Jan 2026).

A plausible implication is that ASIC realization with hard multipliers or an improved arithmetic pipeline could further lower power and improve deterministic latency, crucial for embedded robotic applications.

6. Relation to GPU-Accelerated MPPI and Research Context

GPU-accelerated MPPI implementations, such as Barrier-Rate guided MPPI (BR-MPPI) for articulated vehicles, utilize massively parallel CUDA thread launches, assigning one thread per sampled trajectory. On current NVIDIA architectures (e.g., RTX 2080 Ti), such systems evaluate approximately 5,000 rollouts over horizons of $H=120$, embedding barrier-function constraints and supporting control updates at rates above 100 Hz with eight obstacles (Majd et al., 7 Aug 2025).

• GPU implementations provide high throughput and convenience but may be unsuitable for power-constrained systems. The reported energy and real-time requirements of embedded or battery-powered robots are incompatible with typical desktop/GPU platforms.
• The FPGA-based MPPI accelerator demonstrates, via simulation, the ability to surpass GPU-based solutions not only in energy footprint but, under certain scenarios, in trajectory robustness and constraint satisfaction, despite launching fewer rollouts.
• Both paradigms retain a hybrid CPU role for sampling, reduction, and control update. Neither the FPGA nor current GPU implementations fully offload the entire MPPI loop.

The hardware accelerator concept, therefore, occupies a unique middle ground, combining the application-tailored determinism and low power of embedded hardware with the high-throughput, sample-based planning effectiveness pioneered in stochastic MPPI (Tanguy-Legac et al., 17 Jan 2026, Majd et al., 7 Aug 2025).

7. Future Directions and Extensions

Open research challenges and future directions for hardware-accelerated MPPI encompass:

• Fixed-Point and Mixed-Precision Arithmetic: Transitioning from LUT-based floating point to fixed-point or hybrid pipelines to unlock higher on-chip parallelism and frequency.
• Complete MPPI Pipeline Integration: Offloading exponential weighting, reduction, and control-law update computations to the accelerator, potentially eliminating host dependency and enabling full on-chip autonomy.
• Algorithmic Co-Design: Adapting MPPI algorithmic structure to be more hardware-friendly (e.g., fragmented horizons, hierarchical rollouts) for better pipeline compatibility and higher resource efficiency.
• ASIC Realization: Developing application-specific integrated circuits leveraging hard multipliers and memory hierarchies to achieve further improvement in power/performance trade-offs.
• Fine-Grained Power/Throughput Analysis: Carrying out cycle- and power-accurate measurement on physical prototypes to provide empirical validation and guide future design iterations.

These extensions suggest a trajectory toward embedded, hardware-optimized, fully autonomous MPPI-based controllers capable of real-time, power-efficient operation in resource-constrained environments typical of UAVs, mobile robots, and advanced driver-assistance systems (Tanguy-Legac et al., 17 Jan 2026).