Motoneuron-Inspired Sampling for Model Predictive Path Integral Control

Alexis Poignant; Jan Babič

cs.ROSep 23, 2026

Motoneuron-Inspired Sampling for Model Predictive Path Integral Control

Authors: Alexis Poignant, Jan Babič

Abstract

Model Predictive Path Integral (MPPI) control relies on stochastic trajectory sampling, and its performance under limited rollout budgets depends strongly on the structure of the proposal distribution. Standard implementations commonly perturb control sequences with Gaussian noise, despite growing evidence that temporally correlated and structured sampling can improve finite-budget control. We introduce Spike-MPPI, a motoneuron-inspired proposal that generates temporally structured perturbations through a simplified model of motoneuron dynamics. The proposal is evaluated within a common MPPI framework on torque-actuated and antagonistically actuated MuJoCo Ant models against standard Gaussian sampling and spectrum-matched Gaussian controls. Results show that structured sampling substantially improves executed-control smoothness, while its effect on task performance depends on rollout condition and robot actuation. Spectrum matching reproduces a substantial part of the observed behavior, while the full Spike proposal retains additional effects beyond second-order spectral structure. These results support treating proposal design as a combination of second-order spectral structure and higher-order statistical organization.

Figures & tables

Panel of Figure 1 — Fig. 1: Overview of the Poisson and Spike proposal distributions. (a) Poisson generates sparse signed events from fixed positive and negative event rates and recruitment marks, then decodes the events with a common twitch kernel. (b) Spike uses a shared stochastic drive for agonist and antagonist motor pools. Increasing drive recruits motor units progressively in ordered steps, while derecruitment occurs at lower drive levels, producing hysteresis. Active units then use rate coding and refractory renewal discharge; spike heights illustrate different motor-unit strengths. (c) Motor-unit-specific twitch responses are summed separately for the agonist and antagonist pools. The resulting outputs are converted either to a signed torque perturbation or to separate agonist and antagonist actuator channels.

Fig. 2: Representative perturbation realizations for the five sampling methods. The top row shows the Standard Gaussian proposal and the Gaussian-Poisson and Gaussian-Spike spectrum-matched controls. For Poisson sampling, the middle row shows discrete signed events before filtering and the resulting perturbation after the common twitch kernel. For Spike sampling, the bottom row shows motor-unit discharge events before filtering and the resulting perturbation after heterogeneous motor-unit twitch kernels.

Fig. 3: Representative executed control traces for the five sampling methods on the torque-driven Ant after the MPPI weighted average. The panels show the command increment

\Delta u_{t}=u_{t}-u_{t-1}

and corresponding executed command

u_{t}

for the hip joint of leg 1 over the same time window. In this representative segment, the structured proposals exhibit visibly smaller command increments than Standard.

Task	$w_{p}$	$w_{r}$	$w_{a}$
Run	1.00	0	0
Push box	1.00	0.35	1.00
Tow sled	1.00	0.25	0

TABLE I: Task-specific rollout-cost weights.

Fig. 4: Representative evolution of the Spike controller over a single run and eight selected frames.

Fig. 5: Representative snapshots of the generalization scenarios: mixed terrain, rocky terrain, two asymmetric-leg configurations, box pushing, and sled towing.

Fig. 6: Performance of the sampling methods on the flat running task for Ant and Ant-2 under the three rollout conditions. The panels report mean lap velocity, weighted rollout cost, computation time per control step, and executed-control smoothness measured by

\|\mathbf{u}_{t}-\mathbf{u}_{t-1}\|_{2}

. Distributions are shown across completed retained laps, with horizontal bars indicating the mean. Arrows indicate the preferred direction for each metric.

Fig. 7: Antagonistic actuation characteristics of Ant-2 for the sampling methods under the three rollout conditions. The co-contraction index quantifies simultaneous activation of the agonist and antagonist actuators, while differential action measures the magnitude of the net directional agonist–antagonist command.

Fig. 8: Executed-command coordination for the sampling methods on Ant and Ant-2 under the three rollout conditions. Within-leg coordination measures the consistency of the relative phase between the hip and ankle commands of each leg, averaged across the four legs. Between-leg coordination measures the consistency of the relative phase between homologous joints, averaged across all leg pairs. Higher values indicate a more consistent phase relationship.

Task performance
Outcome	Robot	H1: S–Std	H2: GS–Std	H3: S–GS	H4: S–P
Lap velocity	Ant	$\checkmark/\checkmark/\checkmark$	$\checkmark/-/-$	$-/-/-$	$-/-/-$
	Ant-2	$\checkmark/\checkmark/\checkmark$	$\checkmark/-/-$	$-/-/-$	$\checkmark/\checkmark/\checkmark$
Weighted rollout cost	Ant	$\checkmark/-/-$	$-/-/-$	$-/-/-$	$-/-/-$
	Ant-2	$\checkmark/\checkmark/\checkmark$	$\checkmark/-/-$	$-/-/-$	$\checkmark/\checkmark/\checkmark$
Temporal structure and coordination

TABLE II: Significance summary for all hypotheses at the

0.05

threshold after Holm correction. S: Spike; GS: Gaussian-Spike; P: Poisson; Std: Standard Gaussian. Entries correspond to

32/256/\mathrm{Scr.}

Terrain	Robot	Sampler	Vel. (m/s) $\uparrow$	Laps/seed $\uparrow$	Smooth. $\downarrow$
Mixed	Ant	Standard	$3.270\pm 1.102$	5.7/10	$1.451\pm 0.128$
		Poisson	$3.992\pm 1.199$	9.5/10	$0.734\pm 0.068$
		Spike	$\mathbf{4.186\pm 1.121}$	8.8/10	$\mathbf{0.574\pm 0.048}$
	Ant-2	Standard	$3.831\pm 0.397$	1.6/10	$1.098\pm 0.038$
		Poisson	$3.264\pm 1.105$	3.1/10	$0.533\pm 0.059$
		Spike	$\mathbf{4.110\pm 0.938}$	8.0/10	$\mathbf{0.459\pm 0.038}$

TABLE III: Generalization to mixed and rocky terrain. Velocity and smoothness are reported as mean

\pm

standard deviation over completed laps.

Task	Robot	Sampler	Vel. (m/s) $\uparrow$	Laps/seed $\uparrow$	Smooth. $\downarrow$
Push box	Ant	Standard	$\mathbf{2.324\pm 0.218}$	10.0/10	$1.923\pm 0.033$
		Poisson	$2.176\pm 0.183$	9.1/10	$1.026\pm 0.021$
		Spike	$2.219\pm 0.240$	10.0/10	$\mathbf{0.748\pm 0.015}$
	Ant-2	Standard	$2.372\pm 0.281$	10.0/10	$1.287\pm 0.020$
		Poisson	$2.337\pm 0.224$	9.7/10	$0.701\pm 0.014$
		Spike	$\mathbf{2.429\pm 0.228}$	10.0/10	$\mathbf{0.594\pm 0.010}$

TABLE IV: Generalization to object-manipulation tasks.

Asymmetry	Robot	Sampler	Vel. (m/s) $\uparrow$	Laps/seed $\uparrow$	Smooth. $\downarrow$
Diagonal	Ant	Standard	$4.764\pm 0.351$	10.0/10	$1.497\pm 0.046$
		Poisson	$\mathbf{4.972\pm 0.356}$	10.0/10	$0.739\pm 0.027$
		Spike	$4.930\pm 0.333$	10.0/10	$\mathbf{0.584\pm 0.020}$
	Ant-2	Standard	$4.438\pm 0.395$	10.0/10	$1.007\pm 0.033$
		Poisson	$4.468\pm 0.374$	10.0/10	$0.536\pm 0.020$
		Spike	$\mathbf{4.782\pm 0.340}$	10.0/10	$\mathbf{0.458\pm 0.015}$

TABLE V: Robustness to altered morphology.

Mismatch	Robot	Sampler	Vel. (m/s) $\uparrow$	Laps/seed $\uparrow$	Smooth. $\downarrow$
Fast RK4	Ant	Standard	$4.584\pm 0.347$	7.0/10	$1.573\pm 0.051$
		Poisson	$4.651\pm 0.368$	5.7/10	$0.807\pm 0.029$
		Spike	$\mathbf{4.732\pm 0.305}$	6.9/10	$\mathbf{0.624\pm 0.022}$
	Ant-2	Standard	$4.343\pm 0.296$	7.8/10	$1.041\pm 0.036$
		Poisson	$4.224\pm 0.323$	6.3/10	$0.574\pm 0.022$
		Spike	$\mathbf{4.852\pm 0.307}$	5.0/10	$\mathbf{0.484\pm 0.017}$

TABLE VI: Robustness to planner–plant integrator mismatch.

Appendix figures & tables2 assets

Supplementary material from the paper’s appendix.

Appendix

		H1: S–Std			H2: GS–Std			H3: S–GS			H4: S–P
Outcome	Robot	32	256	Scr.	32	256	Scr.	32	256	Scr.	32	256	Scr.
Lap velocity	Ant	0.016	0.029	0.031	0.029	0.156	0.523	0.484	0.328	0.094	0.803	0.803	0.803
	Ant-2	0.012	0.012	0.031	0.012	0.062	0.062	0.328	0.094	0.125	0.020	0.012	0.020
Weighted rollout cost	Ant	0.023	0.072	0.051	0.078	0.078	0.109	0.146	1.000	0.234	1.000	1.000	0.094
	Ant-2	0.012	0.012	0.023	0.012	0.078	0.078	1.000	0.094	0.146	0.020	0.012	0.020
Control smoothness	Ant	0.012	0.012	0.012	0.012	0.047	0.031	0.012	0.047	0.031	0.012	0.012	0.012

Appendix

TABLE VII: Holm-adjusted

p_{\mathrm{H}}

values for the four hypothesis-driven contrasts. Bold values indicate

p_{\mathrm{H}}<0.05

		H1: S–Std			H2: GS–Std			H3: S–GS			H4: S–P
Outcome	Robot	32	256	Scr.	32	256	Scr.	32	256	Scr.	32	256	Scr.
Lap velocity	Ant	0.004	0.010	0.020	0.006	0.078	0.523	0.484	0.109	0.016	0.268	0.285	0.338
	Ant-2	0.002	0.002	0.016	0.002	0.016	0.016	0.164	0.016	0.031	0.004	0.002	0.004
Weighted rollout cost	Ant	0.006	0.072	0.025	0.020	0.031	0.109	0.029	0.594	0.078	0.531	0.842	0.031
	Ant-2	0.002	0.002	0.008	0.002	0.016	0.016	0.734	0.016	0.031	0.004	0.002	0.004
Control smoothness	Ant	0.002	0.002	0.002	0.002	0.016	0.008	0.002	0.016	0.008	0.002	0.002	0.002

Appendix

TABLE VIII: Raw permutation

p

-values before Holm correction for the four hypothesis-driven contrasts.

MPPI Control

Model Predictive Path Integral (MPPI) control uses sampled future action sequences to optimize feedback actions under nonlinear dynamics and uncertainty.

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MP-MPPI: A Motion Primitive Guided Sampling-Based Optimizer for Model Predictive Control

Marlon Mathisen, Aksel Vaaler, Olav Egeland, Eleni Kelasidi

*Norwegian University of Science and Technology, Dept. of Mechanical and Industrial Engineering, Norway

Model Predictive Control Motion Planning MPPI Control Sampling-Based Motion Planning

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This paper proposes a novel method that extends the Model Predictive Path Integral (MPPI) method with motion primitives for additional structured sampling, which enhances the convergence towards a globally optimal solution. By evaluating motion primitives and perturbed control sequences in a real-time sampling-based optimization loop, this work addresses the limitations of the path planning capabilities of sampling-based controllers. The algorithm is implemented on a quadcopter simulator and tested on an obstacle field navigation task. It is demonstrated that the proposed approach enhances exploration of the control space while maintaining the fast, reactive behavior required for real-time control.

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