BR-MPPI on hardware: the quadrotor negotiates the corridor with its extended body geometry.
Plan through clutter by adapting how quickly each constraint can change. BR-MPPI jointly samples robot controls and barrier rates, then projects the samples onto multiple barrier equalities before rolling out trajectories. The result is a sampling-based controller that can negotiate narrow passages while accounting for the robot’s body geometry.
Five robot models. Four safety-aware MPPI baselines. Real quadrotor experiments.
With analytic barriers, BR-MPPI achieves the highest success rate on every tested model: 87–100% success and zero unsafe outcomes across 500 trials. Learned signed distance fields reduce mean command latency by 2.10–2.52× in the three tested models, with a geometry-dependent accuracy tradeoff.
Explore the project
Why guide the samples?
MPPI evaluates many noisy control sequences and uses their costs to update a plan. In cluttered environments, useful samples can be scarce: a large collision penalty alone may produce detours or leave the robot stuck. Filtering only the next action also leaves the sampled planning horizon poorly informed about the constraints.
The challenge
Find useful trajectories around many obstacles while respecting the robot’s shape and dynamics, without relying only on rejection or large collision penalties.
The BR-MPPI idea
Make each constraint’s rate of change part of the optimization. Guide sampled controls jointly with those rates throughout the rollout horizon.
BR-MPPI versus vanilla MPPI
BR-MPPI and vanilla MPPI with the same 1,000-sample budget.
Both methods use 1,000 samples in these two examples. BR-MPPI navigates the narrow passage with a dynamic unicycle and makes progress with a hexagonal single integrator; vanilla MPPI takes a detour or remains near the start. In the dynamic-unicycle case study, vanilla MPPI needs 20,000 samples for a comparable path. These are case-specific comparisons from Section IV-A.
View the trajectory figure
How BR-MPPI works
For each constraint , BR-MPPI introduces an adaptive rate and uses the barrier equality
When the robot is in the safe region, a negative rate increases the barrier value, moving away from that boundary. A positive rate permits approach. Each obstacle can have its own rate, allowing the planner to balance progress and clearance as the surrounding geometry changes.
An animated walkthrough: augment and sample, project and roll out, then score and reweight.
1.
Augment and sample. Add one rate state per constraint. Sample robot inputs together with rate increments.
2.
Project jointly, then roll out. At each state, map the sampled inputs onto the simultaneous barrier equalities and propagate the resulting trajectory.
3.
Score and reweight. Evaluate goal progress, control effort, and boundary costs. Update the nominal pseudocontrol sequence using MPPI’s cost-weighted samples, execute the first projected input, and replan.
Formulation and implementation details
Simulation: five robot models
The large view shows BR-MPPI; the four smaller views show MPPI-CBF, Shield-MPPI, SC-MPPI, and GS-MPPI. Following cameras make the robot’s local motion and body clearance easier to inspect, while the inset retains the route context.
Single integrator
Translation through a dense obstacle field.
Single integrator · BR-MPPI and four safety-aware MPPI baselines.
Unicycle
Forward motion and heading must work together to move the body through clutter.
Unicycle · BR-MPPI and four safety-aware MPPI baselines.
Dynamic unicycle · live barrier rates
The rate traces below the BR-MPPI trajectory are the applied controller values, synchronized with the replay. Colors match the obstacle outlines, showing how different constraints receive different rates as the robot moves.
Dynamic unicycle · trajectory comparison and synchronized applied barrier rates.
Planar quadrotor
The planner must account for the vehicle’s orientation and coupled dynamics.
Planar quadrotor · BR-MPPI and four safety-aware MPPI baselines.
Mobile arm
The base and articulated arm navigate together, making whole-body clearance important.
Mobile arm · BR-MPPI and four safety-aware MPPI baselines.
Comparison protocol and trajectory details
Benchmark results
The benchmark evaluates 100 trials per method and robot model: 2,500 trials across five methods and five models. BR-MPPI has 475 successful trials out of 500, with no unsafe outcomes under analytic barriers; the remaining 25 trials end in timeout or deadlock.
Success, unsafe outcomes, and computation time across all five robot models. Source: Figure 4.
High success across different dynamics. BR-MPPI’s success rates are 95%, 87%, 100%, 98%, and 95% for the single integrator, unicycle, dynamic unicycle, planar quadrotor, and mobile arm, respectively.
Computation remains practical. Mean command times range from 26.39 to 145.27 ms. BR-MPPI is faster than SC-MPPI on every model, while MPPI-CBF and GS-MPPI are faster than BR-MPPI. The comparison therefore includes both task outcomes and computation cost.
Exact benchmark values
Learned geometry for faster planning
A neural signed distance field learns the distance to the robot body from its geometry. It supplies the barrier representation used to check that body against obstacle point clouds. Training combines a distance loss with an Eikonal term that regularizes the spatial gradient.
Analytic versus neural signed distance fields. Source: Table I.
Replacing the analytic representation reduces mean command latency by 2.10× for the unicycle, 2.52× for the dynamic unicycle, and 2.22× for the planar quadrotor, without retuning the BR-MPPI parameters.
Success, collisions, and timeouts with learned SDFs
Hardware: navigating a narrow obstacle corridor
A quadrotor carries a 0.28 × 0.56 m rectangular frame. BR-MPPI controls planar position and heading using Vicon localization and an obstacle point-cloud representation with 30 points per obstacle. The robot must rotate and translate through the corridor while accounting for its extended geometry.
Synchronized overhead, side, and planner views of one corridor traversal.
One trial, three synchronized views: overhead camera, side camera, and planner. The cyan rectangle helps track the complete robot body in the camera view; the planner panel shows the modeled footprint, sampled trajectories, plan, and goal.
Repeated successful traversals
Four additional recorded trials with BR-MPPI.
These four examples show repeated corridor traversals with different approach motions, complementing the detailed synchronized demonstration.
BibTex
@inproceedings{parwana2026brmppi,
title = {{BR-MPPI}: Barrier-Rate Guided MPPI for Enforcing Multiple
Inequality Constraints with Learned Signed Distance Fields},
author = {Parwana, Hardik and Kim, Taekyung and Long, Kehan and
Hoxha, Bardh and Okamoto, Hideki and Fainekos, Georgios and
Panagou, Dimitra},
booktitle = {arXiv preprint arXiv:2506.07325},
shorttitle = {BR-MPPI},
year = {2026}
}
LaTeX
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