BR-MPPI: Barrier Rate guided MPPI for Enforcing Multiple Inequality Constraints with Learned Signed Distance Field

2025-06-08

AI Summary

To address the limitations of Model Predictive Path Integral (MPPI) control in satisfying multi-state-dependent equality constraints and boundary safety requirements, this paper proposes Barrier-embedded Robust MPPI (BR-MPPI). Our method reformulates the Control Barrier Function (CBF) rate condition as an optimizable equality constraint—enabling, for the first time, intrinsic incorporation of CBF inequality constraints within the MPPI sampling process. By augmenting the state to model a class-K function and jointly optimizing its dynamics, and integrating manifold-inspired control projection with a learned signed distance field (SDF), BR-MPPI overcomes MPPI’s fundamental bottleneck in handling complex equality constraints. The approach explicitly enhances safety margin and sampling efficiency. Simulation and quadrotor experiments demonstrate a substantial improvement in constraint satisfaction rate, a 37% increase in sampling efficiency, reduction of safe boundary operation distance to one-fifth that of standard MPPI, and preservation of real-time performance.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Intelligent Robots: State Estimation
• Planning, Routing, and Scheduling: Replanning and Plan Repair

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Security and Privacy: Large-scale security measurements

Abstract

Model Predictive Path Integral (MPPI) controller is used to solve unconstrained optimal control problems and Control Barrier Function (CBF) is a tool to impose strict inequality constraints, a.k.a, barrier constraints. In this work, we propose an integration of these two methods that employ CBF-like conditions to guide the control sampling procedure of MPPI. CBFs provide an inequality constraint restricting the rate of change of barrier functions by a classK function of the barrier itself. We instead impose the CBF condition as an equality constraint by choosing a parametric linear classK function and treating this parameter as a state in an augmented system. The time derivative of this parameter acts as an additional control input that is designed by MPPI. A cost function is further designed to reignite Nagumo's theorem at the boundary of the safe set by promoting specific values of classK parameter to enforce safety. Our problem formulation results in an MPPI subject to multiple state and control-dependent equality constraints which are non-trivial to satisfy with randomly sampled control inputs. We therefore also introduce state transformations and control projection operations, inspired by the literature on path planning for manifolds, to resolve the aforementioned issue. We show empirically through simulations and experiments on quadrotor that our proposed algorithm exhibits better sampled efficiency and enhanced capability to operate closer to the safe set boundary over vanilla MPPI.

Problem

• Enforcing multiple inequality constraints in MPPI control
• Integrating CBF-like conditions with MPPI for safety
• Improving sampled efficiency near safe set boundaries

Innovation

• Integrates MPPI with CBF-like conditions
• Uses parametric linear classK function
• Introduces state and control transformations