Decentralized collision avoidance remains a core challenge for scalable multi-robot systems. One of the promising approaches to tackle this problem is Model Predictive Path Integral (MPPI) -- a framework that is naturally suited to handle any robot motion model and provides strong theoretical guarantees. Still, in practice MPPI-based controller may provide suboptimal trajectories as its performance relies heavily on uninformed random sampling. In this work, we introduce CoRL-MPPI, a novel fusion of Cooperative Reinforcement Learning and MPPI to address this limitation. We train an action policy (approximated as deep neural network) in simulation that learns local cooperative collision avoidance behaviors. This learned policy is then embedded into the MPPI framework to guide its sampling distribution, biasing it towards more intelligent and cooperative actions. Notably, CoRL-MPPI preserves all the theoretical guarantees of regular MPPI. We evaluate our approach in dense, dynamic simulation environments against state-of-the-art baselines, including ORCA, BVC, and a multi-agent MPPI implementation. Our results demonstrate that CoRL-MPPI significantly improves navigation efficiency (measured by success rate and makespan) and safety, enabling agile and robust multi-robot navigation.

In this letter, we introduce Geometric Model Predictive Path Integral (GMPPI), a sampling-based controller capable of tracking agile trajectories while avoiding obstacles. In each iteration, GMPPI generates a large number of candidate rollout trajectories and then averages them to create a nominal control to be followed by the Unmanned Aerial Vehicle (UAV). We propose using geometric SE(3) control to generate part of the rollout trajectories, significantly increasing precision in agile flight. Furthermore, we introduce varying rollout simulation time step length and dynamic cost and noise parameters, vastly improving tracking performance of smooth and low-speed trajectories over an existing Model Predictive Path Integral (MPPI) implementation. Finally, we propose an integration of GMPPI with a stereo depth camera, enabling online obstacle avoidance at high speeds, a crucial step towards autonomous UAV flights in complex environments. The proposed controller can track simulated agile reference trajectories with position error similar to the geometric SE(3) controller. However, the same configuration of the proposed controller can avoid obstacles in a simulated forest environment at speeds of up to 13m/s, surpassing the performance of a state-of-the-art obstacle-aware planner. In real-world experiments, GMPPI retains the capability to track agile trajectories and avoids obstacles at speeds of up to 10m/s.

We present a unified framework for solving trajectory optimization problems in a derivative-free manner through the use of sequential convex programming. Traditionally, nonconvex optimization problems are solved by forming and solving a sequence of convex optimization problems, where the cost and constraint functions are approximated locally through Taylor series expansions. This presents a challenge for functions where differentiation is expensive or unavailable. In this work, we present a derivative-free approach to form these convex approximations by computing samples of the dynamics, cost, and constraint functions and letting the solver interpolate between them. Our framework includes sample-based trajectory optimization techniques like model-predictive path integral (MPPI) control as a special case and generalizes them to enable features like multiple shooting and general equality and inequality constraints that are traditionally associated with derivative-based sequential convex programming methods. The resulting framework is simple, flexible, and capable of solving a wide variety of practical motion planning and control problems.

Abstract-- While model-based controllers have demonstrated remarkable performance in autonomous drone racing, their performance is often constrained by the reliance on pre-computed reference trajectories. Recent advancements in reinforcement learning (RL) have revealed that many model-based controllers optimize surrogate objectives, such as trajectory tracking, rather than the primary racing goal of directly maximizing progress through gates. Inspired by these findings, this work introduces a reference-free method for time-optimal racing by incorporating this gate progress objective, derived from RL reward shaping, directly into the Model Predictive Path Integral (MPPI) formulation. The sampling-based nature of MPPI makes it uniquely capable of optimizing the discontinuous and non-differentiable objective in real-time. We also establish a unified framework that leverages MPPI to systematically and fairly compare three distinct objective functions with a consistent dynamics model and parameter set: classical trajectory tracking, contouring control, and the proposed gate progress objective. We compare the performance of these three objectives when solved via both MPPI and a traditional gradient-based solver . Our results demonstrate that the proposed reference-free approach achieves competitive racing performance, rivaling or exceeding reference-based methods.

Motion planning for robotic manipulators is a fundamental problem in robotics. Classical optimization-based methods typically rely on the gradients of signed distance fields (SDFs) to impose collision-avoidance constraints. However, these methods are susceptible to local minima and may fail when the SDF gradients vanish. Recently, Configuration Space Distance Fields (CDFs) have been introduced, which directly model distances in the robot's configuration space. Unlike workspace SDFs, CDFs are differentiable almost everywhere and thus provide reliable gradient information. On the other hand, gradient-free approaches such as Model Predictive Path Integral (MPPI) control leverage long-horizon rollouts to achieve collision avoidance. While effective, these methods are computationally expensive due to the large number of trajectory samples, repeated collision checks, and the difficulty of designing cost functions with heterogeneous physical units. In this paper, we propose a framework that integrates CDFs with MPPI to enable direct navigation in the robot's configuration space. Leveraging CDF gradients, we unify the MPPI cost in joint-space and reduce the horizon to one step, substantially cutting computation while preserving collision avoidance in practice. We demonstrate that our approach achieves nearly 100% success rates in 2D environments and consistently high success rates in challenging 7-DOF Franka manipulator simulations with complex obstacles. Furthermore, our method attains control frequencies exceeding 750 Hz, substantially outperforming both optimization-based and standard MPPI baselines. These results highlight the effectiveness and efficiency of the proposed CDF-MPPI framework for high-dimensional motion planning.

Legged robots possess a unique ability to traverse rough terrains and navigate cluttered environments, making them well-suited for complex, real-world unstructured scenarios. However, such robots have not yet achieved the same level as seen in natural systems. Recently, sampling-based predictive controllers have demonstrated particularly promising results. This paper investigates a sampling-based model predictive strategy combining model predictive path integral (MPPI) with cross-entropy (CE) and covariance matrix adaptation (CMA) methods to generate real-time whole-body motions for legged robots across multiple scenarios. The results show that combining the benefits of MPPI, CE and CMA, namely using model predictive optimized path integral (MPOPI), demonstrates greater sample efficiency, enabling robots to attain superior locomotion results using fewer samples when compared to typical MPPI algorithms. Extensive simulation experiments in multiple scenarios on a quadruped robot show that MPOPI can be used as an anytime control strategy, increasing locomotion capabilities at each iteration.

Articulated vehicles such as tractor-trailers, yard trucks, and similar platforms must often reverse and maneuver in cluttered spaces where pedestrians are present. We present how Barrier-Rate guided Model Predictive Path Integral (BR-MPPI) control can solve navigation in such challenging environments. BR-MPPI embeds Control Barrier Function (CBF) constraints directly into the path-integral update. By steering the importance-sampling distribution toward collision-free, dynamically feasible trajectories, BR-MPPI enhances the exploration strength of MPPI and improves robustness of resulting trajectories. The method is evaluated in the high-fidelity CarMaker simulator on a 12 [m] tractor-trailer tasked with reverse and forward parking in a parking lot. BR-MPPI computes control inputs in above 100 [Hz] on a single GPU (for scenarios with eight obstacles) and maintains better parking clearance than a standard MPPI baseline and an MPPI with collision cost baseline.

This paper proposes Constrained Sampling Cluster Model Predictive Path Integral (CSC-MPPI), a novel constrained formulation of MPPI designed to enhance trajectory optimization while enforcing strict constraints on system states and control inputs. Traditional MPPI, which relies on a probabilistic sampling process, often struggles with constraint satisfaction and generates suboptimal trajectories due to the weighted averaging of sampled trajectories. To address these limitations, the proposed framework integrates a primal-dual gradient-based approach and Density-Based Spatial Clustering of Applications with Noise (DBSCAN) to steer sampled input trajectories into feasible regions while mitigating risks associated with weighted averaging. First, to ensure that sampled trajectories remain within the feasible region, the primal-dual gradient method is applied to iteratively shift sampled inputs while enforcing state and control constraints. Then, DBSCAN groups the sampled trajectories, enabling the selection of representative control inputs within each cluster. Finally, among the representative control inputs, the one with the lowest cost is chosen as the optimal action. As a result, CSC-MPPI guarantees constraint satisfaction, improves trajectory selection, and enhances robustness in complex environments. Simulation and real-world experiments demonstrate that CSC-MPPI outperforms traditional MPPI in obstacle avoidance, achieving improved reliability and efficiency. The experimental videos are available at https://cscmppi.github.io

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.

Reactive mobile robot navigation in unstructured environments is challenging when robots encounter unexpected obstacles that invalidate previously planned trajectories. Model predictive path integral control (MPPI) enables reactive planning, but still suffers from limited prediction horizons that lead to local minima traps near obstacles. Current solutions rely on heuristic cost design or scenario-specific pre-training, which often limits their adaptability to new environments. We introduce dynamic repulsive potential augmented MPPI (DRPA-MPPI), which dynamically detects potential entrapments on the predicted trajectories. Upon detecting local minima, DRPA-MPPI automatically switches between standard goal-oriented optimization and a modified cost function that generates repulsive forces away from local minima. Comprehensive testing in simulated obstacle-rich environments confirms DRPA-MPPI's superior navigation performance and safety compared to conventional methods with less computational burden.