Source-linked AI summary
Dual Process Motion Planning
Jiayi Yan, Francesco Fabiano, Alessandro Abate
TL;DR
Motion planning must balance the speed of learned policies with the guarantees and constraint handling of online optimization. The paper introduces Dual-MP, which combines neural System-1 planning, MPC or CBF System-2 fallbacks, and metacognitive arbitration. Across nonlinear benchmarks, the architecture improves reported success and efficiency, while continual learning reuses successful recoveries to strengthen fast planning.
Problem
Motion planning requires efficient, reliable trajectory generation in complex constrained environments, but existing hybrid methods commonly invoke online optimization without deciding whether it is necessary.
Method
Dual-MP combines a neural System-1 policy with MPC or CBF System-2 fallbacks under metacognitive arbitration, accepting verified rollouts and continually learning from successful recoveries.
Results
Dual-MP outperforms standalone baselines in the reported success and efficiency metrics, with the MPC variant achieving the highest success rate while remaining substantially faster than standalone MPC.
Takeaways & Limitations
Verified arbitration provides a practical mechanism for combining the speed of learned policies with the robustness of optimization-based solvers, while reducing dependence on System-2 over time.
Takeaways & Limitations
Continual learning is most effective when teacher behavior matches the student policy class, and MPC-generated behaviors can be difficult for reactive policies to reproduce reliably in closed loop.
Abstract
from arXiv · showhide
Robotic systems are deeply embedded in both industry and everyday life, where they are expected to act with speed, precision, and reliability. Classical control and planning methods have long delivered strong guarantees, but often at the cost of computational efficiency and adaptability. More recently, learning-based approaches have shown promise in overcoming these limitations, enabling agents to leverage experience to accelerate decision-making and address previously intractable problems. In this work, we bridge these two approaches through a neuro-symbolic perspective on nonlinear motion planning. Inspired by the Thinking Fast and Slow paradigm, we introduce a dual-process architecture that combines the strengths of robust reasoning and learning. Our framework integrates state-of-the-art symbolic solvers as a ``System-2'' component with experience-driven ``System-1'' modules. A metacognitive controller dynamically orchestrates their interaction, selecting when to rely on fast intuition versus slower, more precise reasoning. By evaluating the framework across diverse nonlinear benchmark environments, we demonstrate that this architecture yields consistent gains in planning efficiency, accuracy, and generalization, while promoting reuse across tasks. The results suggest that tightly coupling learning with structured reasoning offers a scalable path toward more capable and adaptive robotic systems.
Introduction
Motion planning must produce collision-free, dynamically feasible trajectories in challenging real-world settings, yet classical optimization can be computationally expensive and learned methods can lack guarantees. Dual-MP addresses this gap with a modular architecture that arbitrates fast neural planning and deliberate online solving.
- Motivation: Motion planning computes collision-free trajectories from start to goal states while respecting dynamics and constraints, but high-dimensional continuous environments make this difficult under real-time requirements.The problem spans applications including autonomous driving and multi-agent coordination.
- Motivation: Experience-based planners provide fast online inference by mapping observations to controls or waypoints, but scenario mismatch can produce suboptimal or unsafe performance.Their guarantees are typically weaker than those of optimization-based methods.
- Motivation: Online optimization methods such as MPC and CBF explicitly account for dynamics and environmental constraints, but their computational overhead limits use in time-critical settings.These methods compute trajectories by solving constrained optimization problems at runtime.
- Dual-MP: Dual-MP combines fast experience-based planning with slower online solving through a dual-system architecture designed to improve efficiency and performance.The framework is motivated by learning-augmented planning and the dual-system paradigm.
- Dual-MP: The framework uses a neural System-1 policy, MPC and CBF-based System-2 solvers, and a metacognitive agent to arbitrate between them.The architecture is modular and supports continual learning from successful trajectories.
Related work
Prior motion-planning methods divide between fast experience-based approaches and constraint-aware online optimization, while hybrid methods combine them without deciding when optimization is necessary. Dual-MP targets this allocation problem.
- Experience-based planning: Experience-based planning amortizes prior solutions into neural mappings from observations, goals, and local state information to actions, waypoints, or trajectories.This enables low-latency inference by reusing learned structure.
- Online optimization: Online optimization methods such as MPC and CBF solve constrained problems at runtime to incorporate dynamics and environmental constraints, but they incur significant computational overhead.Their solutions are high-quality and dynamically feasible.
- Hybrid approaches: Learning-augmented approaches combine offline planning efficiency with online optimization accuracy, often by using learned models or datasets to warm-start solvers.Memory-of-Motion is one example of this strategy.
- Hybrid approaches: Existing hybrid approaches usually invoke the online solver regardless of how well the learned prior matches the current scenario, causing unnecessary computation.They lack a principled mechanism for deciding when online optimization is required.
Background
The background presents MPC and CBFs as complementary optimization-based tools and situates them within a dual-process architecture. MPC plans over future trajectories, whereas CBFs enforce local safety constraints, with a metacognitive controller choosing between fast and slow solvers.
- Nonlinear Model Predictive Control: MPC solves a finite-horizon optimization problem at each timestep to compute controls while satisfying system dynamics and constraints.The formulation uses discretized nonlinear dynamics, state and control constraints, and a goal-related cost.
- Nonlinear Model Predictive Control: MPC incorporates obstacle avoidance through collision-free state constraints, but repeatedly solving the resulting nonlinear program can be computationally expensive.Its accuracy comes from optimizing over future trajectories.
- Control Barrier Functions: CBFs act as local safety filters rather than optimizing an entire future trajectory, enforcing obstacle-avoidance constraints during control.They provide a complementary approach to MPC for safety enforcement.
- Control Barrier Functions: CBF safety constraints encourage forward invariance of each safe set through Lie-derivative inequalities with an aggressiveness parameter γ.The safe set is defined by h_i(x) ≥ 0.
- Control Barrier Functions: At each timestep, the CBF controller minimizes deviation from a nominal control subject to safety and control constraints.The nominal input may be goal-directed or proposed by the neural System-1 policy.
- Dual-process architecture: Dual-process architectures combine fast experience-driven System-1 solvers, slower reasoning-based System-2 solvers, and a centralized metacognitive controller.The controller accepts System-1 proposals or invokes System-2 solving based on the incoming problem and proposal confidence.
Dual-MP
Dual-MP combines a fast neural System-1 policy with deliberative System-2 solvers through metacognitive arbitration. It verifies System-1 rollouts, invokes System-2 when needed, and uses successful System-2 trajectories to improve System-1 over time.
- Dual-MP defines nonlinear reach–avoid planning queries over system dynamics, obstacles, start and goal states, workspace, and admissible controls.
- System-1: System-1 is a neural reactive policy that predicts low-level controls from local observations, nonlinear dynamics features, and goal information.Its lightweight architecture conditions control prediction on geometry and nonlinear dynamics.
- System-2: System-2 uses standard formulations of a control-barrier-function safety filter and a nonlinear model-predictive-control planner.
- Metacognitive arbitration: The metacognitive module accepts a System-1 rollout only after collision and goal verification, otherwise invoking System-2 when the time budget permits.If System-2 fails to return a satisfactory solution within budget, Dual-MP falls back to the best available System-1 proposal.
- Verification: Correctness is 1 only for trajectories that reach the goal and remain collision-free; the experiments therefore use a strict correctness threshold of 1.0.Soft correctness otherwise incorporates path length, terminal goal error, and collision penalty, while more permissive thresholds remain supported.
- Learning and difficulty: Dual-MP estimates scenario difficulty from obstacle occupancy, midpoint clearance, planning horizon, goal tolerance, and collision margin, then uses successful System-2 trajectories to train System-1.Neural System-1 is periodically fine-tuned on the original offline data and newly collected System-2 successes.
Experimental Evaluation
Dual-MP is evaluated on six nonlinear reach–avoid benchmark families using paired System-1/System-2 configurations, continual learning, and metrics covering success, runtime, trajectory quality, and solver usage. The results show that verified arbitration improves the success–runtime trade-off when S1 can avoid expensive MPC calls, while gains are limited with cheap fallbacks or difficult route-dependent tasks.
- Evaluation setup: The evaluation uses six nonlinear two-dimensional reach–avoid benchmark families and counts success only when trajectories are both collision-free and goal-reaching.The families stress long-horizon avoidance, dense clutter, constrained passages, route commitment, sustained tracking, and trapping geometries.
- Evaluation setup: Dual-MP variants differ by their System-2 fallback and whether that solver is warm-started from the rejected S1 trajectory.The study compares success rate, mean and 90th-percentile runtime, trajectory quality, and the share of successes produced by S1 versus S2.
- Main results: Dual-MP improves the MPC baseline by filtering easy instances through S1, reducing expensive optimization calls while improving the overall success–runtime trade-off.The largest gains occur in large sparse and dense clutter environments, where S1 frequently solves instances without escalation.
- Main results: Both Dual-MP variants match or improve the success rate of their respective System-2 fallback because verification accepts S1 only after collision and goal checks.S1 can also solve some instances missed by the corresponding fallback solver, particularly in constrained environments.
- Main results: Trajectory quality is the main trade-off: accepted S1 rollouts prioritize fast feasible completion, whereas MPC explicitly optimizes path efficiency and obstacle clearance.Dual-MP may therefore return longer trajectories or trajectories passing closer to obstacles than MPC alone.
- Continual learning: Continual learning improves S1 differently by teacher: CBF demonstrations increase success and direct S1 coverage, while MPC demonstrations mainly improve quality and open-environment success.CBF’s short local corrections are easier for a reactive policy to imitate than MPC’s long-horizon, route-dependent plans.
- Warm-start ablation: Naive warm-starting of MPC from rejected S1 trajectories provides no consistent runtime benefit and can reduce fallback success on the hardest instances.The optimizer may be steered toward the same locally poor region that caused S1 to fail.
- Discussion: The reported results indicate that verified arbitration is most effective when S1 and S2 have complementary strengths and distinct costs.Verification prevents unsafe or incomplete S1 predictions from replacing the fallback, while successful S2 recoveries can be reused for continual learning.
Conclusion
Dual-MP combines a fast neural System-1 policy with a symbolic System-2 fallback, accepting only verified S1 rollouts and reusing successful S2 recoveries for continual learning. With MPC, it achieves the highest success rate while remaining substantially faster than standalone MPC, although naive warm-starting offers no consistent benefit.
- Dual-MP accepts System-1 rollouts only when they are collision-free and goal-reaching; otherwise, it delegates planning to MPC or CBF.
- Successful System-2 recoveries are reused to improve System-1 through continual learning.
- Dual-MP with MPC achieves the highest success rate while remaining substantially faster than standalone MPC.
- Naive warm-starting of MPC from rejected System-1 trajectories provides no consistent benefit.
Computational Resources and Experimental Configuration
The experiments used a 40-core Intel Xeon Gold 6248 CPU server with 125 GiB of memory and Ubuntu 22.04.5 LTS. Training, DAgger collection, and evaluation required several CPU-hours, with configuration details organized in supplementary tables.
- All experiments ran on an Intel Xeon Gold 6248 CPU server with 40 cores, 125 GiB of memory, and Ubuntu 22.04.5 LTS.
- Generating benchmark suites, training System-1 policies, collecting DAgger demonstrations, and evaluating configurations required several CPU-hours.
- Table 6 reports approximate training and DAgger collection time per environment family.
- Tables 7 and 8 summarize model parameters and training, benchmark, and reproducibility hyperparameters.
- The neural System-1 policy used AdamW with a learning rate and weight-decay coefficient of 10−4 / 10−5.
Visualising Trajectory Quality
Trajectory quality is summarized by Q, the geometric mean of path efficiency, smoothness, and obstacle clearance, with higher values indicating better trajectories. Figure 3 compares the corresponding NN, CBF, and MPC trajectories on Bugtrap scenario 6.
- Q is the geometric mean of path efficiency, smoothness, and obstacle-clearance scores.
- Figure 3 compares neural System-1, System-2 CBF, and System-2 MPC trajectories on Bugtrap scenario 6.
- Higher Q indicates a more efficient, smoother, and better-cleared trajectory.
Visualising the Benchmark Families
The evaluation uses six nonlinear two-dimensional obstacle-avoidance families with distinct obstacle layouts and planning challenges. Figure 4 provides a visual index of these benchmark families and an example MPC trajectory.
- The benchmark includes Large Sparse, Dense Clutter, Serial Walls, Maze Branching, Long Slalom, and Bugtrap families.
- The families vary obstacle density, structured barriers, route choices, long alternating corridors, and concave trapping geometry.
- Figure 4 also indexes the trajectory computed by System-2 MPC across the nonlinear environments.
- Figure 4 shows an example map from each benchmark family.