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Active Interaction-Aware Model Predictive Path Integral via Ego-Conditioned Generative Predictions
Khaled A. Mustafa, Mohamed-Khalil Bouzidi, Christian Schlauch, Ahmad Gazar, Nadja Klein, Joerg Reichardt, Javier Alonso-Mora
TL;DR
Dense-traffic planning must account for the mutual influence between ego actions and surrounding-agent reactions, which conventional predict-then-plan methods decouple. The paper integrates ego-conditioned generative autoregressive prediction with MPPI and uses nested sampling to evaluate interaction-dependent costs and collision risk. Closed-loop simulations report improved safety and efficiency across merging and turning scenarios compared with baseline planners.
Problem
Conventional predict-then-plan methods decouple planning from prediction even though surrounding agents’ future behavior depends on the ego vehicle’s actions.
Method
The framework integrates ego-conditioned generative autoregressive multi-agent prediction with MPPI and evaluates candidate behaviors using a tractable nested sampling scheme.
Results
0% collisions were achieved in the on-ramp merge scenario while maintaining competitive merge efficiency.
Takeaways & Limitations
The formulation lets the planner balance task performance with interaction uncertainty reduction without explicit belief-space representations or dedicated exploration terms.
Abstract
from arXiv · showhide
Dense traffic is inherently interactive. The ego vehicle and surrounding agents continuously influence each other's reactions, making "what-if" reasoning essential for safe and efficient driving. To enable such an active interaction-aware behavior, we propose a planning framework that integrates an ego-conditioned generative autoregressive prediction model within Model Predictive Path Integral (MPPI) control. The generative prediction model outputs stochastic, multi-modal predictions of surrounding agents conditioned on each of the ego's considered future actions. A nested sampling scheme enables tractable evaluation of expected cost and collision risk under the induced distribution. This formulation allows the ego to actively probe how different candidate actions shape the interaction outcomes and to identify actions that reduce ambiguity in uncertain interactions. Closed-loop simulations demonstrate improved safety and efficiency compared to conventional predict-then-plan and passive interaction-aware approaches.
I. INTRODUCTION
Interactive driving couples planning with prediction because surrounding agents react to the ego vehicle’s actions. The paper motivates ego-conditioned generative prediction as a way to support active uncertainty reduction in dense traffic.
- Traditional predict-then-plan methods forecast surrounding-agent trajectories independently of the ego plan, creating a frozen robot problem.
- Human drivers can probe other agents’ hidden intent by taking actions that elicit reactions before committing to maneuvers.Inching forward during a merge can reveal whether nearby vehicles will yield or maintain speed.
- Active uncertainty reduction helps drivers navigate ambiguous interactions without becoming overly aggressive or excessively conservative.
- Ego-conditioned prediction addresses the ego’s influence on surrounding agents but introduces a circular dependency between the plan being executed and the prediction used for planning.
- Related approaches include probabilistic predict-then-plan, joint multi-agent optimization, and ego-conditioned planning, each making different compromises around interaction modeling and tractability.Predict-then-plan ignores ego influence, while game-theoretic methods can become intractable as the number of agents grows.
3) Ego-conditioned interaction-aware planner:
The proposed planner combines MPPI with learned ego-conditioned generative prediction so candidate ego behaviors induce corresponding multi-agent hypotheses. This supports interaction-aware, uncertainty-aware planning while retaining tractable sampling-based control.
- Ego-conditioned interaction-aware planner:: The framework closes the loop between prediction and planning by conditioning multi-agent forecasts on sampled ego behaviors.
- Ego-conditioned interaction-aware planner:: A tractable sampling scheme evaluates multi-modal ego-conditioned predictions and estimates collision risk for planning.
- Ego-conditioned interaction-aware planner:: MPPI weighting enables active uncertainty reduction without explicit belief-space representations or dedicated exploration terms.
- Ego-conditioned interaction-aware planner:: The planner represents ego state, control, and surrounding-agent state separately, with deterministic ego evolution and stochastic learned-agent evolution over a finite horizon.
- Ego-conditioned interaction-aware planner:: MPPI samples diverse candidate ego trajectories, and the generative predictor updates surrounding-agent rollouts in response to each hypothesized plan.
A. Model Predictive Path Integral Control
MPPI solves finite-horizon stochastic control by sampling perturbed control sequences, evaluating their trajectory costs, and updating a nominal sequence through exponential importance weighting.
- MPPI samples M random control sequences around a nominal sequence over a horizon T.
- Each perturbed control sequence is rolled out through deterministic ego dynamics to obtain a state trajectory and total cost.
- The optimal control sequence is approximated using an exponential importance-sampling update based on the sampled costs.
- The inverse temperature β controls selective pressure over samples, while subtracting the minimum cost improves numerical stability and η normalizes the weights.
- Following receding-horizon control, only the first optimal input is applied before the procedure repeats with a time-shifted warm start.
IV. METHODOLOGY
The framework models surrounding-agent behavior as stochastic and explicitly conditioned on candidate ego trajectories. Embedded in MPPI, this produces an active objective that jointly accounts for task cost and uncertainty reduction.
- The generative autoregressive prediction model conditions joint surrounding-agent trajectories on the ego trajectory and observed traffic context.The model represents future behavior through an ego-conditioned predictive distribution rather than a deterministic forecast.
- Surrounding-agent futures are modeled stochastically because latent objectives, interaction effects, and unobserved internal states prevent deterministic prediction.
- The autoregressive model uses traffic topology, guidance, current surrounding-agent state, and historical observations as prediction context.The context includes observations over the past H time steps for all agents.
- The planning objective takes an expectation over MPPI-sampled ego trajectories and the corresponding ego-conditioned predictions of surrounding agents.Ego states are determined by sampled controls and ego dynamics, coupling the outer rollout distribution to the inner predictive distribution.
- Different ego trajectories induce different predictive distributions, so minimizing expected cost implicitly balances task objectives against active uncertainty reduction.
B. Sampling-Based Approximation
Because the ego-conditioned objective is high-dimensional and circular, the framework approximates it with nested sampling over ego trajectories and surrounding-agent behavior.
- Nested sampling makes the intractable objective tractable by approximating the outer ego-trajectory expectation with M MPPI rollouts.
1) Ego-Conditioned Autoregressive Sampling:
For each sampled ego trajectory, the method generates multiple stochastic, autoregressive behavior hypotheses while preserving dominant multi-modal outcomes efficiently.
- Ego-Conditioned Autoregressive Sampling:: For each MPPI ego trajectory, the method generates B stochastic surrounding-agent behavior rollouts from the ego-conditioned predictive distribution.A downsized SMART variant is used to generate these behavior rollouts.
- Ego-Conditioned Autoregressive Sampling:: The autoregressive transformer decodes each agent’s next token in parallel using the joint previous prediction step as shared context.Inter-agent influence is represented through conditioning on past joint prediction steps.
- Ego-Conditioned Autoregressive Sampling:: The joint distribution remains coupled across agents through shared context and stepwise rollout updates, despite factorizing the one-step distribution over agents.
- Ego-Conditioned Autoregressive Sampling:: Top-K sampling retains dominant behavioral modes while reducing the computational burden of exhaustive Monte Carlo sampling.
- Ego-Conditioned Autoregressive Sampling:: Per-agent rollout likelihoods are computed recursively to quantify the plausibility of each sampled hypothesis under the learned model.
2) Gaussian Mixture Surrogate Distribution:
The method converts stochastic ego-conditioned agent samples into a weighted Gaussian-mixture surrogate, enabling tractable expected-cost and collision-risk evaluation within MPPI. The surrogate also represents evolving multimodal uncertainty and can favor trajectories that reduce interaction ambiguity.
- Gaussian Mixture Surrogate Distribution: The surrogate models each sampled agent position as a Gaussian component whose mixing weight is determined by the autoregressive rollout likelihood.This converts discrete stochastic predictions into a smooth continuous density while retaining multimodal behavior.
- Gaussian Mixture Surrogate Distribution: A fixed isotropic covariance Σ = σ2I regularizes uncertainty around each sampled rollout because the generator provides discrete coordinates rather than variance bounds.The variance σ2 is treated as a hyperparameter.
- Gaussian Mixture Surrogate Distribution: The surrogate is rebuilt at each timestep so new ego-conditioned information can shift both predicted locations and relative mode weights.Per-agent weighting follows the factorized formulation, while the joint context remains updated autoregressively across agents.
- MPPI Evaluation: Nested sampling evaluates expected cost by averaging MPPI ego rollouts and marginalizing stochastic agent hypotheses using mixture weights.For each of M ego rollouts, B agent behavior samples approximate the inner predictive expectation.
- MPPI Evaluation: The collision-risk approximation integrates the surrogate density over inflated ego-agent collision regions and combines agent risks under a timestep-wise independence assumption.The inflated ego footprint is represented through a Minkowski sum, and circular approximations make Gaussian-component integration tractable.
- MPPI Evaluation: The stage cost combines ego tracking and speed terms with stochastic risk penalties, while MPPI converts rollout costs into importance weights and an updated control sequence.The risk term includes a continuous lower-risk bias and a hard penalty when collision probability exceeds threshold δ.
- MPPI Evaluation: Ego behaviors that disambiguate intent tend to concentrate mixture weights on fewer hypotheses, reducing estimated risk and implicitly incentivizing uncertainty reduction.To reduce predictor-conditioning cost, similar sampled control sequences may share predictions after k-means clustering, assuming behavior varies slowly across similar trajectories.
V. RESULTS
The evaluation uses nuPlan interactive urban-driving scenarios with varied agent cooperativeness and compares the proposed method against four shared-backbone baselines. Qualitative results show successful active merging, while baselines remain conservative or miss feasible opportunities; the proposed method also achieves the highest merge success rate and reduced merge time.
- Evaluation Setup: The evaluation covers three interaction-critical nuPlan scenario types, with 20 runs per scenario and cooperativeness varied from cooperative to non-cooperative.Agent behavior is varied using the MR-IDM model.
- Baselines: All four baselines use the same SMART-based backbone to isolate planning-design effects and avoid architectural confounds.Baselines 1–3 represent prior paradigms, while Baseline 4 is a pure ablation.
- Lane Merging: In qualitative lane merging, the proposed method completes the merge by actively eliciting neighboring-vehicle responses, whereas baselines remain conservative or fail to find a feasible opportunity.The comparison is shown in the nuPlan simulation environment.
- Intent Prediction: Figure 3 compares intent probabilities for cooperative and non-cooperative cases with GARPM variants with and without ego-conditioning.Only the ego-conditioned predictor feeds the proposed framework, and the caption reports faster ambiguity resolution.
- Active Probing: Figure 4 contrasts probing and non-probing MPPI rollouts: assertive probing elicits yielding and concentrates cooperative intent, while passive behavior leaves predictions more ambiguous.The comparison concerns an adjacent-lane merge.
A. Scenario 1: Merging in Adjacent Lane
In adjacent-lane merging, the ego vehicle must infer whether nearby vehicles will yield or maintain speed. The proposed approach actively elicits responses to identify feasible merge opportunities, unlike baselines that are overly conservative or fail to recognize them.
- The ego vehicle must infer whether nearby vehicles will yield or maintain speed before committing to an adjacent-lane merge.
- The proposed approach completes the merge by actively probing neighboring vehicles and inferring their cooperativeness.
- Baselines either remain overly conservative or fail to identify a feasible merge opportunity.
B. Scenario 2: On-Ramp Merge
For an on-ramp merge with an approaching vehicle, the proposed method infers non-cooperation and delays merging until the lane is safe. It achieves zero collisions while retaining competitive merge efficiency, whereas other ego-conditioned baselines can be optimistic or overly conservative.
- The ego vehicle must infer whether an approaching vehicle will yield or maintain speed before committing to the on-ramp merge.
- The proposed method correctly infers non-cooperation and delays merging until the lane is safe.
- 0% collision rate is achieved by the proposed method while maintaining competitive merge efficiency.Table III reports on-ramp merging results over 20 runs; CR denotes collision rate.
- Ego-conditioned Baselines 2, 3, and 4 frequently collide at 15-25% because overly optimistic predictions underestimate joint collision risk.
- Baseline 1 overestimates risk and behaves conservatively but still fails to reliably anticipate interaction outcomes.
C. Scenario 3: Unprotected Left Turn
In an unprotected left turn across dense oncoming traffic, the proposed approach infers oncoming-vehicle cooperativeness and executes the maneuver efficiently. It achieves the lowest collision and deadlock rates among the evaluated methods.
- The ego vehicle must infer whether oncoming vehicles will maintain speed or yield before committing to an unprotected left turn.
- The proposed approach achieves the lowest collision and deadlock rates among all methods.Table IV reports unprotected-left-turn results over 20 runs; DL stands for deadlocks.
- The proposed approach infers cooperative behavior through probing interactions and executes the left turn efficiently.
- Baseline 2 fails to resolve interaction uncertainty and produces deadlock situations.
- Baseline 3 waits for the approaching vehicle to pass, reflecting an overly conservative strategy.