DRCC-LPVMPC: Robust Data-Driven Control for Autonomous Driving and Obstacle Avoidance

Safety in autonomous driving, particularly obstacle avoidance, is critical, and while traditional Model Predictive Control (MPC) methods face issues with discrepancies between simplified vehicle models and real-world behavior under uncertainty, this framework proposes a novel solution. The proposed DRCC-LPVMPC framework addresses these challenges by explicitly accounting for model mismatches and additive disturbances through a data-driven distributionally robust chance-constrained approach, achieving real-time performance via quadratic programming.

The gist: This paper introduces a distributionally robust chance-constrained linear parameter-varying MPC (DRCC-LPVMPC) framework that explicitly accounts for discrepancies between simplified linearized models and real vehicle dynamics, as well as additive disturbances from sensors and localization, by constructing chance constraints from finite sampled data and employing a Wasserstein ambiguity set.

Model Representation

The paper utilizes a quasi-linear parametervarying (quasi-LPV) form to represent the single-track vehicle dynamics derived from a simplified STM. This approach linearizes the dynamics using a scheduling parameter vector, denoted as the scheduling parameter vector, which is defined as a function of selected system states and inputs. The state transition is formulated as:

zk+1 = A(pk)zk + B(pk)uk,

where A(pk) = I6 + Aˆ(pk)∆t and B(pk) = Bˆ(pk)∆t are the discrete-time quasi-LPV system matrices. The paper notes that the scheduling parameter vector cannot be directly accessible because it contains the steering input δk, so it is approximated using the previously optimized solution: p ik ≈ p⋆ i-1k+1.

Uncertainty Modeling and Disturbance Capture

The framework explicitly accounts for two primary sources of uncertainty: model discrepancies and additive disturbances.

Model Discrepancy:

1. The quasi-LPV model introduces the first source of discrepancy by using a linear cornering-stiffness approximation in Eq. (1), which differs from the nonlinear STM dynamics governed by Eq. (2).

2. The scheduling parameter vector is approximated, introducing additional approximation error.

3. The true vehicle dynamics are further complicated by a full four-wheel model or other real-world complexities not captured by the quasi-LPV representation.

Additive Disturbances:

1. These include localization inaccuracies, sensor noise, and other measurement errors.

2. These discrepancies manifest as a state disturbance denoted at time step k as ξk = [ξxk, ξyk, ξψk, ξvxk, ξvyk, ξωk]⊤ ∈ R6×1.

3. The true distribution of the uncertainty is unknown; therefore, a data-driven strategy is adopted where discrepancies between measured sensor states and quasi-LPV predictions are used to generate empirical disturbance samples that form ambiguity sets for the DRCC formulation.

Chance Constraint Formulation (DRCC)

The core innovation lies in reformulating hard constraints into chance constraints using a distributionally robust approach.

Initial Reformulation:

1. The original LPVMPC constraint, d i k DkLNX - c i k ≥ 0, is modified to include the disturbance term: d i k DkLNX + d i k DkHN ηN − c i k ≥ 0, where η˜N represents the unknown distribution of the uncertainty.

2. The DRCC requires that constraints hold with probability at least 1 − ϵ for all distributions P within the ambiguity set P, formally expressed as: inf P∈P P(dkDkLNX − ck ≥ w˜ k, ∀k ∈ [N]) ≥ 1 - ϵ.

3. This infinite-dimensional constraint is reformulated using a CVaR representation, which converts it into a finite-dimensional convex constraint: sup P∈P P(dkDkLNX − ck < w˜ k, ∃k ∈ [N]) ≤ ϵ.

Tractability and Solution via Mixed-Integer Programming

To solve the resulting infinite-dimensional problem efficiently, the paper employs a mixed-integer reformulation based on sampled data.

Data-Driven Reformulation:

1. The CVaR constraint is converted into a finite set of constraints using a total of J samples drawn from the true distribution P∞, leading to Eq. (22).

2. Theorem 1 establishes that the DRCC problem is equivalent to: min λkσ − ϵ ≤ 1/N X j∈[J] min(f(X, wˆ j) − γk, 0), where f(X, wˆ j) is a function derived from the empirical samples.

Based on the provided research paper, here are specific improvements for an existing AI system (such as an autonomous vehicle control system or a robotics navigation stack) by implementing the DRCC-LPVMPC framework:

The proposed framework, DRCC-LPVMPC (Distributionally Robust Chance-Constrained Linear Parameter-Varying Model Predictive Control), significantly enhances the safety and reliability of AI systems operating in uncertain, dynamic environments. Here are the specific improvements and capabilities it enables:

1. Aims for Safety Beyond Traditional Constraints:

Safety is improved by moving from deterministic constraints (which fail when model or sensor errors occur) to probabilistic safety guarantees enforced through a Distributionally Robust framework.

2. Explicitly Accounts for Model Discrepancies:

The system explicitly models and compensates for the gap between simplified vehicle dynamics (quasi-LPV/STM) and real-world behavior by treating these discrepancies as additive, unknown distribution uncertainties. This prevents control failure when the actual vehicle dynamics deviate from the linear approximation used in standard LPVMPC.

3. Handles Sensor Noise and Localization Errors Robustly:

The framework integrates additive disturbances (sensor noise, localization inaccuracies) directly into the chance constraints using data-driven ambiguity sets (Wasserstein ambiguity set). This makes the control system resilient to real-world measurement errors, which are a primary cause of collisions in current systems.

4. Enables Real-Time Operation on Resource-Constrained Hardware:

By reformulating the complex DRCC problem into a tractable Quadratic Programming (QP) problem, the system achieves real-time performance. This allows for fast decision-making critical for high-speed autonomous driving and dynamic obstacle avoidance, even when running on embedded hardware like NVIDIA Jetson AGX Orin.

5. Provides Superior Obstacle Clearance and Maneuverability:

Compared to conventional LPVMPC or NMPC, DRCC-LPVMPC demonstrates superior safety margins. It can execute maneuvers that result in significantly larger obstacle clearances and more reliable tracking, especially when operating under significant uncertainty (e.g., during aggressive racing or complex obstacle avoidance).

6. Improves Computational Efficiency for Complex Scenarios:

By using a quasi-LPV formulation instead of full nonlinear MPC (NMPC), the system maintains high computational efficiency while still capturing essential time-varying dynamics, making it feasible for real-time applications where high computational load is prohibitive.

This improved AI system (DRCC-LPVMPC) can perform the following specific actions:

1. Navigate and drive autonomously on complex tracks with a proven ability to avoid dynamic obstacles (vehicles, pedestrians) that are not perfectly modeled.

2. Execute aggressive maneuvers in obstacle avoidance scenarios where sensor noise or model inaccuracies are expected, maintaining a higher probability of collision avoidance than traditional controllers.

3. Maintain accurate path tracking while simultaneously ensuring the vehicle stays within defined safety corridors during high-speed operations on unpredictable surfaces or under adverse weather conditions (as tested in CARLA and real-world experiments).

4. Operate reliably in environments where the underlying physical model is imperfect (e.g., a bicycle model approximating a four-wheel vehicle), by using empirical data from the system's own operation to define its uncertainty bounds.

5. Provide robust control during emergency situations where unexpected disturbances occur, ensuring that the vehicle does not enter an infeasible region or collide with obstacles, even when facing significant modeling errors or sensor inaccuracies.