<aside> 💡 Official project page of the paper Addressing Behavior Model Inaccuracies for Safe Motion Control in Uncertain Dynamic Environments, Minjun Sung, Hunmin Kim, and Naira Hovakimyan, Submitted to RA-L. [arXiv]

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If you find our work useful in your research please consider citing our paper:

@inproceedings{sung2024Robust,
    title     = {Addressing Behavior Model Inaccuracies for Safe Motion Control in Uncertain Dynamic Environments},
    author    = {Minjun Sung and Hunmin Kim and Naira Hovakimyan},
    booktitle = {arxiv},
    year      = {2024}
}

Abstract

Uncertainties in the environment and behavior model inaccuracies compromise the state estimation of a dynamic obstacle and its trajectory predictions, introducing biases in estimation and shifts in predictive distributions. Addressing these challenges is crucial to safely control an autonomous system. In this paper, we propose a novel algorithm SIED-MPC, which synergistically integrates Simultaneous State and Input Estimation (SSIE) and Distributionally Robust Model Predictive Control (DR-MPC) using model confidence evaluation. The SSIE process produces unbiased state estimates and optimal input gap estimates to assess the confidence of the behavior model, defining the ambiguity radius for DR-MPC to handle predictive distribution shifts. This systematic confidence evaluation leads to producing safe inputs with an adequate level of conservatism. Our algorithm demonstrated a reduced collision rate in autonomous driving simulations through improved state estimation, with a 54% shorter average computation time.

<aside> 💡 Small bias in estimation and behavior model inaccuracies lead to large shifts in obstacle trajectory’s predictive distribution. Our work addresses these correlated challenges in a integrated manner.

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Videos

• Vanilla MPC :

  • Does not employ obstacle motion forecasts
  • Fails to safely avoid the obstacle

  out.mp4

• DR MPC + EKF

  • Safety margin is large, but it makes the MPC infeasible or too conservative

  • Over-conservative ⬇️

    out.mp4

  • Infeasible ⬇️

    DR-Kalman.mp4

• Mean MPC

  • Only forecasts the obstacle mean positions without taking its (co)variance
  • Safety margin is small → collision.

  out.mp4

• SIED-MPC (Ours)

  • Safety is assured while the MPC is solved with flexibility
  • The ambiguity radius is controlled according to the model confidence

out.mp4

SSIE

<aside> 💡 Kalman filters and its variants can be used as an optimal filter when the input to the system is specified. Hence, it cannot be directly used to estimate the accurate obstacle state, unless its input or a behavior model is accurately specified. One may have an approximate behavior model , however, its bias makes implementing EKF/KF inadequate, because these filters require the uncertainties to be zero-mean Gaussian. Furthermore, the input gap can be amplified in predicting the obstacle trajectories.

The SSIE algorithm is a systematic approach to first estimate the input gap to unbias the resulting state estimation.

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• Estimation Performance

DR-MPC

<aside> 💡 The obstacle trajectory prediction relies on accurate estimation and behavior model. While the SSIE algorithm removes the bias in the expected sense, each estimation may involve some inaccuracies. On top of the this, repeated incorporation of predicted control inputs from the behavior model in each prediction step compounds inaccuracies in the state prediction distribution. To address this, we solve a Distributionally Robust Optimization(DRO) problem at each time step. The extent of conservatism in the DRO formulation is characterized by the input gap estimation from the SSIE module.

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