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This work presents an optimal sampling-based method to solve the real-time motion planning problem in static and dynamic environments, exploiting the Rapid-exploring Random Trees (RRT) algorithm and the Model Predictive Path Integral (MPPI) algorithm. The RRT algorithm provides a nominal mean value of the random control distribution in the MPPI algorithm, resulting in satisfactory control performance in static and dynamic environments without a need for fine parameter tuning. We also discuss the importance of choosing the right mean of the MPPI algorithm, which balances exploration and optimality gap, given a fixed sample size. In particular, a sufficiently large mean is required to explore the state space enough, and a sufficiently small mean is required to guarantee that the samples reconstruct the optimal control. The proposed methodology automates the procedure of choosing the right mean by incorporating the RRT algorithm. The simulations demonstrate that the proposed algorithm can solve the motion planning problem for static or dynamic environments. 

Safe control designs for robotic systems remain challenging because of the difficulties of explicitly solving optimal control with nonlinear dynamics perturbed by stochastic noise. However, recent technological advances in computing devices enable online optimization or sampling-based methods to solve control problems. For example, Control Barrier Functions (CBFs) have been proposed to numerically solve convex optimization problems that ensure the control input to stay in the safe set. Model Predictive Path Integral (MPPI) control uses forward sampling of stochastic differential equations to solve optimal control problems online. Both control algorithms are widely used for nonlinear systems because they avoid calculating the derivatives of the nonlinear dynamic functions. In this paper, we use Stochastic Control Barrier Functions (SCBFs) constraints to limit sample regions in the samplingbased algorithm, ensuring safety in a probabilistic sense and improving sample efficiency with a stochastic differential equation. We also show that our algorithm needs fewer samples than the original MPPI algorithm does by providing a sampling complexity analysis. 

We propose a reinforcement learning framework where an agent uses an internal nominal model for stochastic model predictive control (MPC) while compensating for a disturbance. Our work builds on the existing risk-aware optimal control with stochastic differential equations (SDEs) that aims to deal with such disturbance. However, the risk sensitivity and the noise strength of the nominal SDE in the riskaware optimal control are often heuristically chosen. In the proposed framework, the risk-taking policy determines the behavior of the MPC to be risk-seeking (exploration) or riskaverse (exploitation). Specifcally, we employ the risk-aware path integral control that can be implemented as a Monte-Carlo (MC) sampling with fast parallel simulations using a GPU. The MC sampling implementations of the MPC have been successful in robotic applications due to their real-time computation capability. The proposed framework that adapts the noise model and the risk sensitivity outperforms the standard model predictive path integ 

Abstract Advances in deep learning have revolutionized cyber‐physical applications, including the development of autonomous vehicles. However, real‐world collisions involving autonomous control of vehicles have raised significant safety concerns regarding the use of deep neural networks (DNNs) in safety‐critical tasks, particularly perception. The inherent unverifiability of DNNs poses a key challenge in ensuring their safe and reliable operation. In this work, we propose perception simplex ( ), a fault‐tolerant application architecture designed for obstacle detection and collision avoidance. We analyse an existing LiDAR‐based classical obstacle detection algorithm to establish strict bounds on its capabilities and limitations. Such analysis and verification have not been possible for deep learning‐based perception systems yet. By employing verifiable obstacle detection algorithms, identifies obstacle existence detection faults in the output of unverifiable DNN‐based object detectors. When faults with potential collision risks are detected, appropriate corrective actions are initiated. Through extensive analysis and software‐in‐the‐loop simulations, we demonstrate that provides deterministic fault tolerance against obstacle existence detection faults, establishing a robust safety guarantee. 

Perception of obstacles remains a critical safety concern for autonomous vehicles. Real-world collisions have shown that the autonomy faults leading to fatal collisions originate from obstacle existence detection. Open source autonomous driving implementations show a perception pipeline with complex interdependent Deep Neural Networks. These networks are not fully verifiable, making them unsuitable for safety-critical tasks. In this work, we present a safety verification of an existing LiDAR based classical obstacle detection algorithm. We establish strict bounds on the capabilities of this obstacle detection algorithm. Given safety standards, such bounds allow for determining LiDAR sensor properties that would reliably satisfy the standards. Such analysis has as yet been unattainable for neural network based perception systems. We provide a rigorous analysis of the obstacle detection s 

Road condition is an important environmental factor for autonomous vehicle control. A dramatic change in the road condition from the nominal status is a source of uncertainty that can lead to a system failure. Once the vehicle encounters an uncertain environment, such as hitting an ice patch, it is too late to reduce the speed, and the vehicle can lose control. To cope with unforeseen uncertainties in advance, we study a proactive robust adaptive control architecture for autonomous vehicles' lane-keeping control problems. The data center generates a prior environmental uncertainty estimate by combining weather forecasts and measurements from anonymous vehicles through a spatio-temporal filter. The prior estimate contributes to designing a robust heading controller and nominal longitudinal velocity for proactive adaptation to each new condition. The control parameters are updated based on posterior information fusion with on-board measurements.