In this article, we propose GPU-Accelerated TRajectory Optimization (GATRO), a framework that casts trajectory optimization as a simplified Semidefinite Programming (SDP) problem and employs a custom parallelized differentiable solver for GPU acceleration. We primarily demonstrate GATRO on tractor-trailer trajectory planning, as it represents one of the most challenging scenarios in autonomous vehicle motion planning due to its non-holonomic kinematics and complex constraints. The trajectory optimization is reformulated as a simplified SDP by leveraging differential flatness for non-holonomic kinematics elimination, approximating constraints (e.g., physical constraints and collision avoidance constraints) as convex polytopes, and coupling piecewise polynomial parameterization with the Markov-Luk´acs theorem. Exploiting the fact that the SDP problem consists of many Positive Semidefinite (PSD) matrices, we develop a parallelized Primal-Dual Hybrid Gradient (PDHG) solver to expedite the solving process. Moreover, by differentiating the Lagrangian of the SDP problem, our solver derives the analytical gradient of the optimal objective with respect to temporal parameters, which is used to further optimize the spatiotemporal trajectory. Numerical simulations show that GATRO outperforms existing trajectory optimization methods in computational time while preserving non-holonomic kinematics and satisfying all constraints. Our PDHG solver demonstrates superior performance compared to state-of-the-art commercial and open-source SDP solvers, particularly for large-scale problems. The approach is validated on a full-scale operational autonomous tractor-trailer.

For fully automated heavy-duty truck platoons, the uncertain behavior of surrounding traffic participants makes platooning control and stability extremely complex. This may lead to a deterioration in fuel efficiency and could even result in collisions. To mitigate the impact of traffic participants’ uncertainty and enhance fuel economy, this paper proposes an energy-efficient speed planning method for automated truck platoons considering uncertainty-aware trajectory prediction. In trajectory prediction uncertainty modeling, perceptual uncertainty is incorporated into the loss function of the prediction module to reduce overconfidence in long-horizon predictions. To generate accurate long-horizon platoon speed trajectories that better align with vehicle dynamic characteristics, vehicle response delays are identified and and integrated into the planning process. With varying levels of prediction uncertainty and response delays, the platoon speed planning method adapts more safely and proactively to multi-vehicle interaction scenarios. Experimental results from two representative traffic flow conditions demonstrate that the proposed method effectively enhances both safety and energy efficiency in complex traffic conditions, particularly in cut-in events.

In this paper, we propose a differential-flatness-based controller (DFBC) for precise trajectory tracking of tractor-trailers, particularly during reversing maneuvers, which are challenging due to unstable equilibrium points. The proposed controller leverages the differential flatness property of tractor-trailers, equivalently transforming the nonlinear kinematics into a brunovsky canonical form, allowing the application of linear control theory for control design. Compared to traditional linear quadratic regulator (LQR) controllers, the proposed DFBC method achieves higher precision and robustness in reversing maneuvers. We also showcase the performance of the proposed DFBC method through physical experiments conducted on our self-developed 1/10 scale autonomous tractor-trailer.

Deep reinforcement learning (RL) is a powerful approach for solving optimal control problems. However, RL-trained policies often suffer from the action fluctuation problem, where the consecutive actions significantly differ despite only slight state variations. This problem results in mechanical components' wear and tear and poses safety hazards. The action fluctuation is caused by the high Lipschitz constant of actor networks. To address this problem, we propose a neural network named LipsNet. We propose the Multi-dimensional Gradient Normalization (MGN) method, to constrain the Lipschitz constant of networks with multi-dimensional input and output. Benefiting from MGN, LipsNet achieves Lipschitz continuity, allowing smooth actions while preserving control performance by adjusting Lipschitz constant. LipsNet addresses the action fluctuation problem at network level rather than algorithm level, which can serve as actor networks in most RL algorithms, making it more flexible and user-friendly than previous works. Experiments demonstrate that LipsNet has good landscape smoothness and noise robustness, resulting in significantly smoother action compared to the Multilayer Perceptron.

Model-based policy gradient (MBPG) has been employed to seek an approximate solution to the optimal control problem. However, there is coupling between adjacent states due to temporal dependencies, making the training time grow linearly with the time horizon. This paper reshapes the training process of MBPG with the time-splitting technique to establish a time-independent algorithm called Training Through Time-Splitting (T3S). First, copy the coupled variables to obtain two independent variables. Meanwhile, an extra variable together with an equivalence constraint is introduced for problem consistency. Then, the transformed problem divides into subproblems with carefully derived loss functions. Subproblems own decoupled variables and shared policy networks, which means they can be optimized concurrently. Guided by the algorithm design, this paper further proposes an asynchronous parallel training scheme to accelerate training efficiency. Numerical simulation shows that the T3S algorithm outperforms the MBPG algorithm by 83.6% in wall-clock time with a trajectory tracking task.

We propose a robust object tracking algorithm for distance keeping. Taking advantage of a context-based region of interest, we are able to maximize the performance of each sensor, and reduce the computation time since we only focus on the targets inside the region. Tracking targets in road coordinates enables finding the distance-keeping target on any curved road, while a commercial Adaptive Cruise Control (ACC) system works best on straight roads. We demonstrate that the overall performance of the proposed algorithm is better than that of a commercial ACC system. The distance-keeping target can either be used for lane following for a standalone ACC system or an autonomous vehicle. Our object tracking algorithm can also be extended to find the target of interest for lane changing or ramp merging for an autonomous vehicle.

We present a motion planning framework for autonomous on-road driving considering both the uncertainty caused by an autonomous vehicle and other traffic participants. The future motion of traffic participants is predicted using a local planner, and the uncertainty along the predicted trajectory is computed based on Gaussian propagation. For the autonomous vehicle, the uncertainty from localization and control is estimated based on a Linear-Quadratic Gaussian (LQG) framework. Compared with other safety assessment methods, our framework allows the planner to avoid unsafe situations more efficiently, thanks to the direct uncertainty information feedback to the planner. We also demonstrate our planner's ability to generate safer trajectories compared to planning only with a LQG framework.

In this paper, we propose a novel planning framework that can greatly improve the level of intelligence and driving quality of autonomous vehicles. A reference planning layer first generates kinematically and dynamically feasible paths assuming no obstacles on the road, then a behavioral planning layer takes static and dynamic obstacles into account. Instead of directly commanding a desired trajectory, it searches for the best directives for the controller, such as lateral bias and distance keeping aggressiveness. It also considers the social cooperation between the autonomous vehicle and surrounding cars. Based on experimental results from both simulation and a real autonomous vehicle platform, the proposed behavioral planning architecture improves the driving quality considerably, with a 90.3% reduction of required computation time in representative scenarios.

“Socially cooperative driving” is an integral part of our everyday driving, hence requiring special attention to imbue the autonomous driving with a more natural driving behavior. In this paper, an intention-integrated Prediction- and Cost function-Based algorithm (iPCB) framework is proposed to enable an autonomous vehicle to perform cooperative social behavior. An intention estimator is developed to extract the probability of surrounding agents' intentions in real time. Then for each candidate strategy, a prediction engine considering the interaction between host and surrounding agents is used to predict future scenarios. A cost function-based evaluation is applied to compute the cost for each scenario and select the decision corresponding to the lowest cost. The algorithm was tested in simulation on an autonomous vehicle cooperating with vehicles merging from freeway entrance ramps with 10,000 randomly generated scenarios. Compared with approaches that do not take social behavior into account, the iPCB algorithm shows a 41.7% performance improvement based on the chosen cost functions.

We present an autonomous driving research vehicle with minimal appearance modifications that is capable of a wide range of autonomous and intelligent behaviors, including smooth and comfortable trajectory generation and following; lane keeping and lane changing; intersection handling with or without V2I and V2V; and pedestrian, bicyclist, and workzone detection. Safety and reliability features include a fault-tolerant computing system; smooth and intuitive autonomous-manual switching; and the ability to fully disengage and power down the drive-by-wire and computing system upon E-stop. The vehicle has been tested extensively on both a closed test field and public roads.

In this paper, an efficient real-time autonomous driving motion planner with trajectory optimization is proposed. The planner first discretizes the plan space and searches for the best trajectory based on a set of cost functions. Then an iterative optimization is applied to both the path and speed of the resultant trajectory. The post-optimization is of low computational complexity and is able to converge to a higher-quality solution within a few iterations. Compared with the planner without optimization, this framework can reduce the planning time by 52% and improve the trajectory quality. The proposed motion planner is implemented and tested both in simulation and on a real autonomous vehicle in three different scenarios. Experiments show that the planner outputs high-quality trajectories and performs intelligent driving behaviors.

In this paper, a point-based Markov Decision Process (QMDP) algorithm is used for robust single-lane autonomous driving behavior control under uncertainties. Autonomous vehicle decision making is modeled as a Markov Decision Process (MDP), then extended to a QMDP framework. Based on MDP/QMDP, three kinds of uncertainties are taken into account: sensor noise, perception constraints and surrounding vehicles' behavior. In simulation, the QMDP-based reasoning framework makes the autonomous vehicle perform with differing levels of conservativeness corresponding to different perception confidence levels. Road tests also indicate that the proposed algorithm helps the vehicle in avoiding potentially unsafe situations under these uncertainties. In general, the results indicate that the proposed QMDP-based algorithm makes autonomous driving more robust to limited sensing ability and occasional sensor failures.

In this paper, a prediction- and cost function-based algorithm (PCB) is proposed to implement robust freeway driving in autonomous vehicles. A prediction engine is built to predict the future microscopic traffic scenarios. With the help of a human-understandable and representative cost function library, the predicted traffic scenarios are evaluated and the best control strategy is selected based on the lowest cost. The prediction- and cost function-based algorithm is verified using the simulator of the autonomous vehicle Boss from the DARPA Urban Challenge 2007. The results of both case tests and statistical tests using PCB show enhanced performance of the autonomous vehicle in performing distance keeping, lane selecting and merging on freeways.

This paper proposes a multi-level collaborative driving framework (MCDF) for human-autonomous vehicle interaction. There are three components in MCDF; the mission-behavior-motion block diagram, the functionality-module relationship and the human participation level table. Through integration of the three components, a human driver can cooperate with the vehicle's intelligence to achieve better driving performance, robustness and safety. The MCDF is successfully implemented in TROCS, a real-time autonomous vehicle control system developed by the Tartan Racing Team for the 2007 DARPA Urban Challenge. The performance of MCDF is analyzed and a preliminary test in TROCS simulation mode shows that MCDF is effective in improving the driving performance.