Vehicle safety depends on (a) the range of identified hazards and (b) the operational situations for which mitigations of these hazards are acceptably decreasing risk. Moreover, with an increasing degree of autonomy, risk ownership is likely to increase for vendors towards regulatory certification. Hence, highly automated vehicles have to be equipped with verified controllers capable of reliably identifying and mitigating hazards in all possible operational situations. To this end, available methods for the design and verification of automated vehicle controllers have to be supported by models for hazard analysis and mitigation.
Jha and Raman @cite_10 discuss the synthesis of vehicle trajectories from probabilistic temporal logic assertions. Synthesized trajectories take into account perception uncertainty through approximation of sensed obstacles by combining Gaussian polytopes. In a similar context, Rizaldi and Althoff @cite_6 formalize safe driving policies to derive safe control strategies implementing worst-case braking scenarios in autonomous driving. They apply a hybrid-trace-based formalization of physics required for model checking of recorded @cite_6 and planned @cite_3 strategies. @cite_10 @cite_6 @cite_3 discuss low-level control for a specific class of driving scenarios, whereas our approach provides for (i) the investigation and combination of many related operational situations, thus, forming a more comprehensive perspective of driving safety, (ii) regarding various kinds of hazards that might play a role in high- and low-level control beyond safe and optimal trajectory planning and collision avoidance.
@cite_3 @cite_10 @cite_6
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Autonomous vehicles need to plan trajectories to a specified goal that avoid obstacles. Previous approaches that used a constrained optimization approach to solve for finite sequences of optimal control inputs have been highly effective. For robust execution, it is essential to take into account the inherent uncertainty in the problem, which arises due to uncertain localization, modeling errors, and disturbances. Prior work has handled the case of deterministically bounded uncertainty. We present here an alternative approach that uses a probabilistic representation of uncertainty, and plans the future probabilistic distribution of the vehicle state so that the probability of collision with obstacles is below a specified threshold. This approach has two main advantages; first, uncertainty is often modeled more naturally using a probabilistic representation (for example in the case of uncertain localization); second, by specifying the probability of successful execution, the desired level of conservatism in the plan can be specified in a meaningful manner. The key idea behind the approach is that the probabilistic obstacle avoidance problem can be expressed as a disjunctive linear program using linear chance constraints. The resulting disjunctive linear program has the same complexity as that corresponding to the deterministic path planning problem with no representation of uncertainty. Hence the resulting problem can be solved using existing, efficient techniques, such that planning with uncertainty requires minimal additional computation. Finally, we present an empirical validation of the new method with a number of aircraft obstacle avoidance scenarios. The automation of driving tasks is of increasing interest for highway traffic management. The emerging technologies of global positioning and intervehicular wireless communications, combined with in-vehicle computation and sensing capabilities, can potentially provide remarkable improvements in safety and efficiency. We address the problem of designing intelligent in-tersections, where traffic lights and stop signs are removed, and cars negotiate the intersection through an interaction of centralized and distributed decision making. Intelligent intersections are representative of complex hybrid systems that are increasingly of interest, where the challenge is to design tractable distributed algorithms that guarantee safety and provide good performance. Systems of automatically driven vehicles will need an under lying collision avoidance system with provable safety properties to be acceptable. This condition raises several challenges. We need to ensure perpetual collision avoidance so that cars do not get into future problematic positions to avoid an immediate collision. The architecture needs to allow distributed freedom of action to cars yet should guard against worst-case behavior of other cars to guarantee collision avoidance. The algorithms should be tractable both computationally and in information requirements and robust to uncertainties in sensing and communication. To address these challenges, we propose a hybrid architecture with an appropriate interplay between centralized coordination and distributed freedom of action. The approach is built around a core where each car has an infinite horizon contingency plan, which is updated at each sampling instant and distributed by the cars, in a computationally tractable manner. We also define a dynamically changing partial-order relation between cars, which specifies, for each car, a set of cars whose worst-case behaviors it should guard against. The architecture is hybrid, involving a centralized component that coordinates intersection traversals. We prove the safety and liveness of the overall scheme. The mathematical challenge of accurately quantifying performance remains as a difficult challenge; therefore, we conduct a simulation study that shows the benefits over stop signs and traffic lights. It is hoped that our effort can provide methodologies for the design of tractable solutions for complex distributed systems that require safety and liveness guarantees. High-end vehicles are already equipped with safety systems, such as assistive braking and automatic lane following, enhancing vehicle safety. Yet, these current solutions can only help in low-complexity driving situations. In this paper, we introduce a parallel autonomy , or shared control, framework that computes safe trajectories for an automated vehicle, based on human inputs. We minimize the deviation from the human inputs while ensuring safety via a set of collision avoidance constraints. Our method achieves safe motion even in complex driving scenarios, such as those commonly encountered in an urban setting. We introduce a receding horizon planner formulated as nonlinear model predictive control (NMPC), which includes the analytic descriptions of road boundaries and the configuration and future uncertainties of other road participants. The NMPC operates over both steering and acceleration simultaneously. We introduce a nonslip model suitable for handling complex environments with dynamic obstacles, and a nonlinear combined slip vehicle model including normal load transfer capable of handling static environments. We validate the proposed approach in two complex driving scenarios. First, in an urban environment that includes a left-turn across traffic and passing on a busy street. And second, under snow conditions on a race track with sharp turns and under complex dynamic constraints. We evaluate the performance of the method with various human driving styles. We consequently observe that the method successfully avoids collisions and generates motions with minimal intervention for parallel autonomy. We note that the method can also be applied to generate safe motion for fully autonomous vehicles. This paper presents a generic approach for tactical decision-making under uncertainty in the context of driving. The complexity of this task mainly stems from the fact that rational decision-making in this context must consider several sources of uncertainty: The temporal evolution of situations cannot be predicted without uncertainty because other road users behave stochastically and their goals and plans cannot be measured. Even more important, road users are only able to perceive a tiny part of the current situation with their sensors because measurements are noisy and most of the environment is occluded. In order to anticipate the consequences of decisions a probabilistic approach, considering both forms of uncertainty, is necessary. The authors address this by formulating the task of driving as a continuous Partially Observable Markov Decision Process (POMDP) that can be automatically optimized for different scenarios. As driving is a continuous-space problem, the belief space is infinite-dimensional. The authors do not use a symbolic representation or discretize the state space a priori because there is no representation of the state space that is optimal for every situation. Instead, they employ a continuous POMDP solver that learns a good representation of the specific situation. Automated driving requires decision making in dynamic and uncertain environments. The uncertainty from the prediction originates from the noisy sensor data and from the fact that the intention of human drivers cannot be directly measured. This problem is formulated as a partially observable Markov decision process (POMDP) with the intended route of the other vehicles as hidden variables. The solution of the POMDP is a policy determining the optimal acceleration of the ego vehicle along a preplanned path. Therefore, the policy is optimized for the most likely future scenarios resulting from an interactive, probabilistic motion model for the other vehicles. Considering possible future measurements of the surrounding cars allows the autonomous car to incorporate the estimated change in future prediction accuracy in the optimal policy. A compact representation results in a low-dimensional state-space. Thus, the problem can be solved online for varying road layouts and number of vehicles. This is done with a point-based solver in an anytime fashion on a continuous state-space. Our evaluation is threefold: At first, the convergence of the algorithm is evaluated and it is shown how the convergence can be improved with an additional search heuristic. Second, we show various planning scenarios to demonstrate how the introduction of different considered uncertainties results in more conservative planning. At the end, we show online simulations for the crossing of complex (unsignalized) intersections. We can demonstrate that our approach performs nearly as good as with full prior information about the intentions of the other vehicles and clearly outperforms reactive approaches. We describe a framework for analyzing probabilistic reachability and safety problems for discrete time stochastic hybrid systems within a dynamic games setting. In particular, we consider finite horizon zero-sum stochastic games in which a control has the objective of reaching a target set while avoiding an unsafe set in the hybrid state space, and a rational adversary has the opposing objective. We derive an algorithm for computing the maximal probability of achieving the control objective, subject to the worst-case adversary behavior. From this algorithm, sufficient conditions of optimality are also derived for the synthesis of optimal control policies and worst-case disturbance strategies. These results are then specialized to the safety problem, in which the control objective is to remain within a safe set. We illustrate our modeling framework and computational approach using both a tutorial example with jump Markov dynamics and a practical application in the domain of air traffic management. In this paper, we study the safe navigation of a mobile robot through crowds of dynamic agents with uncertain trajectories. Existing algorithms suffer from the “freezing robot” problem: once the environment surpasses a certain level of complexity, the planner decides that all forward paths are unsafe, and the robot freezes in place (or performs unnecessary maneuvers) to avoid collisions. Since a feasible path typically exists, this behavior is suboptimal. Existing approaches have focused on reducing the predictive uncertainty for individual agents by employing more informed models or heuristically limiting the predictive covariance to prevent this overcautious behavior. In this work, we demonstrate that both the individual prediction and the predictive uncertainty have little to do with the frozen robot problem. Our key insight is that dynamic agents solve the frozen robot problem by engaging in “joint collision avoidance”: They cooperatively make room to create feasible trajectories. We develop IGP, a nonparametric statistical model based on dependent output Gaussian processes that can estimate crowd interaction from data. Our model naturally captures the non-Markov nature of agent trajectories, as well as their goal-driven navigation. We then show how planning in this model can be efficiently implemented using particle based inference. Lastly, we evaluate our model on a dataset of pedestrians entering and leaving a building, first comparing the model with actual pedestrians, and find that the algorithm either outperforms human pedestrians or performs very similarly to the pedestrians. We also present an experiment where a covariance reduction method results in highly overcautious behavior, while our model performs desirably. This thesis addresses the question of planning under uncertainty within a time-dependent changing environment. Original motivation for this work came from the problem of building an autonomous agent able to coordinate with its uncertain environment; this environment being composed of other agents communicating their intentions or non-controllable processes for which some discrete-event model is available. We investigate several approaches for modeling continuous time-dependency in the framework of Markov Decision Processes (MDPs), leading us to a definition of Temporal Markov Decision Problems. Then our approach focuses on two separate paradigms. First, we investigate time-dependent problems as processes and describe them through the formalism of Time-dependent MDPs (TMDPs). We extend the existing results concerning optimality equations and present a new Value Iteration algorithm based on piecewise polynomial function representations in order to solve a more general class of TMDPs. This paves the way to a more general discussion on parametric actions in hybrid state and action spaces MDPs with continuous time. In a second time, we investigate the option of separately modeling the concurrent contributions of exogenous events. This approach of modeling leads to the use of Generalized Semi-Markov Decision Processes (GSMDP). We establish a link between the general framework of Discrete Events Systems Specification (DEVS) and the formalism of GSMDP, allowing us to build sound discrete-event compatible simulators. Then we introduce a simulation-based Policy Iteration approach for explicit-event Temporal Markov Decision Problems. This algorithmic contribution brings together results from simulation theory, forward search in MDPs, and statistical learning theory. The implicit-event approach was tested on a specific version of the Mars rover planning problem and on a drone patrol mission planning problem while the explicit-event approach was evaluated on a subway network control problem. When driving in urban environments, an autonomous vehicle must account for the interaction with other traffic participants. It must reason about their future behavior, how its actions affect their future behavior, and potentially consider multiple motion hypothesis. In this paper we introduce a method for joint behavior estimation and trajectory planning that models interaction and multi-policy decision-making. The method leverages Partially Observable Markov Decision Processes to estimate the behavior of other traffic participants given the planned trajectory for the ego-vehicle, and Receding-Horizon Control for generating safe trajectories for the ego-vehicle. To achieve safe navigation we introduce chance constraints over multiple motion policies in the receding-horizon planner. These constraints account for uncertainty over the behavior of other traffic participants. The method is capable of running in real-time and we show its performance and good scalability in simulated multi-vehicle intersection scenarios. This work studies the design of reliable control laws of robotic systems operating in uncertain environments. We introduce a new approach to stochastic policy optimization based on probably approximately correct (PAC) bounds on the expected performance of control policies. An algorithm is constructed which directly minimizes an upper confidence bound on the expected cost of trajectories instead of employing a standard approach based on the expected cost itself. This algorithm thus has built-in robustness to uncertainty, since the bound can be regarded as a certificate for guaranteed future performance. The approach is evaluated on two challenging robot control scenarios in simulation: a car with side slip and a quadrotor navigating through obstacle-ridden environments. We show that the bound accurately predicts future performance and results in improved robustness measured by lower average cost and lower probability of collision. The performance of the technique is studied empirically and compared to several existing policy search algorithms. Abstract In this paper we present an approach to control a vehicle in a hostile environment with static obstacles and moving adversaries. The vehicle is required to satisfy a mission objective expressed as a temporal logic specification over a set of properties satisfied at regions of a partitioned environment. We model the movements of adversaries in between regions of the environment as Poisson processes. Furthermore, we assume that the time it takes for the vehicle to traverse in between two facets of a region is exponentially distributed, and we obtain the rate of this exponential distribution from a simulator of the environment. We capture the motion of the vehicle and the vehicle updates of adversaries distributions as a Markov Decision Process. Using tools in Probabilistic Computational Tree Logic, we find a control strategy for the vehicle that maximizes the probability of accomplishing the mission objective. We demonstrate our approach with illustrative case studies. The article deals with the analysis and interpretation of dynamic scenes typical of urban driving. The key objective is to assess risks of collision for the ego-vehicle. We describe our concept and methods, which we have integrated and tested on our experimental platform on a Lexus car and a driving simulator. The on-board sensors deliver visual, telemetric and inertial data for environment monitoring. The sensor fusion uses our Bayesian Occupancy Filter for a spatio-temporal grid representation of the traffic scene. The underlying probabilistic approach is capable of dealing with uncertainties when modeling the environment as well as detecting and tracking dynamic objects. The collision risks are estimated as stochastic variables and are predicted for a short period ahead with the use of Hidden Markov Models and Gaussian processes. The software implementation takes advantage of our methods, which allow for parallel computation. Our tests have proven the relevance and feasibility of our approach for improving the safety of car driving. This paper deals with the trajectory generation problem faced by an autonomous vehicle in moving traffic. Being given the predicted motion of the traffic flow, the proposed semi-reactive planning strategy realizes all required long-term maneuver tasks (lane-changing, merging, distance-keeping, velocity-keeping, precise stopping, etc.) while providing short-term collision avoidance. The key to comfortable, human-like as well as physically feasible trajectories is the combined optimization of the lateral and longitudinal movements in street-relative coordinates with carefully chosen cost functionals and terminal state sets (manifolds). The performance of the approach is demonstrated in simulated traffic scenarios. Autonomous vehicles require optimal path planning algorithms to achieve mission goals while avoiding obstacles and being robust to uncertainties. The uncertainties arise from exogenous disturbances, modeling errors, and sensor noise, which can be characterized via stochastic models. Previous work dened a notion of robustness in a stochastic setting by using the concept of chance constraints. This requires that mission constraint violation can occur with a probability less than a prescribed value. In this paper we describe a novel method for optimal chance constrained path planning with feedback design. The approach optimizes both the reference trajectory to be followed and the feedback controller used to reject uncertainty. Our method extends recent results in constrained control synthesis based on convex optimization to solve control problems with nonconvex constraints. This extension is essential for path planning problems, which inherently have nonconvex obstacle avoidance constraints. Unlike previous approaches to chance constrained path planning, the new approach optimizes the feedback gain as well as the reference trajectory. The key idea is to couple a fast, nonconvex solver that does not take into account uncertainty, with existing robust approaches that apply only to convex feasible regions. By alternating between robust and nonrobust solutions, the new algorithm guarantees convergence to a global optimum. We apply the new method to an unmanned aircraft and show simulation results that demonstrate the ecacy of the approach. Autonomous vehicles have found wide-ranging adoption in aerospace, terrestrial as well as marine use. These systems often operate in uncertain environments and in the presence of noisy sensors, and use machine learning and statistical sensor fusion algorithms to form an internal model of the world that is inherently probabilistic. Autonomous vehicles need to operate using this uncertain world-model, and hence, their correctness cannot be deterministically specified. Even once probabilistic correctness is specified, proving that an autonomous vehicle will operate correctly is a challenging problem. In this paper, we address these challenges by proposing a correct-by-synthesis approach to autonomous vehicle control. We propose a probabilistic extension of temporal logic, named Chance Constrained Temporal Logic C2TL, that can be used to specify correctness requirements in presence of uncertainty. We present a novel automated synthesis technique that compiles C2TL specification into mixed integer constraints, and uses second-order quadratic cone programming to synthesize optimal control of autonomous vehicles subject to the C2TL specification. We demonstrate the effectiveness of the proposed approach on a diverse set of illustrative examples. We consider task and motion planning in complex dynamic environments for problems expressed in terms of a set of Linear Temporal Logic (LTL) constraints, and a reward function. We propose a methodology based on reinforcement learning that employs deep neural networks to learn low-level control policies as well as task-level option policies. A major challenge in this setting, both for neural network approaches and classical planning, is the need to explore future worlds of a complex and interactive environment. To this end, we integrate Monte Carlo Tree Search with hierarchical neural net control policies trained on expressive LTL specifications. This paper investigates the ability of neural networks to learn both LTL constraints and control policies in order to generate task plans in complex environments. We demonstrate our approach in a simulated autonomous driving setting, where a vehicle must drive down a road in traffic, avoid collisions, and navigate an intersection, all while obeying given rules of the road. Estimating and predicting traffic situations over time is an essential capability for sophisticated driver assistance systems and autonomous driving. When longer prediction horizons are needed, e.g., in decision making or motion planning, the uncertainty induced by incomplete environment perception and stochastic situation development over time cannot be neglected without sacrificing robustness and safety. Building consistent probabilistic models of drivers interactions with the environment, the road network and other traffic participants poses a complex problem. In this paper, we model the decision making process of drivers by building a hierarchical Dynamic Bayesian Model that describes physical relationships as well as the driver's behaviors and plans. This way, the uncertainties in the process on all abstraction levels can be handled in a mathematically consistent way. As drivers behaviors are difficult to model, we present an approach for learning continuous, non-linear, context-dependent models for the behavior of traffic participants. We propose an Expectation Maximization (EM) approach for learning the models integrated in the DBN from unlabeled observations. Experiments show a significant improvement in estimation and prediction accuracy over standard models which only consider vehicle dynamics. Finally, a novel approach to tactical decision making for autonomous driving is outlined. It is based on a continuous Partially Observable Markov Decision Process (POMDP) that uses the presented model for prediction. This paper examines techniques for finding falsifying trajectories of hybrid systems using an approach that we call trajectory splicing. Many formal verification techniques for hybrid systems, including flowpipe construction, can identify plausible abstract counterexamples for property violations. However, there is often a gap between the reported abstract counterexamples and the concrete system trajectories. Our approach starts with a candidate sequence of disconnected trajectory segments, each segment lying inside a discrete mode. However, such disconnected segments do not form concrete violations due to the gaps that exist between the ending state of one segment and the starting state of the subsequent segment. Therefore, trajectory splicing uses local optimization to minimize the gap between these segments, effectively splicing them together to form a concrete trajectory. We demonstrate the use of our approach for falsifying safety properties of hybrid systems using standard optimization techniques. As such, our approach is not restricted to linear systems. We compare our approach with other falsification approaches including uniform random sampling and a robustness guided falsification approach used in the tool S-Taliro. Our preliminary evaluation clearly shows the potential of our approach to search for candidate trajectory segments and use them to find concrete property violations. Future vehicle systems for active pedestrian safety will not only require a high recognition performance but also an accurate analysis of the developing traffic situation. In this paper, we present a study on pedestrian path prediction and action classification at short subsecond time intervals. We consider four representative approaches: two novel approaches (based on Gaussian process dynamical models and probabilistic hierarchical trajectory matching) that use augmented features derived from dense optical flow and two approaches as baseline that use positional information only (a Kalman filter and its extension to interacting multiple models). In experiments using stereo vision data obtained from a vehicle, we investigate the accuracy of path prediction and action classification at various time horizons, the effect of various errors (image localization, vehicle egomotion estimation), and the benefit of the proposed approaches. The scenario of interest is that of a crossing pedestrian, who might stop or continue walking at the road curbside. Results indicate similar performance of the four approaches on walking motion, with near-linear dynamics. During stopping, however, the two newly proposed approaches, with nonlinear and or higher order models and augmented motion features, achieve a more accurate position prediction of 10-50 cm at a time horizon of 0-0.77 s around the stopping event. Safe autonomous navigation of microair vehicles in cluttered dynamic environments is challenging due to the uncertainties arising from robot localization, sensing, and motion disturbances. This letter presents a probabilistic collision avoidance method for navigation among other robots and moving obstacles, such as humans. The approach explicitly considers the collision probability between each robot and obstacle and formulates a chance constrained nonlinear model predictive control problem (CCNMPC). A tight bound for approximation of collision probability is developed, which makes the CCNMPC formulation tractable and solvable in real time. For multirobot coordination, we describe three approaches, one distributed without communication (constant velocity assumption), one distributed with communication (of previous plans), and one centralized (sequential planning). We evaluate the proposed method in experiments with two quadrotors sharing the space with two humans and verify the multirobot coordination strategy in simulation with up to sixteen quadrotors.