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Computing Reachable States for Nonlinear Biological Models
"... Abstract. In this paper we describe reachability computation for continuous and hybrid systems and its potential contribution to the process of building and debugging biological models. We then develop a novel algorithm for computing reachable states for nonlinear systems and report experimental res ..."
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Cited by 9 (4 self)
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Abstract. In this paper we describe reachability computation for continuous and hybrid systems and its potential contribution to the process of building and debugging biological models. We then develop a novel algorithm for computing reachable states for nonlinear systems and report experimental results obtained using a prototype implementation. We believe these results constitute a promising contribution to the analysis of complex models of biological systems. 1
ModelBased Probabilistic Collision Detection in Autonomous Driving
, 2009
"... Safety of planned paths of autonomous cars with respect to the movement of other traffic participants is considered. Thereto, the stochastic occupancy of the road by other vehicles is predicted. The prediction considers uncertainties originating from the measurements and the possible behaviors of o ..."
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Cited by 7 (2 self)
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Safety of planned paths of autonomous cars with respect to the movement of other traffic participants is considered. Thereto, the stochastic occupancy of the road by other vehicles is predicted. The prediction considers uncertainties originating from the measurements and the possible behaviors of other traffic participants. In addition, the interaction of traffic participants as well as the limitation of driving maneuvers due to the road geometry is considered. The result of the presented approach is the probability of a crash for a specific trajectory of the autonomous car. The presented approach is efficient as most intensive computations are performed offline, resulting in a lean online algorithm for realtime application.
Safety Verification of Autonomous Vehicles for Coordinated Evasive Maneuvers
"... Abstract — The verification of evasive maneuvers for autonomous vehicles driving with constant velocity is considered. Modeling uncertainties, uncertain measurements, and disturbances can cause substantial deviations from an initially planned evasive maneuver. From this follows that the maneuver, wh ..."
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Cited by 7 (1 self)
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Abstract — The verification of evasive maneuvers for autonomous vehicles driving with constant velocity is considered. Modeling uncertainties, uncertain measurements, and disturbances can cause substantial deviations from an initially planned evasive maneuver. From this follows that the maneuver, which is safe under perfect conditions, might become unsafe. In this work, the possible set of deviations is computed with methods from reachability analysis, which allows to verify evasive maneuvers under consideration of the mentioned uncertainties. Since the presented approach has a short response time, it can be applied for real time safety decisions. The methods are presented for a numerical example where two autonomous cars plan a coordinated evasive maneuver in order to prevent a collision with a wrongway driver. I.
Hybridization Domain Construction using Curvature Estimation ∗ ABSTRACT
"... This paper is concerned with the reachability computation for nonlinear systems using hybridization. The main idea of hybridization is to approximate a nonlinear vector field by a piecewiseaffine one. The piecewiseaffine vector field is defined by building around the set of current states of the ..."
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Cited by 2 (0 self)
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This paper is concerned with the reachability computation for nonlinear systems using hybridization. The main idea of hybridization is to approximate a nonlinear vector field by a piecewiseaffine one. The piecewiseaffine vector field is defined by building around the set of current states of the system a simplicial domain and using linear interpolation over its vertices. To achieve a good timeefficiency and accuracy of the reachability computation on the approximate system, it is important to find a simplicial domain which, on one hand, is as large as possible and, on the other hand, guarantees a small interpolation error. In our previous work [8], we proposed a method for constructing hybridization domains based on the curvature of the dynamics and showed how the method can be applied to quadratic systems. In this paper we pursue this work further and present two main results. First, we prove an optimality property of the domain construction method for a class of quadratic systems. Second, we propose an algorithm of curvature estimation for more general nonlinear systems with nonconstant Hessian matrices. This estimation can then be used to determine efficient hybridization domains. We also describe some experimental results to illustrate the main ideas of the algorithm as well as its performance. 1.
Computing Reachable Sets of Hybrid Systems Using a Combination of Zonotopes and Polytopes
, 2009
"... The computation of reachable sets for hybrid systems with linear continuous dynamics is addressed. Zonotopes are used for the representation of reachable sets, resulting in an algorithm with low computational complexity with respect to the dimension of the considered system. However, zonotopes have ..."
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Cited by 2 (0 self)
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The computation of reachable sets for hybrid systems with linear continuous dynamics is addressed. Zonotopes are used for the representation of reachable sets, resulting in an algorithm with low computational complexity with respect to the dimension of the considered system. However, zonotopes have drawbacks when being intersected with transition guards which determine the discrete behavior of the hybrid system. For this reason, in the proposed approach, reachable sets are represented by polytopes within guard sets as an intermediate step in order to enclose them by zonotopes afterwards. Different methods for the conservative conversion from zonotopes to polytopes and vice versa are proposed and numerically evaluated.
SetBased Computation of Vehicle Behaviors for the Online Verification of Autonomous Vehicles
"... Abstract — We compute the set of all possible behaviors of an autonomous vehicle using reachability analysis. A reachable set is the set of states a system can possibly reach for a given set of initial states, disturbances, and sensor noise values. We consider autonomous vehicles which plan trajecto ..."
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Cited by 1 (1 self)
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Abstract — We compute the set of all possible behaviors of an autonomous vehicle using reachability analysis. A reachable set is the set of states a system can possibly reach for a given set of initial states, disturbances, and sensor noise values. We consider autonomous vehicles which plan trajectories for a certain lookahead horizon which are followed using feedback control. While a perfectly followed trajectory might not violate specified safety properties (e.g. lane departures or vehicle collisions), there might exist a violating deviation from the planned trajectory. Given the mathematical model of the controlled vehicle and bounds on uncertainty, our approach detects any possible violation. In addition, the approach provides results faster than real time such that maneuvers of vehicles can be checked before they are fully executed. I.
CNRS/VERIMAG Centre Equation, 2 av de
"... This paper is concerned with reachable set computation for nonlinear systems using hybridization. The essence of hybridization is to approximate a nonlinear vector field by a simpler (such as affine) vector field. This is done by partitioning the state space into small regions within each of which ..."
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This paper is concerned with reachable set computation for nonlinear systems using hybridization. The essence of hybridization is to approximate a nonlinear vector field by a simpler (such as affine) vector field. This is done by partitioning the state space into small regions within each of which a simpler vector field is defined. This approach relies on the availability of methods for function approximation and for handling the resulting dynamical systems. Concerning function approximation using interpolation, the accuracy depends on the shapes and sizes of the regions which can compromise as well the speed of reachability computation since it may generate spurious classes of trajectories. In this paper we study the relationship between the region geometry and reachable set accuracy and propose a method for constructing hybridization regions using tighter interpolation error bounds. In addition, our construction exploits the dynamics of the system to adapt the orientation of the regions, in order to achieve better timeefficiency. We also present some experimental results on a highdimensional biological system, to demonstrate the performance improvement. 1.
Computing Reachable States for . . .
, 2010
"... In this paper we describe reachability computation for continuous and hybrid systems and its potential contribution to the process of building and debugging biological models. We summarize the stateoftheart for linear systems and then develop a novel algorithm for computing reachable states for n ..."
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In this paper we describe reachability computation for continuous and hybrid systems and its potential contribution to the process of building and debugging biological models. We summarize the stateoftheart for linear systems and then develop a novel algorithm for computing reachable states for nonlinear systems. We report experimental results obtained using a prototype implementation applied to several biological models. We believe these results constitute a promising contribution to the analysis of complex models of biological systems.
HySon: Precise Simulation of Hybrid Systems with Imprecise Inputs
"... Hybrid systems are a widely used model to represent and reason about controlcommand systems. Most of the work in this domain is devoted to compute reachable sets of hybrid automata or equivalent models. However, in an industrial context, controlcommand systems are often implemented in Simulink and ..."
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Hybrid systems are a widely used model to represent and reason about controlcommand systems. Most of the work in this domain is devoted to compute reachable sets of hybrid automata or equivalent models. However, in an industrial context, controlcommand systems are often implemented in Simulink and their validity is checked using numerical simulation. In this article, we present a tool named HySon that performs setbased simulation of hybrid systems with uncertain parameters, expressed in Simulink. Our tool handles advanced features such as nonlinear operations, zerocrossing events or discrete sampling. It is based on wellknown, efficient numerical algorithms that were adapted to handle setbased domains. We demonstrate the performance of our method on various examples. 1.
Reachability Computation of LowOrder Models for the Safety Verification of HighOrder Road Vehicle Models
"... Abstract — We present an approach to verify the planned maneuvers of an automated car. The main idea is to compute the occupancy of the automated car on the road using reachable sets, which makes it possible to check if one collides with other traffic participants, or leaves the drivable area. The s ..."
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Abstract — We present an approach to verify the planned maneuvers of an automated car. The main idea is to compute the occupancy of the automated car on the road using reachable sets, which makes it possible to check if one collides with other traffic participants, or leaves the drivable area. The specialty of the presented approach is that all possible uncertainties in the form of sensor noise, uncertain friction coefficient, and uncertain initial states, are considered. Maneuvers are periodically verified onboard to account for the variety of possible traffic situations, requiring an efficient algorithm. Thus, the underlying vehicle model has to be a compromise between accuracy and simplicity. The inexactness of the model is compensated by adding disturbance to the model such that it contains highorder model behavior. This is demonstrated by exploring the state space with rapidlyexploring random trees (RRTs) of a highorder model and check whether it leaves the reachable area of the loworder model used for verification. I.