Real-Time Risk-Bounded Tube-Based Trajectory Safety Verification

Jasour, Ashkan; Han, Weiqiao; Williams, Brian

doi:10.1109/cdc45484.2021.9683600

Cited by 6 publications

(6 citation statements)

References 19 publications

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“…The most important sub-procedure for the algorithm is to verify if the tube with parameter c is safe. As in (25), we can verify the safety of the tube using SOS programming Jasour et al (2021b). Let S(t) = {x : g i (x, t) ≥ 0, i = 1, ..., ℓ} be the feasible set of optimization (29) at time t, t ∈ [t 0 , t f ], i.e., the set constructed by the polynomial constraints of all the risk contours Ĉ∆ ri , i = 1, ..., n os , Ĉ∆ rj (t), j = n os + 1, ..., n o d , as well as the upperbound constraint…”

Section: Continuous-time Risk Bounded Tube Design Using Risk Contoursmentioning

confidence: 99%

Convex Risk Bounded Continuous-Time Trajectory Planning in Uncertain Nonconvex Environments

Jasour¹,

Han²,

Williams³

2021

Robotics: Science and Systems XVII

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In this paper, we address the trajectory planning problem in uncertain nonconvex static and dynamic environments that contain obstacles with probabilistic location, size, and geometry. To address this problem, we provide a risk bounded trajectory planning method that looks for continuous-time trajectories with guaranteed bounded risk over the planning time horizon. Risk is defined as the probability of collision with uncertain obstacles. Existing approaches to address risk bounded trajectory planning problems either are limited to Gaussian uncertainties and convex obstacles or rely on sampling-based methods that need uncertainty samples and time discretization. To address the risk bounded trajectory planning problem, we leverage the notion of risk contours to transform the risk bounded planning problem into a deterministic optimization problem. Risk contours are the set of all points in the uncertain environment with guaranteed bounded risk. The obtained deterministic optimization is, in general, nonlinear and nonconvex time-varying optimization. We provide convex methods based on sum-of-squares optimization to efficiently solve the obtained nonconvex time-varying optimization problem and obtain the continuous-time risk bounded trajectories without time discretization. The provided approach deals with arbitrary probabilistic uncertainties, nonconvex and nonlinear, static and dynamic obstacles, and is suitable for online trajectory planning problems.

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Section: Continuous-time Risk Bounded Tube Design Using Risk Contoursmentioning

confidence: 99%

Convex Risk Bounded Continuous-Time Trajectory Planning in Uncertain Nonconvex Environments

Jasour¹,

Han²,

Williams³

2021

Robotics: Science and Systems XVII

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Section: Methodsmentioning

confidence: 99%

“…In this section, we first review how to convert uncertain obstacles in the environment into risk contours [23]. Second, we review how to verify the safety of the tube using risk contours and SOS programming [23]. Next we present how to generate motion primitives and their corresponding tubes, and discuss several points to optimize implementation in online execution.…”

Section: Methodsmentioning

confidence: 99%

“…In the proof of the Theorem above we use concentration inequalities to provide bounds on random variables [23]. More precisely, by Cantelli's inequality, for any random variable z,…”

Section: A Risk Contour Representation Of Uncertain Environmentsmentioning

confidence: 99%

“…The provided method verifies the safety of the tube in the presence of uncertain obstacles without the need for uncertainty samples and time discretization. Curious readers are suggested to refer to [23] for more details. Given a polynomial trajectory P(t) parameterized by t, a tube around it takes the form…”

Section: B Tube Verificationmentioning

confidence: 99%

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Non-Gaussian Risk Bounded Trajectory Optimization for Stochastic Nonlinear Systems in Uncertain Environments

Han¹,

Jasour²,

Williams³

2022

2022 International Conference on Robotics and Automation (ICRA)

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We consider the motion planning problem for stochastic nonlinear systems in uncertain environments. More precisely, in this problem the robot has stochastic nonlinear dynamics and uncertain initial locations, and the environment contains multiple dynamic uncertain obstacles. Obstacles can be of arbitrary shape, can deform, and can move. All uncertainties do not necessarily have Gaussian distribution. This general setting has been considered and solved in [1]. In addition to the assumptions above, in this paper, we consider long-term tasks, where the planning method in [1] would fail, as the uncertainty of the system states grows too large over a long time horizon. Unlike [1], we present a real-time online motion planning algorithm. We build discrete-time motion primitives and their corresponding continuous-time tubes offline, so that almost all system states of each motion primitive are guaranteed to stay inside the corresponding tube. We convert probabilistic safety constraints into a set of deterministic constraints called risk contours. During online execution, we verify the safety of the tubes against deterministic risk contours using sum-ofsquares (SOS) programming. The provided SOS-based method verifies the safety of the tube in the presence of uncertain obstacles without the need for uncertainty samples and time discretization in real-time. By bounding the probability the system states staying inside the tube and bounding the probability of the tube colliding with obstacles, our approach guarantees bounded probability of system states colliding with obstacles. We demonstrate our approach on several long-term robotics tasks.

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Real-Time Tube-Based Non-Gaussian Risk Bounded Motion Planning for Stochastic Nonlinear Systems in Uncertain Environments via Motion Primitives

Han,

Jasour,

Williams

2023

2023 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)

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Real-Time Risk-Bounded Tube-Based Trajectory Safety Verification

Cited by 6 publications

References 19 publications

Convex Risk Bounded Continuous-Time Trajectory Planning in Uncertain Nonconvex Environments

Convex Risk Bounded Continuous-Time Trajectory Planning in Uncertain Nonconvex Environments

Non-Gaussian Risk Bounded Trajectory Optimization for Stochastic Nonlinear Systems in Uncertain Environments

Real-Time Tube-Based Non-Gaussian Risk Bounded Motion Planning for Stochastic Nonlinear Systems in Uncertain Environments via Motion Primitives

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