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

• URL: http://arxiv.org/abs/2305.17291v2
• Date: Sun, 4 Jun 2023 04:28:15 GMT
• Title: Convex Risk Bounded Continuous-Time Trajectory Planning and Tube Design in Uncertain Nonconvex Environments
• Authors: Ashkan Jasour, Weiqiao Han, and Brian Williams
• Abstract summary: We provide a method that looks for continuous-time trajectories with guaranteed risk planning. We leverage the notion of risk bounded planning to transform risk into a set of points.
• Score: 7.874203691787801
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 (and known) probabilistic uncertainties, nonconvex and nonlinear, static and dynamic obstacles, and is suitable for online trajectory planning problems. In addition, we provide convex methods based on sum-of-squares optimization to build the max-sized tube with respect to its parameterization along the trajectory so that any state inside the tube is guaranteed to have bounded risk.

Related papers

• LaPlaSS: Latent Space Planning for Stochastic Systems [8.529245639496274]
  We propose a "generate-and-test" approach to risk-bounded planning for autonomous mobile agents. We use a variational autoencoder to learn a latent linear dynamics model and encode the planning problem into the latent space to generate the candidate trajectory. We demonstrate that our algorithm, LaPlaSS, is able to generate trajectory plans with bounded risk for a real-world agent with learned dynamics.
  arXiv  Detail & Related papers  (2024-04-10T14:52:35Z)
• Information-Theoretic Safe Bayesian Optimization [59.758009422067005]
  We consider a sequential decision making task, where the goal is to optimize an unknown function without evaluating parameters that violate an unknown (safety) constraint. Most current methods rely on a discretization of the domain and cannot be directly extended to the continuous case. We propose an information-theoretic safe exploration criterion that directly exploits the GP posterior to identify the most informative safe parameters to evaluate.
  arXiv  Detail & Related papers  (2024-02-23T14:31:10Z)
• Real-Time Tube-Based Non-Gaussian Risk Bounded Motion Planning for Stochastic Nonlinear Systems in Uncertain Environments via Motion Primitives [9.088960941718]
  We consider the motion planning problem for nonlinear systems in uncertain environments. Unlike [1], we present a real-time online motion planning algorithm. We verify the safety of the tubes against deterministic risk using sum-of-squares programming.
  arXiv  Detail & Related papers  (2023-03-02T23:36:26Z)
• Non-Gaussian Uncertainty Minimization Based Control of Stochastic Nonlinear Robotic Systems [9.088960941718]
  We design a state feedback controller that minimizes deviations of the states of the system from the nominal state trajectories due to uncertainties and disturbances. We use moments and characteristic functions to propagate uncertainties throughout the nonlinear motion model of robotic systems.
  arXiv  Detail & Related papers  (2023-03-02T23:31:32Z)
• Safe Online Bid Optimization with Return-On-Investment and Budget Constraints subject to Uncertainty [87.81197574939355]
  We study the nature of both the optimization and learning problems. We provide an algorithm, namely GCB, guaranteeing sublinear regret at the cost of a potentially linear number of constraints violations. More interestingly, we provide an algorithm, namely GCB_safe(psi,phi), guaranteeing both sublinear pseudo-regret and safety w.h.p. at the cost of accepting tolerances psi and phi.
  arXiv  Detail & Related papers  (2022-01-18T17:24:20Z)
• Risk Conditioned Neural Motion Planning [14.018786843419862]
  Risk-bounded motion planning is an important yet difficult problem for safety-critical tasks. We propose an extension of soft actor critic model to estimate the execution risk of a plan through a risk critic. We show the advantage of our model in terms of both computational time and plan quality, compared to a state-of-the-art mathematical programming baseline.
  arXiv  Detail & Related papers  (2021-08-04T05:33:52Z)
• Towards Safe Policy Improvement for Non-Stationary MDPs [48.9966576179679]
  Many real-world problems of interest exhibit non-stationarity, and when stakes are high, the cost associated with a false stationarity assumption may be unacceptable. We take the first steps towards ensuring safety, with high confidence, for smoothly-varying non-stationary decision problems. Our proposed method extends a type of safe algorithm, called a Seldonian algorithm, through a synthesis of model-free reinforcement learning with time-series analysis.
  arXiv  Detail & Related papers  (2020-10-23T20:13:51Z)
• A Stochastic Subgradient Method for Distributionally Robust Non-Convex Learning [2.007262412327553]
  robustness is with respect to uncertainty in the underlying data distribution. We show that our technique converges to satisfying perturbationity conditions. We also illustrate the performance of our algorithm on real datasets.
  arXiv  Detail & Related papers  (2020-06-08T18:52:40Z)
• Robust Reinforcement Learning with Wasserstein Constraint [49.86490922809473]
  We show the existence of optimal robust policies, provide a sensitivity analysis for the perturbations, and then design a novel robust learning algorithm. The effectiveness of the proposed algorithm is verified in the Cart-Pole environment.
  arXiv  Detail & Related papers  (2020-06-01T13:48:59Z)
• Chance-Constrained Trajectory Optimization for Safe Exploration and Learning of Nonlinear Systems [81.7983463275447]
  Learning-based control algorithms require data collection with abundant supervision for training. We present a new approach for optimal motion planning with safe exploration that integrates chance-constrained optimal control with dynamics learning and feedback control.
  arXiv  Detail & Related papers  (2020-05-09T05:57:43Z)
• High-Dimensional Robust Mean Estimation via Gradient Descent [73.61354272612752]
  We show that the problem of robust mean estimation in the presence of a constant adversarial fraction can be solved by gradient descent. Our work establishes an intriguing connection between the near non-lemma estimation and robust statistics.
  arXiv  Detail & Related papers  (2020-05-04T10:48:04Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.