Probabilistic Feasibility for Nonlinear Systems with Non-Gaussian Uncertainty using RRT

For motion planning problems involving many or unbounded forms of uncertainty, it may not be possible to identify a path guaranteed to be feasible, requiring consideration of the trade-o between planner conservatism and the risk of infeasibility. Recent work developed the chance constrained rapidly-exploring random tree (CC-RRT) algorithm, a real-time planning algorithm which can e ciently compute risk at each timestep in order to guarantee probabilistic feasibility. However, the results in that paper require the dual assumptions of a linear system and Gaussian uncertainty, two assumptions which are often not applicable to many real-life path planning scenarios. This paper presents several extensions to the CC-RRT framework which allow these assumptions to be relaxed. For nonlinear systems subject to Gaussian process noise, state distributions can be approximated as Gaussian by considering a linearization of the dynamics at each timestep; simulation results demonstrate the e ective of this approach for both open-loop and closed-loop dynamics. For systems subject to non-Gaussian uncertainty, we propose a particle-based representation of the uncertainty, and thus the state distributions; as the number of particles increases, the particles approach the true uncertainty. A key aspect of this approach relative to previous work is the consideration of probabilistic bounds on constraint satisfaction, both at every timestep and over the duration of entire paths.United States. Air Force (USAF, grant FA9550-08-1-0086)United States. Air Force Office of Scientific Research (AFOSR, Grant FA9550-08-1-0086

Chance-Constrained Optimal Path Planning With Obstacles

Autonomous vehicles need to plan trajectories to a specified goal that avoid obstacles. For robust execution, we must take into account uncertainty, which arises due to uncertain localization, modeling errors, and disturbances. Prior work handled the case of set-bounded uncertainty. We present here a chance-constrained approach, which uses instead a probabilistic representation of uncertainty. The new approach plans the future probabilistic distribution of the vehicle state so that the probability of failure is below a specified threshold. Failure occurs when the vehicle collides with an obstacle or leaves an operator-specified region. The key idea behind the approach is to use bounds on the probability of collision to show that, for linear-Gaussian systems, we can approximate the nonconvex chance-constrained optimization problem as a disjunctive convex program. This can be solved to global optimality using branch-and-bound techniques. In order to improve computation time, we introduce a customized solution method that returns almost-optimal solutions along with a hard bound on the level of suboptimality. We present an empirical validation with an aircraft obstacle avoidance example.National Science Foundation (U.S.) (Grant IIS-1017992)Boeing Company (Grant MIT-BA-GTA-1

Real-time feasibility of nonlinear model predictive control for semi-batch reactors subject to uncertainty and disturbances

This paper presents two nonlinear model predictive control based methods for solving closed-loop stochastic dynamic optimisation problems, ensuring both robustness and feasibility with respect to state output constraints. The first one is a new deterministic approach, using the wait-and-see strategy. The key idea is to specifically anticipate violation of output hard-constraints, which are strongly affected by instantaneous disturbances, by backing off of their bounds along the moving horizon. The second method is a stochastic approach to solve nonlinear chance-constrained dynamic optimisation problems under uncertainties. The key aspect is the explicit consideration of the stochastic properties of both exogenous and endogenous uncertainties in the problem formulation (here-and-now strategy). The approach considers a nonlinear relation between uncertain inputs and the constrained state outputs. The performance of the proposed methodologies is assessed via an application to a semi-batch reactor under safety constraints, involving strongly exothermic reactions

Stochastic receding horizon control with output feedback and bounded controls

International audienceWe study the problem of receding horizon control for stochastic discrete-time systems with bounded control inputs and incomplete state information. Given a suitable choice of causal control policies, we first present a slight extension of the Kalman filter to estimate the state optimally in mean-square sense. We then show how to augment the underlying optimization problem with a negative drift-like constraint, yielding a second-order cone program to be solved periodically online. We prove that the receding horizon implementation of the resulting control policies renders the state of the overall system mean-square bounded under mild assumptions. We also discuss how some quantities required by the finite-horizon optimization problem can be computed off-line, thus reducing the on-line computation