Related papers: Reachability as a Unifying Framework for Computing…
We propose a reachability approach for infinite and finite horizon multi-objective optimization problems for low-thrust spacecraft trajectory design. The main advantage of the proposed method is that the Pareto front can be efficiently…
The decision logic for the ACAS X family of aircraft collision avoidance systems is represented as a large numeric table. Due to storage constraints of certified avionics hardware, neural networks have been suggested as a way to…
Autonomous mobile robots must maintain safety, but should not sacrifice performance, leading to the classical reach-avoid problem: find a trajectory that is guaranteed to reach a goal and avoid obstacles. This paper addresses the near…
Probabilistic guarantees of safety and performance are important in constrained dynamical systems with stochastic uncertainty. We consider the stochastic reachability problem, which maximizes the probability that the state remains within…
We address the problem of optimal path planning for a simple nonholonomic vehicle in the presence of obstacles. Most current approaches are either split hierarchically into global path planning and local collision avoidance, or neglect some…
Harmonic potentials provide globally convergent potential fields that are provably free of local minima. Due to its analytical format, it is particularly suitable for generating safe and reliable robot navigation policies. However, for…
Ensuring safe driving while maintaining travel efficiency for autonomous vehicles in dynamic and occluded environments is a critical challenge. This paper proposes an occlusion-aware contingency safety-critical planning approach for…
Advanced combustion technologies such as homogeneous charge compression ignition (HCCI) engines have a narrow stable operating region defined by complex control strategies such as exhaust gas recirculation (EGR) and variable valve timing…
Reachability analysis aims at identifying states reachable by a system within a given time horizon. This task is known to be computationally expensive for linear hybrid systems. Reachability analysis works by iteratively applying continuous…
Density of the reachable states can help understand the risk of safety-critical systems, especially in situations when worst-case reachability is too conservative. Recent work provides a data-driven approach to compute the density…
In legged locomotion the projection of the robot Center of Mass (CoM) being inside the convex hull of the contact points is a commonly accepted sufficient condition to achieve static balancing. However, some of these configurations cannot…
We study the Hamilton-Jacobi equation for undiscounted exit time control problems with general nonnegative Lagrangians using the dynamic programming approach. We prove theorems characterizing the value function as the unique…
Operating unmanned aerial vehicles (UAVs) in complex environments that feature dynamic obstacles and external disturbances poses significant challenges, primarily due to the inherent uncertainty in such scenarios. Additionally, inaccurate…
We present an algorithm to perform fuel-optimal stationkeeping for spacecraft in unstable halo orbits with additional constraints to ensure safety in the event of a control failure. We formulate a convex trajectory-optimization problem to…
In optimal control problems of control-affine systems, whose solutions are bang-bang or singular type, verification of optimality using the Hamilton-Jacobi-Bellman (HJB) equation involves the computation of partial derivatives of switching…
We establish a well-posedness and error-estimation framework that solves Hamilton-Jacobi equations by minimizing the least-squares residual of monotone finite-difference discretizations. This approach also applies naturally to second-order…
In this paper, we consider the stochastic optimal control problem for jump diffusion systems with state constraints. In general, the value function of such problems is a discontinuous viscosity solution of the Hamilton-Jacobi-Bellman (HJB)…
Knowing and predicting dangerous factors within a scene are two key components during autonomous driving, especially in a crowded urban environment. To navigate safely in environments, risk assessment is needed to quantify and associate the…
We develop data-driven algorithms for reachability analysis and control of systems with a priori unknown nonlinear dynamics. The resulting algorithms not only are suitable for settings with real-time requirements but also provide provable…
We consider the problem of time-optimal path planning for simple nonholonomic vehicles. In previous similar work, the vehicle has been simplified to a point mass and the obstacles have been stationary. Our formulation accounts for a…