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To generate safe and real-time trajectories for an autonomous vehicle in dynamic environments, path and speed decoupled planning methods are often considered. This paper studies speed planning, which mainly deals with dynamic obstacle…
This paper proposes an algorithmic technique for a class of optimal control problems where it is easy to compute a pointwise minimizer of the Hamiltonian associated with every applied control. The algorithm operates in the space of relaxed…
Distributed control algorithms are known to reduce overall computation time compared to centralized control algorithms. However, they can result in inconsistent solutions leading to the violation of safety-critical constraints. Inconsistent…
Industrial manipulators are normally operated in cluttered environments, making safe motion planning important. Furthermore, the presence of model-uncertainties make safe motion planning more difficult. Therefore, in practice the speed is…
This paper presents the design and analysis of a Hybrid High-Order (HHO) approximation for a distributed optimal control problem governed by the Poisson equation. We propose three distinct schemes to address unconstrained control problems…
In many human-in-the-loop robotic applications such as robot-assisted surgery and remote teleoperation, predicting the intended motion of the human operator may be useful for successful implementation of shared control, guidance virtual…
This paper focuses on the problem of collaborative collision avoidance for autonomous inland ships. Two solutions are provided to solve the problem in a distributed manner. We first present a distributed model predictive control (MPC)…
This paper deals with the problem of preventive maintenance (PM) scheduling of pipelines subject to external corrosion defects. The preventive maintenance strategy involves an inspection step at some epoch, together with a repair schedule.…
We present a Poincar\'e covariant cascade algorithm based on the constrained Hamiltonian dynamics in an $8N$-dimensional phase space to simulate the Boltzmann-type two-body collision term. We compare this covariant cascade algorithm with…
A novel algorithm is presented for the estimation of collision probabilities between dynamic objects with uncertain trajectories, where the trajectories are given as a sequence of poses with Gaussian distributions. We propose an adaptive…
This paper presents a computationally efficient model predictive control formulation that uses an integral Chebyshev collocation method to enable rapid operations of autonomous agents. By posing the finite-horizon optimal control problem…
As mobile robots and autonomous vehicles become increasingly prevalent in human-centred environments, there is a need to control the risk of collision. Perceptual modules, for example machine vision, provide uncertain estimates of object…
Hyperbolic polynomials is a class of real-roots polynomials that has wide range of applications in theoretical computer science. Each hyperbolic polynomial also induces a hyperbolic cone that is of particular interest in optimization due to…
In this paper we propose two numerical algorithms to solve a coupled PDE-ODE system which models a slow vehicle (bottleneck) moving on a road together with other cars. The resulting system is fully coupled because the dynamics of the slow…
The goal of diagnosis is to compute good repair strategies in response to anomalous system behavior. In a decision theoretic framework, a good repair strategy has low expected cost. In a general formulation of the problem, the computation…
We propose an output feedback control-based motion planning technique for agents to enable them to converge to a specified polynomial trajectory while imposing a set of safety constraints on our controller to avoid collisions within the…
The circumcentered-reflection method (CRM) has been applied for solving convex feasibility problems. CRM iterates by computing a circumcenter upon a composition of reflections with respect to convex sets. Since reflections are based on…
A case study is presented of a collision avoidance system that directly integrates the kinematics of a bi-steerable car with a suitable path planning algorithm. The first step is to identify a path using the method of rapidly exploring…
We propose a new algorithm for numerical path tracking in polynomial homotopy continuation. The algorithm is `robust' in the sense that it is designed to prevent path jumping and in many cases, it can be used in (only) double precision…
We provide theoretical foundations and computational tools for the systematic design of optimization-based control laws with constraints that have different priorities. By introducing the concept of prioritized intersections, we extend and…