arXiv subjects

Kristoffer Bergman

Publications and source records attributed to Kristoffer Bergman.

8 recordsLinked to original sources

arXiv2026

Optimized and kinematically feasible multi-agent motion planning

Multi-agent motion planning (MAMP) is an important problem for autonomous systems with multiple agents. In this work we propose a two-step method for finding optimized and kinematically feasible solutions to MAMP problems. The first step finds an initial feasible solution using state-of-the-art methods such as conflict-based search (CBS) or priority-based search (PBS), and the second step is an improvement step which improves the solution by solving a multi-phase optimal control problem (OCP) where the initial solution is used to warm-start the solver. We also propose a method for generating motion primitives in an optimized way under the constraint that the primitive durations are all multiples of the same sample time. We evaluate our proposed framework on a MAMP problem for tractor-trailer systems. We extend the safe interval path planning with interval projections (SIPP-IP) algorithm so it can handle more general cost functions and larger agents, but our results show that for the tractor-trailer system a simple lattice-based planner performs better due to less conservative collision checks. Our experiments also indicate that CBS performs better than PBS for this system as it achieves a higher success rate in environments with obstacles and had a lower average runtime, although both planners achieve solutions of similar quality after the improvement step.

cs.RO↗

arXiv2021

A COLREGs-Compliant Motion Planner for Autonomous Maneuvering of Marine Vessels in Complex Environments

An enabling technology for future sea transports is safe and energy-efficient autonomous maritime navigation in narrow environments with other marine vessels present. This requires that the algorithm controlling the ship is able to account for the vessel's dynamics, and obeys the rules specified in the international regulations for preventing collision at sea (COLREGs). To account for these properties, this work proposes a two-step optimization-based and COLREGs-compliant motion planner tailored for large vessels. In the first step, a lattice-based motion planner is used to compute a suboptimal trajectory based on a library of precomputed motion primitives. To comply with the rules specified in COLREGs, the lattice-based planner is augmented with discrete states that represent what type of COLREGs situations that are active with respect to other nearby vessels. The trajectory computed by the lattice-based planner is then used as warm-start for the second receding-horizon step based on direct optimal control techniques. The aim of the second step is to solve the problem to local optimality with the discrete COLREGs states remained fixed. The applicability of the proposed motion planner is demonstrated in simulations, where it computes energy-efficient and COLREGs-compliant trajectories. The results also show that the motion planner is able to prevent complex collision situations from occurring.

math.OC↗

arXiv2020

An Optimization-Based Motion Planner for Autonomous Maneuvering of Marine Vessels in Complex Environments

The task of maneuvering ships in confined environments is a difficult task for a human operator. One major reason is due to the complex and slow dynamics of the ship which need to be accounted for in order to successfully steer the vehicle. In this work, a two-step optimization-based motion planner is proposed for autonomous maneuvering of ships in constrained environments such as harbors. A lattice-based motion planner is used in a first step to compute a feasible, but suboptimal solution to a discretized version of the motion planning problem. This solution is then used to enable efficient warm-start and as a terminal manifold for a second receding-horizon improvement step. Both steps of the algorithm use a high-fidelity model of the ship to plan feasible and energy-efficient trajectories. Moreover, a novel algorithm is proposed for automatic computation of spatial safety envelopes around the trajectory computed by the lattice-based planner. These safety envelopes are used in the second improvement step to obtain collision-avoidance constraints which complexity scales very well with an increased number of surrounding obstacles. The proposed optimization-based motion planner is evaluated with successful results in a simulation study for autonomous docking problems in a model of the Cape Town~harbor.

math.OC↗

arXiv2020

Optimization-based motion planning for multi-steered articulated vehicles

The task of maneuvering a multi-steered articulated vehicle in confined environments is difficult even for experienced drivers. In this work, we present an optimization-based trajectory planner targeting low-speed maneuvers in unstructured environments for multi-steered N-trailer vehicles, which are comprised of a car-like tractor and an arbitrary number of interconnected trailers with fixed or steerable wheels. The proposed trajectory planning framework is divided into two steps, where a lattice-based trajectory planner is used in a first step to compute a resolution optimal solution to a discretized version of the trajectory planning problem. The output from the lattice planner is then used in a second step to initialize an optimal control problem solver, which enables the framework to compute locally optimal trajectories that start at the vehicle's initial state and reaches the goal state exactly. The performance of the proposed optimization-based trajectory planner is evaluated in a set of practically relevant scenarios for a multi-steered 3-trailer vehicle with a car-like tractor where the last trailer is steerable.

math.OC↗

arXiv2019

An Optimization-Based Receding Horizon Trajectory Planning Algorithm

This paper presents an optimization-based receding horizon trajectory planning algorithm for dynamical systems operating in unstructured and cluttered environments. The proposed approach is a two-step procedure that uses a motion planning algorithm in a first step to efficiently find a feasible, but possibly suboptimal, nominal solution to the trajectory planning problem where in particular the combinatorial aspects of the problem are solved. The resulting nominal trajectory is then improved in a second optimization-based receding horizon planning step which performs local trajectory refinement over a sliding time window. In the second step, the nominal trajectory is used in a novel way to both represent a terminal manifold and obtain an upper bound on the cost-to-go online. This enables the possibility to provide theoretical guarantees in terms of recursive feasibility, objective function value, and convergence to the desired terminal state. The established theoretical guarantees and the performance of the proposed algorithm are verified in a set of challenging trajectory planning scenarios for a truck and trailer system.

math.OC↗

arXiv2019

Improved Path Planning by Tightly Combining Lattice-based Path Planning and Numerical Optimal Control

This paper presents a unified optimization-based path planning approach to efficiently compute locally optimal solutions to advanced path planning problems. The approach is motivated by first showing that a lattice-based path planner can be cast and analyzed as a bilevel optimization problem. This information is then used to tightly integrate a lattice-based path planner and numerical optimal control in a novel way. The lattice-based path planner is applied to the problem in a first step using a discretized search space, where system dynamics and objective function are chosen to coincide with those used in a second numerical optimal control step. As a consequence, the lattice planner provides the numerical optimal control step with a resolution optimal solution to the problem, which is highly suitable as a warm-start to the second step. This novel tight combination of a sampling-based path planner and numerical optimal control makes, in a structured way, benefit of the former method's ability to solve combinatorial parts of the problem and the latter method's ability to obtain locally optimal solutions not constrained to a discretized search space. Compared to previously presented combinations of sampling-based path planners and optimization, the proposed approach is shown in several path planning experiments to provide significant improvements in terms of computation time, numerical reliability, and objective function value.

math.OC↗

arXiv2019

Improved Optimization of Motion Primitives for Motion Planning in State Lattices

In this paper, we propose a framework for generating motion primitives for lattice-based motion planners automatically. Given a family of systems, the user only needs to specify which principle types of motions, which are here denoted maneuvers, that are relevant for the considered system family. Based on the selected maneuver types and a selected system instance, the algorithm not only automatically optimizes the motions connecting pre-defined boundary conditions, but also simultaneously optimizes the end-point boundary conditions as well. This significantly reduces the time consuming part of manually specifying all boundary value problems that should be solved, and no exhaustive search to generate feasible motions is required. In addition to handling static a priori known system parameters, the framework also allows for fast automatic re-optimization of motion primitives if the system parameters change while the system is in use, e.g, if the load significantly changes or a trailer with a new geometry is picked up by an autonomous truck. We also show in several numerical examples that the framework can enhance the performance of the motion planner in terms of total cost for the produced solution.

math.OC↗

arXiv2017

Combining Homotopy Methods and Numerical Optimal Control to Solve Motion Planning Problems

This paper presents a systematic approach for computing local solutions to motion planning problems in non-convex environments using numerical optimal control techniques. It extends the range of use of state-of-the-art numerical optimal control tools to problem classes where these tools have previously not been applicable. Today these problems are typically solved using motion planners based on randomized or graph search. The general principle is to define a homotopy that perturbs, or preferably relaxes, the original problem to an easily solved problem. By combining a Sequential Quadratic Programming (SQP) method with a homotopy approach that gradually transforms the problem from a relaxed one to the original one, practically relevant locally optimal solutions to the motion planning problem can be computed. The approach is demonstrated in motion planning problems in challenging 2D and 3D environments, where the presented method significantly outperforms a state-of-the-art open-source optimizing sampled-based planner commonly used as benchmark.

math.OC↗