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Safe motion planning algorithms are necessary for deploying autonomous robots in unstructured environments. Motion plans must be safe to ensure that the robot does not harm humans or damage any nearby objects. Generating these motion plans…
We propose a continuous feedback control strategy that steers a point-mass vehicle safely to a destination, in a quasi-optimal manner, in sphere worlds. The main idea consists in avoiding each obstacle via the shortest path on the cone's…
This work presents proximally optimal predictive control algorithm, which is essentially a model-based lateral controller for steered autonomous vehicles that selects an optimal steering command within the neighborhood of previous steering…
Differential-driven wheeled robots (DWR) represent the quintessential type of mobile robots and find extensive appli- cations across the robotic field. Most high-performance control approaches for DWR explicitly utilize the linear and…
In this paper, we address the problem of time-optimal coordination of mobile robots under kinodynamic constraints along specified paths. We propose a novel approach based on time discretization that leads to a mixed-integer linear…
To achieve optimal robot behavior in dynamic scenarios we need to consider complex dynamics in a predictive manner. In the vehicle dynamics community, it is well know that to achieve time-optimal driving on low surface, the vehicle should…
It is a challenging task for ground robots to autonomously navigate in harsh environments due to the presence of non-trivial obstacles and uneven terrain. This requires trajectory planning that balances safety and efficiency. The primary…
We present a unified treatment of the abstract problem of finding the best approximation between a cone and spheres in the image of affine transformations. Prominent instances of this problem are phase retrieval and source localization. The…
This paper presents a spatial-based trajectory planning method for automated vehicles under actuator, obstacle avoidance, and vehicle dimension constraints. Starting from a nonlinear kinematic bicycle model, vehicle dynamics are transformed…
Sequential Convex Programming (SCP) has recently gained popularity as a tool for trajectory optimization due to its sound theoretical properties and practical performance. Yet, most SCP-based methods for trajectory optimization are…
We address the problem of planning robot motions in constrained configuration spaces where the constraints change throughout the motion. The problem is formulated as a fixed sequence of intersecting manifolds, which the robot needs to…
Trained humans exhibit highly agile spatial skills, enabling them to operate vehicles with complex dynamics in demanding tasks and conditions. Prior work shows that humans achieve this performance by using strategies such as satisficing,…
This paper presents an enhanced direct-method-based approach for the real-time solution of optimal control problems to handle path constraints, such as obstacles. The principal contributions of this work are twofold: first, the existing…
This paper focuses on the energy-time optimal control of wheeled mobile robots undergoing point-to-point transitions in an obstacles free space. Two interchangeable models are used to arrive at the necessary conditions for optimality. The…
We study the parameterized complexity of a generalization of the coordinated motion planning problem on graphs, where the goal is to route a specified subset of a given set of $k$ robots to their destinations with the aim of minimizing the…
Safety-guaranteed motion planning is critical for self-driving cars to generate collision-free trajectories. A layered motion planning approach with decoupled path and speed planning is widely used for this purpose. This approach is prone…
The Capacitated Vehicle Routing Problem (CVRP) is a core NP-hard problem in the field of combinatorial optimization. It aims to plan optimal routes for a fleet of vehicles with uniform capacity, serving a set of customers with specific…
The minimum-time path for intercepting a moving target with a prescribed impact angle is studied in the paper. The candidate paths from Pontryagin's maximum principle are analyzed, so that each candidate is related to a zero of a…
Pathfinding in Euclidean space is a common problem faced in robotics and computer games. For long-distance navigation on the surface of the earth or in outer space however, approximating the geometry as Euclidean can be insufficient for…
In this paper the computational challenges of time-optimal path following are addressed. The standard approach is to minimize the travel time, which inevitably leads to singularities at zero path speed, when reformulating the optimization…