Related papers: An RRT* algorithm based on Riemannian metric model…
In this paper, the Riemannian gradient algorithm and the natural gradient algorithm are applied to solve descent direction problems on the manifold of positive definite Hermitian matrices, where the geodesic distance is considered as the…
Optimization with orthogonality constraints frequently arises in various fields such as machine learning. Riemannian optimization offers a powerful framework for solving these problems by equipping the constraint set with a Riemannian…
Various tasks in scientific computing can be modeled as an optimization problem on the indefinite Stiefel manifold. We address this using the Riemannian approach, which basically consists of equipping the feasible set with a Riemannian…
Constrained motion planning is a common but challenging problem in robotic manipulation. In recent years, data-driven constrained motion planning algorithms have shown impressive planning speed and success rate. Among them, the latent…
On-line motion planning in unknown environments is a challenging problem as it requires (i) ensuring collision avoidance and (ii) minimizing the motion time, while continuously predicting where to go next. Previous approaches to on-line…
Path planning plays an important role in autonomous robot systems. Effective understanding of the surrounding environment and efficient generation of optimal collision-free path are both critical parts for solving path planning problem.…
This paper proposes the Real-Time Fast Marching Tree (RT-FMT), a real-time planning algorithm that features local and global path generation, multiple-query planning, and dynamic obstacle avoidance. During the search, RT-FMT quickly looks…
Planning safe paths in 3D workspace for high DoF robotic systems, such as manipulators, is a challenging problem, especially when the environment is populated with the dynamic obstacles that need to be avoided. In this case the time…
Bayesian optimization is a data-efficient technique which can be used for control parameter tuning, parametric policy adaptation, and structure design in robotics. Many of these problems require optimization of functions defined on…
Path planning for wheeled mobile robots is a critical component in the field of automation and intelligent transportation systems. Car-like vehicles, which have non-holonomic constraints on their movement capability impose additional…
Optimal transport (OT) is a powerful tool for measuring the distance between two defined probability distributions. In this paper, we develop a new manifold named the coupling matrix manifold (CMM), where each point on CMM can be regarded…
Trajectory planning tasks for non-holonomic or collaborative systems are naturally modeled by state spaces with non-Euclidean metrics. However, existing proofs of convergence for sample-based motion planners only consider the setting of…
Learning motion planners to move robot from one point to another within an obstacle-occupied space in a collision-free manner requires either an extensive amount of data or high-quality demonstrations. This requirement is caused by the fact…
This paper introduces a new metric and mean on the set of positive semidefinite matrices of fixed-rank. The proposed metric is derived from a well-chosen Riemannian quotient geometry that generalizes the reductive geometry of the positive…
Cooperative path planning is gaining its importance due to the increasing demand on using multiple unmanned aerial vehicles (UAVs) for complex missions. This work addresses the problem by introducing a new algorithm named MultiRRT that…
This paper presents a novel image-based path planning algorithm that was developed using computer vision techniques, as well as its comparative analysis with well-known deterministic and probabilistic algorithms, namely A* and Probabilistic…
Manifold learning has been proven to be an effective method for capturing the implicitly intrinsic structure of non-Euclidean data, in which one of the primary challenges is how to maintain the distortion-free (isometry) of the data…
We propose a new algorithm to solve optimization problems of the form $\min f(X)$ for a smooth function $f$ under the constraints that $X$ is positive semidefinite and the diagonal blocks of $X$ are small identity matrices. Such problems…
In this work, we present a method for minimizing the time required for a redundant dual-arm robot to follow a desired relative Cartesian path at constant path speed by optimizing its joint trajectories, subject to position, velocity, and…
Probabilistic sampling-based algorithms, such as the probabilistic roadmap (PRM) and the rapidly-exploring random tree (RRT) algorithms, represent one of the most successful approaches to robotic motion planning, due to their strong…