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Trajectory optimization methods for motion planning attempt to generate trajectories that minimize a suitable objective function. Such methods efficiently find solutions even for high degree-of-freedom robots. However, a globally optimal…
Motion planning for a general 2-trailer system poses a hard problem for any motion planning algorithm and previous methods have lacked any completeness or optimality guarantees. In this work we present a lattice-based motion planning…
We consider the speed planning problem for a robotic manipulator. In particular, we present an algorithm for finding the time-optimal speed law along an assigned path that satisfies velocity and acceleration constraints and respects the…
In this paper we present a method for automatically planning robust optimal paths for a group of robots that satisfy a common high level mission specification. Each robot's motion in the environment is modeled as a weighted transition…
Gaussian mixture alignment is a family of approaches that are frequently used for robustly solving the point-set registration problem. However, since they use local optimisation, they are susceptible to local minima and can only guarantee…
We address the problem of minimizing a class of energy functions consisting of data and smoothness terms that commonly occur in machine learning, computer vision, and pattern recognition. While discrete optimization methods are able to give…
In this paper, we introduce dynamics factor graphs as a graphical framework to solve dynamics problems and kinodynamic motion planning problems with full consideration of whole-body dynamics and contacts. A factor graph representation of…
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…
As autonomous robots move into complex, dynamic real-world environments, they must learn to navigate safely in real time, yet anticipating all possible behaviors is infeasible. We propose a composable, model-free reinforcement learning…
We consider the problem of learning a linear control policy for a linear dynamical system, from demonstrations of an expert regulating the system. The standard approach to this problem is policy fitting, which fits a linear policy by…
Equipping approximate dynamic programming (ADP) with inputconstraints has a tremendous significance. This enables ADP to be applied tothe systems with actuator limitations, which is quite common for dynamicalsystems. In a conventional…
We address the risk bounded trajectory optimization problem of stochastic nonlinear robotic systems. More precisely, we consider the motion planning problem in which the robot has stochastic nonlinear dynamics and uncertain initial…
Autonomous motion planning is critical for efficient and safe underwater manipulation in dynamic marine environments. Current motion planning methods often fail to effectively utilize prior motion experiences and adapt to real-time…
Learning Mahalanobis metric spaces is an important problem that has found numerous applications. Several algorithms have been designed for this problem, including Information Theoretic Metric Learning (ITML) [Davis et al. 2007] and Large…
The K-means algorithm is one of the most widely studied clustering algorithms in machine learning. While extensive research has focused on its ability to achieve a globally optimal solution, there still lacks a rigorous analysis of its…
Recent work [Ran22] formulated a class of optimal control problems involving positive linear systems, linear stage costs, and elementwise constraints on control. It was shown that the problem admits linear optimal cost and the associated…
In applications with significant class imbalance or asymmetric costs, metrics such as the $F_\beta$-measure, AM measure, Jaccard similarity coefficient, and weighted accuracy offer more suitable evaluation criteria than standard binary…
Algorithms for motion planning in unknown environments are generally limited in their ability to reason about the structure of the unobserved environment. As such, current methods generally navigate unknown environments by relying on…
Geometric motion planning offers effective and interpretable gait analysis and optimization tools for locomoting systems. However, due to the curse of dimensionality in coordinate optimization, a key component of geometric motion planning,…
Generalized linear models (GLMs) arise in high-dimensional machine learning, statistics, communications and signal processing. In this paper we analyze GLMs when the data matrix is random, as relevant in problems such as compressed sensing,…