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Trajectory planning for quadrotors in cluttered environments has been challenging in recent years. While many trajectory planning frameworks have been successful, there still exists potential for improvements, particularly in enhancing the…
This paper proposes a novel mission planning algorithm for autonomous robots that selects an optimal waypoint sequence from a predefined set to maximize total reward while satisfying obstacle avoidance, state, input, derivative, mission…
We introduce a convergent finite difference method for solving the optimal transportation problem on the sphere. The method applies to both the traditional squared geodesic cost (arising in mesh generation) and a logarithmic cost (arising…
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…
This paper considers a trajectory planning problem for a robot navigating complex terrains, which arises in applications ranging from autonomous mining vehicles to planetary rovers. The problem seeks to find a low-cost dynamically feasible…
Optimization-based methods are widely used for computing fast, diverse solutions for complex tasks such as collision-free movement or planning in the presence of contacts. However, most of these methods require enforcing non-penetration…
Path planning has long been one of the major research areas in robotics, with PRM and RRT being two of the most effective classes of planners. Though generally very efficient, these sampling-based planners can become computationally…
Existing motion planning methods often have two drawbacks: 1) goal configurations need to be specified by a user, and 2) only a single solution is generated under a given condition. In practice, multiple possible goal configurations exist…
In this series of papers, we present a motion planning framework for planning comfortable and customizable motion of nonholonomic mobile robots such as intelligent wheelchairs and autonomous cars. In this first one we present the…
In this paper, we address the problem of safe trajectory planning for autonomous search and exploration in constrained, cluttered environments. Guaranteeing safe (collision-free) trajectories is a challenging problem that has garnered…
Trajectory planning is a critical component in ensuring the safety, stability, and efficiency of autonomous vehicles. While existing trajectory planning methods have achieved progress, they often suffer from high computational costs,…
This paper initiates a systematic development of a theory of non-commutative optimization. It aims to unify and generalize a growing body of work from the past few years which developed and analyzed algorithms for natural geodesically…
Bernstein polynomial approximation to a continuous function has a slower rate of convergence as compared to other approximation methods. "The fact seems to have precluded any numerical application of Bernstein polynomials from having been…
Intelligent autonomous path planning is essential for enhancing the exploration efficiency of mobile robots operating in uneven terrains like planetary surfaces and off-road environments.In this paper, we propose the NNPP model for…
We describe a general probabilistic framework to address a variety of Frechet-distance optimization problems. Specifically, we are interested in finding minimal bottleneck-paths in $d$-dimensional Euclidean space between given start and…
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…
Automated chemical synthesis, materials fabrication, and spectroscopic physical measurements often bring forth the challenge of process trajectory optimization, i.e., discovering the time dependence of temperature, electric field, or…
In this paper we propose a variant of the random coordinate descent method for solving linearly constrained convex optimization problems with composite objective functions. If the smooth part of the objective function has Lipschitz…
The Euclidean space notion of convex sets (and functions) generalizes to Riemannian manifolds in a natural sense and is called geodesic convexity. Extensively studied computational problems such as convex optimization and sampling in convex…
Geofences have attracted significant attention in the design of spatial and virtual regions for managing and engaging spatiotemporal events. By using geofences to monitor human activity across their boundaries, content providers can create…