Learning scalable and transferable multi-robot/machine sequential assignment planning via graph embedding

Can the success of reinforcement learning methods for simple combinatorial optimization problems be extended to multi-robot sequential assignment planning? In addition to the challenge of achieving near-optimal performance in large problems, transferability to an unseen number of robots and tasks is another key challenge for real-world applications. In this paper, we suggest a method that achieves the first success in both challenges for robot/machine scheduling problems. Our method comprises of three components. First, we show a robot scheduling problem can be expressed as a random probabilistic graphical model (PGM). We develop a mean-field inference method for random PGM and use it for Q-function inference. Second, we show that transferability can be achieved by carefully designing two-step sequential encoding of problem state. Third, we resolve the computational scalability issue of fitted Q-iteration by suggesting a heuristic auction-based Q-iteration fitting method enabled by transferability we achieved. We apply our method to discrete-time, discrete space problems (Multi-Robot Reward Collection (MRRC)) and scalably achieve 97% optimality with transferability. This optimality is maintained under stochastic contexts. By extending our method to continuous time, continuous space formulation, we claim to be the first learning-based method with scalable performance among multi-machine scheduling problems; our method scalability achieves comparable performance to popular metaheuristics in Identical parallel machine scheduling (IPMS) problems

The Critical Radius in Sampling-based Motion Planning

We develop a new analysis of sampling-based motion planning in Euclidean space with uniform random sampling, which significantly improves upon the celebrated result of Karaman and Frazzoli (2011) and subsequent work. Particularly, we prove the existence of a critical connection radius proportional to ${\Theta(n^{-1/d})}$ for $n$ samples and ${d}$ dimensions: Below this value the planner is guaranteed to fail (similarly shown by the aforementioned work, ibid.). More importantly, for larger radius values the planner is asymptotically (near-)optimal. Furthermore, our analysis yields an explicit lower bound of ${1-O( n^{-1})}$ on the probability of success. A practical implication of our work is that asymptotic (near-)optimality is achieved when each sample is connected to only ${\Theta(1)}$ neighbors. This is in stark contrast to previous work which requires ${\Theta(\log n)}$ connections, that are induced by a radius of order ${\left(\frac{\log n}{n}\right)^{1/d}}$. Our analysis is not restricted to PRM and applies to a variety of PRM-based planners, including RRG, FMT* and BTT. Continuum percolation plays an important role in our proofs. Lastly, we develop similar theory for all the aforementioned planners when constructed with deterministic samples, which are then sparsified in a randomized fashion. We believe that this new model, and its analysis, is interesting in its own right

Scaling Robot Motion Planning to Multi-core Processors and the Cloud

Imagine a world in which robots safely interoperate with humans, gracefully and efficiently accomplishing everyday tasks. The robot's motions for these tasks, constrained by the design of the robot and task at hand, must avoid collisions with obstacles. Unfortunately, planning a constrained obstacle-free motion for a robot is computationally complex---often resulting in slow computation of inefficient motions. The methods in this dissertation speed up this motion plan computation with new algorithms and data structures that leverage readily available parallel processing, whether that processing power is on the robot or in the cloud, enabling robots to operate safer, more gracefully, and with improved efficiency. The contributions of this dissertation that enable faster motion planning are novel parallel lock-free algorithms, fast and concurrent nearest neighbor searching data structures, cache-aware operation, and split robot-cloud computation. Parallel lock-free algorithms avoid contention over shared data structures, resulting in empirical speedup proportional to the number of CPU cores working on the problem. Fast nearest neighbor data structures speed up searching in SO(3) and SE(3) metric spaces, which are needed for rigid body motion planning. Concurrent nearest neighbor data structures improve searching performance on metric spaces common to robot motion planning problems, while providing asymptotic wait-free concurrent operation. Cache-aware operation avoids long memory access times, allowing the algorithm to exhibit superlinear speedup. Split robot-cloud computation enables robots with low-power CPUs to react to changing environments by having the robot compute reactive paths in real-time from a set of motion plan options generated in a computationally intensive cloud-based algorithm. We demonstrate the scalability and effectiveness of our contributions in solving motion planning problems both in simulation and on physical robots of varying design and complexity. Problems include finding a solution to a complex motion planning problem, pre-computing motion plans that converge towards the optimal, and reactive interaction with dynamic environments. Robots include 2D holonomic robots, 3D rigid-body robots, a self-driving 1/10 scale car, articulated robot arms with and without mobile bases, and a small humanoid robot.Doctor of Philosoph