A Mixed-Integer Conic Program for the Moving-Target Traveling Salesman Problem based on a Graph of Convex Sets

This paper introduces a new formulation that finds the optimum for the Moving-Target Traveling Salesman Problem (MT-TSP), which seeks to find a shortest path for an agent, that starts at a depot, visits a set of moving targets exactly once within their assigned time-windows, and returns to the depot. The formulation relies on the key idea that when the targets move along lines, their trajectories become convex sets within the space-time coordinate system. The problem then reduces to finding the shortest path within a graph of convex sets, subject to some speed constraints. We compare our formulation with the current state-of-the-art Mixed Integer Conic Program (MICP) solver for the MT-TSP. The experimental results show that our formulation outperforms the MICP for instances with up to 20 targets, with up to two orders of magnitude reduction in runtime, and up to a 60\% tighter optimality gap. We also show that the solution cost from the convex relaxation of our formulation provides significantly tighter lower bounds for the MT-TSP than the ones from the MICP.

PINSAT: Parallelized Interleaving of Graph Search and Trajectory Optimization for Kinodynamic Motion Planning

Trajectory optimization is a widely used technique in robot motion planning for letting the dynamics and constraints on the system shape and synthesize complex behaviors. Several previous works have shown its benefits in high-dimensional continuous state spaces and under differential constraints. However, long time horizons and planning around obstacles in non-convex spaces pose challenges in guaranteeing convergence or finding optimal solutions. As a result, discrete graph search planners and sampling-based planers are preferred when facing obstacle-cluttered environments. A recently developed algorithm called INSAT effectively combines graph search in the low-dimensional subspace and trajectory optimization in the full-dimensional space for global kinodynamic planning over long horizons. Although INSAT successfully reasoned about and solved complex planning problems, the numerous expensive calls to an optimizer resulted in large planning times, thereby limiting its practical use. Inspired by the recent work on edge-based parallel graph search, we present PINSAT, which introduces systematic parallelization in INSAT to achieve lower planning times and higher success rates, while maintaining significantly lower costs over relevant baselines. We demonstrate PINSAT by evaluating it on 6 DoF kinodynamic manipulation planning with obstacles.

Preprocessing-based Kinodynamic Motion Planning Framework for Intercepting Projectiles using a Robot Manipulator

We are interested in studying sports with robots and starting with the problem of intercepting a projectile moving toward a robot manipulator equipped with a shield. To successfully perform this task, the robot needs to (i) detect the incoming projectile, (ii) predict the projectile's future motion, (iii) plan a minimum-time rapid trajectory that can evade obstacles and intercept the projectile, and (iv) execute the planned trajectory. These four steps must be performed under the manipulator's dynamic limits and extreme time constraints (<350ms in our setting) to successfully intercept the projectile. In addition, we want these trajectories to be smooth to reduce the robot's joint torques and the impulse on the platform on which it is mounted. To this end, we propose a kinodynamic motion planning framework that preprocesses smooth trajectories offline to allow real-time collision-free executions online. We present an end-to-end pipeline along with our planning framework, including perception, prediction, and execution modules. We evaluate our framework experimentally in simulation and show that it has a higher blocking success rate than the baselines. Further, we deploy our pipeline on a robotic system comprising an industrial arm (ABB IRB-1600) and an onboard stereo camera (ZED 2i), which achieves a 78% success rate in projectile interceptions.

DMS*: Minimizing Makespan for Multi-Agent Combinatorial Path Finding

Multi-Agent Combinatorial Path Finding (MCPF) seeks collision-free paths for multiple agents from their initial to goal locations, while visiting a set of intermediate target locations in the middle of the paths. MCPF is challenging as it involves both planning collision-free paths for multiple agents and target sequencing, i.e., solving traveling salesman problems to assign targets to and find the visiting order for the agents. Recent work develops methods to address MCPF while minimizing the sum of individual arrival times at goals. Such a problem formulation may result in paths with different arrival times and lead to a long makespan, the maximum arrival time, among the agents. This paper proposes a min-max variant of MCPF, denoted as MCPF-max, that minimizes the makespan of the agents. While the existing methods (such as MS*) for MCPF can be adapted to solve MCPF-max, we further develop two new techniques based on MS* to defer the expensive target sequencing during planning to expedite the overall computation. We analyze the properties of the resulting algorithm Deferred MS* (DMS*), and test DMS* with up to 20 agents and 80 targets. We demonstrate the use of DMS* on differential-drive robots.

C*: A New Bounding Approach for the Moving-Target Traveling Salesman Problem

We introduce a new bounding approach called Continuity* (C*) that provides optimality guarantees to the Moving-Target Traveling Salesman Problem (MT-TSP). Our approach relies on relaxing the continuity constraints on the agent's tour. This is done by partitioning the targets' trajectories into small sub-segments and allowing the agent to arrive at any point in one of the sub-segments and depart from any point in the same sub-segment when visiting each target. This lets us pose the bounding problem as a Generalized Traveling Salesman Problem (GTSP) in a graph where the cost of traveling an edge requires us to solve a new problem called the Shortest Feasible Travel (SFT). We also introduce C*-lite, which follows the same approach as C*, but uses simple and easy to compute lower-bounds to the SFT. We first prove that the proposed algorithms provide lower bounds to the MT-TSP. We also provide computational results to corroborate the performance of C* and C*-lite for instances with up to 15 targets. For the special case where targets travel along lines, we compare our C* variants with the SOCP based method, which is the current state-of-the-art solver for MT-TSP. While the SOCP based method performs well for instances with 5 and 10 targets, C* outperforms the SOCP based method for instances with 15 targets. For the general case, on average, our approaches find feasible solutions within ~4% of the lower bounds for the tested instances.

Motion Informed Needle Segmentation in Ultrasound Images

Segmenting a moving needle in ultrasound images is challenging due to the presence of artifacts, noise, and needle occlusion. This task becomes even more demanding in scenarios where data availability is limited. Convolutional Neural Networks (CNNs) have been successful in many computer vision applications, but struggle to accurately segment needles without considering their motion. In this paper, we present a novel approach for needle segmentation that combines classical Kalman Filter (KF) techniques with data-driven learning, incorporating both needle features and needle motion. Our method offers two key contributions. First, we propose a compatible framework that seamlessly integrates into commonly used encoder-decoder style architectures. Second, we demonstrate superior performance compared to recent state-of-the-art needle segmentation models using our novel convolutional neural network (CNN) based KF-inspired block, achieving a 15\% reduction in pixel-wise needle tip error and an 8\% reduction in length error. Third, to our knowledge we are the first to implement a learnable filter to incorporate non-linear needle motion for improving needle segmentation.

Multi-Objective Sparse Sensing with Ergodic Optimization

We consider a search problem where a robot has one or more types of sensors, each suited to detecting different types of targets or target information. Often, information in the form of a distribution of possible target locations, or locations of interest, may be available to guide the search. When multiple types of information exist, then a distribution for each type of information must also exist, thereby making the search problem that uses these distributions to guide the search a multi-objective one. In this paper, we consider a multi-objective search problem when the cost to use a sensor is limited. To this end, we leverage the ergodic metric, which drives agents to spend time in regions proportional to the expected amount of information there. We define the multi-objective sparse sensing ergodic (MO-SS-E) metric in order to optimize when and where each sensor measurement should be taken while planning trajectories that balance the multiple objectives. We observe that our approach maintains coverage performance as the number of samples taken considerably degrades. Further empirical results on different multi-agent problem setups demonstrate the applicability of our approach for both homogeneous and heterogeneous multi-agent teams.

Heuristic Search for Path Finding with Refuelling

This paper considers a generalization of the Path Finding (PF) with refueling constraints referred to as the Refuelling Path Finding (RF-PF) problem. Just like PF, the RF-PF problem is defined over a graph, where vertices are gas stations with known fuel prices, and edge costs depend on the gas consumption between the corresponding vertices. RF-PF seeks a minimum-cost path from the start to the goal vertex for a robot with a limited gas tank and a limited number of refuelling stops. While RF-PF is polynomial-time solvable, it remains a challenge to quickly compute an optimal solution in practice since the robot needs to simultaneously determine the path, where to make the stops, and the amount to refuel at each stop. This paper develops a heuristic search algorithm called Refuel A* (RF-A* ) that iteratively constructs partial solution paths from the start to the goal guided by a heuristic function while leveraging dominance rules for state pruning during planning. RF-A* is guaranteed to find an optimal solution and runs more than an order of magnitude faster than the existing state of the art (a polynomial time algorithm) when tested in large city maps with hundreds of gas stations.

Multi-agent Collective Construction using 3D Decomposition

This paper addresses a Multi-Agent Collective Construction (MACC) problem that aims to build a three-dimensional structure comprised of cubic blocks. We use cube-shaped robots that can carry one cubic block at a time, and move forward, reverse, left, and right to an adjacent cell of the same height or climb up and down one cube height. To construct structures taller than one cube, the robots must build supporting stairs made of blocks and remove the stairs once the structure is built. Conventional techniques solve for the entire structure at once and quickly become intractable for larger workspaces and complex structures, especially in a multi-agent setting. To this end, we present a decomposition algorithm that computes valid substructures based on intrinsic structural dependencies. We use Mixed Integer Linear Programming (MILP) to solve for each of these substructures and then aggregate the solutions to construct the entire structure. Extensive testing on 200 randomly generated structures shows an order of magnitude improvement in the solution computation time compared to an MILP approach without decomposition. Additionally, compared to Reinforcement Learning (RL) based and heuristics-based approaches drawn from the literature, our solution indicates orders of magnitude improvement in the number of pick-up and drop-off actions required to construct a structure. Furthermore, we leverage the independence between substructures to detect which sub-structures can be built in parallel. With this parallelization technique, we illustrate a further improvement in the number of time steps required to complete building the structure. This work is a step towards applying multi-agent collective construction for real-world structures by significantly reducing solution computation time with a bounded increase in the number of time steps required to build the structure.

Unsupervised Deformable Image Registration for Respiratory Motion Compensation in Ultrasound Images

In this paper, we present a novel deep-learning model for deformable registration of ultrasound images and an unsupervised approach to training this model. Our network employs recurrent all-pairs field transforms (RAFT) and a spatial transformer network (STN) to generate displacement fields at online rates (apprx. 30 Hz) and accurately track pixel movement. We call our approach unsupervised recurrent all-pairs field transforms (U-RAFT). In this work, we use U-RAFT to track pixels in a sequence of ultrasound images to cancel out respiratory motion in lung ultrasound images. We demonstrate our method on in-vivo porcine lung videos. We show a reduction of 76% in average pixel movement in the porcine dataset using respiratory motion compensation strategy. We believe U-RAFT is a promising tool for compensating different kinds of motions like respiration and heartbeat in ultrasound images of deformable tissue.