Robotic pick-and-place (PnP) operations on moving conveyors find a wide range of industrial applications. In practice, simple greedy heuristics (e.g., prioritization based on the time to process a single object) are applied that achieve reasonable efficiency. We show analytically that, under a simplified telescoping robot model, these greedy approaches do not ensure time optimality of PnP operations. To address the shortcomings of classical solutions, we develop algorithms that compute optimal object picking sequences for a predetermined finite horizon. Employing dynamic programming techniques and additional heuristics, our methods scale to up to tens to hundreds of objects. In particular, the fast algorithms we develop come with running time guarantees, making them suitable for real-time PnP applications demanding high throughput. Extensive evaluation of our algorithmic solution over dominant industrial PnP robots used in real-world applications, i.e., Delta robots and Selective Compliance Assembly Robot Arm (SCARA) robots, shows that a typical efficiency gain of around 10-40% over greedy approaches can be realized. Figure 1: A few conveyor-based robotic PnP systems (a) Two Selective Compliance Assembly Robot Arm (SCARA) robots working on picking and placing machine parts (b) (c) Delta robots packing food items.A fairly thorough fundamental algorithmic study of conveyor-based robotic PnP is carried out [9], where several polynomial-time approximation algorithms are provided for a variety of PnP problems. The work also pointed out that many such problems are at least NP-Hard [10,11], given the similarity between robotic PnP and the traveling salesperson problem (TSP). This and other studies, e.g., [12], also link the robotic PnP problem to classical vehicle routing problems (VRP), which has many variations on its own [13][14][15][16]. We note that while polynomial-time approximation algorithms for PnP have been proposed [9], the algorithms optimize over metrics like L 1 and the approximately optimal solutions are not practical. The study also does not sufficiently consider robot geometry and dynamics, which are very important factors in real-world applications.When it comes to practically efficient algorithmic solutions for PnP operations over a conveyer, the first proposed solutions resorted to a first-in first-out (FIFO) rule for prioritizing the object picking order [17,18]. As pointed out, the FIFO heuristic can result in fairly sub-optimal solutions [19]. To address this, a job scheduling rule called shortest processing time (SPT) [20] was employed [19]. With further improvements, SPT and variants are shown to be consistently superior to FIFO. Since [19], research on PnP over conveyor appears to have shifted to using multiple robot arms to further boost the throughput. Among these, noncooperative game theory was explored [21] whereas FIFO and SPT heuristics are employed [22]. A recent approach combines randomized adaptive search with Monte Carlo simulation [23]. Contributions. The main contributions of this ...

We perform structural and algorithmic studies of significantly generalized versions of the optimal perimeter guarding (OPG) problem [1]. As compared with the original OPG where robots are uniform, in this paper, many mobile robots with heterogeneous sensing capabilities are to be deployed to optimally guard a set of one-dimensional segments. Two complimentary formulations are investigated where one limits the number of available robots (OPGLR) and the other seeks to minimize the total deployment cost (OPGMC ). In contrast to the original OPG which admits low-polynomial time solutions, both OPGLR and OPGMC are computationally intractable with OPGLR being strongly NP-hard. Nevertheless, we develop fairly scalable pseudo-polynomial time algorithms for practical, fixed-parameter subcase of OPGLR; we also develop pseudo-polynomial time algorithm for general OPGMC and polynomial time algorithm for the fixed-parameter OPGMC case. The applicability and effectiveness of selected algorithms are demonstrated through extensive numerical experiments.

We investigate the problem of optimally assigning a large number of robots (or other types of autonomous agents) to guard the perimeters of closed 2D regions, where the perimeter of each region to be guarded may contain multiple disjoint polygonal chains. Each robot is responsible for guarding a subset of a perimeter and any point on a perimeter must be guarded by some robot. In allocating the robots, the main objective is to minimize the maximum 1D distance to be covered by any robot along the boundary of the regions. For this optimization problem which we call optimal perimeter guarding (OPG), thorough structural analysis is performed, which is then exploited to develop fast exact algorithms that run in guaranteed low polynomial time. In addition to formal analysis and proofs, experimental evaluations and simulations are performed that further validate the correctness and effectiveness of our algorithmic results.