We study robot construction problems where multiple autonomous robots rearrange stacks of prefabricated blocks to build stable structures. These problems are challenging due to ramifications of actions, true concurrency, and requirements of supportedness of blocks by other blocks and stability of the structure at all times. We propose a formal hybrid planning framework to solve a wide range of robot construction problems, based on Answer Set Programming. This framework not only decides for a stable final configuration of the structure, but also computes the order of manipulation tasks for multiple autonomous robots to build the structure from an initial configuration, while simultaneously ensuring the stability, supportedness and other desired properties of the partial construction at each step of the plan. We prove the soundness and completeness of our formal method with respect to these properties. We introduce a set of challenging robot construction benchmark instances, including bridge building and stack overhanging scenarios, discuss the usefulness of our framework over these instances, and demonstrate the applicability of our method using a bimanual Baxter robot.
Later, Fahlman @cite_29 has introduced a set of robot construction problems where the goal is for a robot to build specified structures out of simple blocks of different shapes and sizes. These problems allow incorporation of subassemblies into the final design, and the use of extra blocks as temporary supports or counterweights during construction; they also consider collisions of blocks and instability of the structures, but not motion planning. Since Fahlman's main interest was in maximizing common sense (rather than soundness, completeness or optimality), he implemented a planning system guided with heuristics to solve some of these problems. These problems have not been investigated with a formal approach since then.
@cite_29
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We present an algorithm that enables a humanoid robot to reason about its environment and use the available objects to build bridges, stairs and lever-fulcrum systems. Facing a challenge that is otherwise intractable, such as climbing a height or moving a heavy object, the proposed planner reasons about the physical limitations of the robot to design functional structures. Inducing constraints on the space of possible designs within a classical planning framework, the algorithm outputs feasible structures that can be used towards accomplishing goals. We present results in dynamic simulation with Golem Hubo, walking on a bridge to cross a hazardous area, and in real-world with Golem Krang, overturning 100 kg loads and pushing 240 kg obstacles. We present a scalable robot motion planning algorithm for reach-avoid problems. We assume a discrete-time, linear model of the robot dynamics and a workspace described by a set of obstacles and a target region, where both the obstacles and the region are polyhedra. Our goal is to construct a trajectory, and the associated control strategy, that steers the robot from its initial point to the target while avoiding obstacles. Differently from previous approaches, based on the discretization of the continuous state space or uniform discretization of the workspace, our approach, inspired by the lazy satisfiability modulo theory paradigm, decomposes the planning problem into smaller subproblems, which can be efficiently solved using specialized solvers. At each iteration, we use a coarse, obstacle-based discretization of the workspace to obtain candidate high-level, discrete plans that solve a set of Boolean constraints, while completely abstracting the low-level continuous dynamics. The feasibility of the proposed plans is then checked via a convex program, under constraints on both the system dynamics and the control inputs, and new candidate plans are generated until a feasible one is found. To achieve scalability, we show how to generate succinct explanations for the infeasibility of a discrete plan by exploiting a relaxation of the convex program that allows detecting the earliest possible occurrence of an infeasible transition between workspace regions. Simulation results show that our algorithm favorably compares with state-of-the-art techniques and scales well for complex systems, including robot dynamics with up to 50 continuous states. This paper presents a novel randomized motion planner for robots that must achieve a specified goal under kinematic and or dynamic motion constraints while avoiding collision with moving obstacles with known trajectories. The planner encodes the motion constraints on the robot with a control system and samples the robot's state × time space by picking control inputs at random and integrating its equations of motion. The result is a probabilistic roadmap of sampled state ×time points, called milestones, connected by short admissible trajectories. The planner does not precompute the roadmap; instead, for each planning query, it generates a new roadmap to connect an initial and a goal state×time point. The paper presents a detailed analysis of the planner's convergence rate. It shows that, if the state×time space satisfies a geometric property called expansiveness, then a slightly idealized version of our implemented planner is guaranteed to find a trajectory when one exists, with probability quickly converg... We consider the problem of navigating a mobile robot through dense human crowds. We begin by exploring a fundamental impediment to classical motion planning algorithms called the âfreezing robot problemâ: once the environment surpasses a certain level of dynamic complexity, the planner decides that all forward paths are unsafe, and the robot freezes in place or performs unnecessary maneuvers to avoid collisions. We argue that this problem can be avoided if the robot anticipates human cooperation, and accordingly we develop interacting Gaussian processes, a prediction density that captures cooperative collision avoidance, and a âmultiple goalâ extension that models the goal-driven nature of human decision making. We validate this model with an empirical study of robot navigation in dense human crowds 488 runs, specifically testing how cooperation models effect navigation performance. The multiple goal interacting Gaussian processes algorithm performs comparably with human teleoperators in crowd densities nearing 0.8 humans m2, while a state-of-the-art non-cooperative planner exhibits unsafe behavior more than three times as often as the multiple goal extension, and twice as often as the basic interacting Gaussian process approach. Furthermore, a reactive planner based on the widely used dynamic window approach proves insufficient for crowd densities above 0.55 people m2. We also show that our non-cooperative planner or our reactive planner capture the salient characteristics of nearly any dynamic navigation algorithm. Based on these experimental results and theoretical observations, we conclude that a cooperation model is critical for safe and efficient robot navigation in dense human crowds.