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.
Toussaint @cite_8 has utilized stability checks for building some tallest stable tower from a set of unlabeled cylinders and blocks; no goal condition is specified. His method applies a restricted version of task planning to decide for the order of manipulation actions, based on simple Strips operators and Monte Carlo tree search, and considers a restricted form of stability check that depends on whether the objects are placed on support areas of other objects. Due to these restrictions, his method is limited to building towers with sequential plans.
@cite_8
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Motivated by the need to simultaneously guarantee safety and stability of safety-critical dynamical systems, we construct permissive barrier certificates in this paper that explicitly maximize the region where the system can be stabilized without violating safety constraints. An iterative search algorithm is developed to search for the maximum volume barrier certified region of safe stabilization. The barrier certified region, which is allowed to take any arbitrary shape, is proved to be strictly larger than safe regions generated with Lyapunov sublevel set based methods. The proposed approach effectively unites a Lyapunov function with multiple barrier functions that might not be compatible with each other. Simulation results of the iterative search algorithm demonstrate the effectiveness of the proposed method. In this paper, we carry on investigating the line of research questioning the power of randomization for the design of distributed algorithms. In their seminal paper, Naor and Stockmeyer [STOC 1993] established that, in the context of network computing, in which all nodes execute the same algorithm in parallel, any construction task that can be solved locally by a randomized Monte-Carlo algorithm can also be solved locally by a deterministic algorithm. This result however holds in a specific context. In particular, it holds only for distributed tasks whose solutions can be locally checked by a deterministic algorithm. In this paper, we extend the result of Naor and Stockmeyer to a wider class of tasks. Specifically, we prove that the same derandomization result holds for every task whose solutions can be locally checked using a 2-sided error randomized Monte-Carlo algorithm. This extension finds applications to, e.g., the design of lower bounds for construction tasks which tolerate that some nodes compute incorrect values. In a nutshell, we show that randomization does not help for solving such resilient tasks. This paper presents a safe learning framework that employs an adaptive model learning method together with barrier certificates for systems with possibly nonstationary agent dynamics. To extract the dynamic structure of the model, we use a sparse optimization technique, and the resulting model will be used in combination with control barrier certificates which constrain policies (feedback controllers) in order to maintain safety, which refers to avoiding certain regions of the state space. Under certain conditions, recovery of safety in the sense of Lyapunov stability after violations of safety due to the nonstationarity is guaranteed. In addition, we reformulate action-value function approximation to make any kernel-based nonlinear function estimation method applicable to our adaptive learning framework. Lastly, solutions to the barrier-certified policy optimization are guaranteed to be globally optimal, ensuring greedy policy updates under mild conditions. The resulting framework is validated via simulations of a quadrotor, which has been used in the safe learnings literature under stationarity assumption, and then tested on a real robot called brushbot , whose dynamics is unknown, highly complex, and most probably nonstationary. Here, we propose a planning method for knotting unknotting of deformable linear objects. First, we propose a topological description of the state of a linear object. Second, transitions between these states are defined by introducing four basic operations. Then, possible sequences of crossing state transitions, i.e. possible manipulation processes, can be generated once the initial and the objective states are given. Third, a method for determining grasping points and their directions of movement is proposed to realize derived manipulation processes. Our proposed method indicated that it is theoretically possible for any knotting manipulation of a linear object placed on a table to be realized by a one-handed robot with three translational DOF and one rotational DOF. Furthermore, criteria for evaluation of generated plans are introduced to reduce the candidates of manipulation plans. Fourth, a planning method for tying knots tightly is established because they fulfill their fixing function by tightening them. Finally, we report knotting unknotting manipulation performed by a vision-guided system to demonstrate the usefulness of our approach.