This paper addresses the challenge of planning a sequence of tasks to be performed by multiple robots while minimizing the overall completion time subject to timing and precedence constraints. Our approach uses the Timed Partial Orders (TPO) model to specify these constraints. We translate this problem into a Traveling Salesman Problem (TSP) variant with timing and precedent constraints, and we solve it as a Mixed Integer Linear Programming (MILP) problem. Our contributions include a general planning framework for TPO specifications, a MILP formulation accommodating time windows and precedent constraints, its extension to multi-robot scenarios, and a method to quantify plan robustness. We demonstrate our framework on several case studies, including an aircraft turnaround task involving three Jackal robots, highlighting the approach’s potential applicability to important real-world problems. Our benchmark results show that our MILP method outperforms state-of-the-art open-source TSP solvers OR-Tools.

We present an algorithm for learning switched linear dynamical systems in discrete time from noisy observations of the system's full state or output. Switched linear systems use multiple linear dynamical modes to fit the data within some desired tolerance. They arise quite naturally in applications to robotics and cyber-physical systems. Learning switched systems from data is a NP-hard problem that is nearly identical to the $k$-linear regression problem of fitting $k > 1$ linear models to the data. A direct mixed-integer linear programming (MILP) approach yields time complexity that is exponential in the number of data points. In this paper, we modify the problem formulation to yield an algorithm that is linear in the size of the data while remaining exponential in the number of state variables and the desired number of modes. To do so, we combine classic ideas from the ellipsoidal method for solving convex optimization problems, and well-known oracle separation results in non-smooth optimization. We demonstrate our approach on a set of microbenchmarks and a few interesting real-world problems. Our evaluation suggests that the benefits of this algorithm can be made practical even against highly optimized off-the-shelf MILP solvers.

This paper proposes a framework for learning task specifications from demonstrations, while ensuring that the learned specifications do not violate safety constraints. Furthermore, we show how these specifications can be used in a planning problem to control the robot under environments that can be different from those encountered during the learning phase. We formulate the specification learning problem as a grammatical inference problem, using probabilistic automata to represent specifications. The edge probabilities of the resulting automata represent the demonstrator's preferences. The main novelty in our approach is to incorporate the safety property during the learning process. We prove that the resulting automaton always respects a pre-specified safety property, and furthermore, the proposed method can easily be included in any Evidence-Driven State Merging (EDSM)-based automaton learning scheme. Finally, we introduce a planning algorithm that produces the most desirable plan by maximizing the probability of an accepting trace of the automaton. Case studies show that our algorithm learns the true probability distribution most accurately while maintaining safety. Since, specification is detached from the robot's environment model, a satisfying plan can be synthesized for a variety of different robots and environments including both mobile robots and manipulators.

In this paper, we present an accelerometer-based kinematic calibration algorithm to accurately estimate the pose of multiple sensor units distributed along a robot body. Our approach is self-contained, can be used on any robot provided with a Denavit-Hartenberg kinematic model, and on any skin equipped with Inertial Measurement Units (IMUs). To validate the proposed method, we first conduct extensive experimentation in simulation and demonstrate a sub-cm positional error from ground truth data—an improvement of six times with respect to prior work; subsequently, we then perform a real-world evaluation on a seven degrees-of-freedom collaborative platform. For this purpose, we additionally introduce a novel design for a stand-alone artificial skin equipped with an IMU for use with the proposed algorithm and a proximity sensor for sensing distance to nearby objects. In conclusion, in this work, we demonstrate seamless integration between a novel hardware design, an accurate calibration method, and preliminary work on applications: the high positional accuracy effectively enables to locate distributed proximity data and allows for a distributed avoidance controller to safely avoid obstacles and people without the need of additional sensing.