To make a modular robotic system both capable and scalable, the controller must be equally as modular as the mechanism. Given the large number of designs that can be generated from even a small set of modules, it becomes impractical to create a new system-wide controller for each design. Instead, we construct a modular control policy that handles a broad class of designs. We take the view that a module is both form and function, i.e. both mechanism and controller. As the modules are physically re-configured, the policy automatically re-configures to match the kinematic structure. This novel policy is trained with a new model-based reinforcement learning algorithm, which interleaves model learning and trajectory optimization to guide policy learning for multiple designs simultaneously. Training the policy on a varied set of designs teaches it how to adapt its behavior to the design. We show that the policy can then generalize to a larger set of designs not seen during training. We demonstrate one policy controlling many designs with different combinations of legs and wheels to locomote both in simulation and on real robots.
Dynamical systems with a distributed yet interconnected structure, like multi-rigid-body robots or large-scale multi-agent systems, introduce valuable sparsity into the system dynamics that can be exploited in an optimal control setting for speeding up computation and improving numerical conditioning. Conventional approaches for solving the Optimal Control Problem (OCP) rarely capitalize on such structural sparsity, and hence suffer from a cubic computational complexity growth as the dimensionality of the system scales. In this paper, we present an OCP formulation that relies on graphical models to capture the sparsely-interconnected nature of the system dynamics. Such a representational choice allows the use of contemporary graphical inference algorithms that enable our solver to achieve a linear time complexity in the state and control dimensions as well as the time horizon. We demonstrate the numerical and computational advantages of our approach on a canonical dynamical system in simulation.
In multi-agent applications such as surveillance and logistics, fleets of mobile agents are often expected to coordinate and safely visit a large number of goal locations as efficiently as possible. The multi-agent planning problem in these applications involves allocating and sequencing goals for each agent while simultaneously producing conflict-free paths for the agents. In this article, we introduce a new algorithm called MS* which computes an optimal solution for this multi-agent problem by fusing and advancing state of the art solvers for multi-agent path finding (MAPF) and multiple travelling salesman problem (mTSP). MS* leverages our prior subdimensional expansion approach for MAPF and embeds the mTSP solvers to optimally allocate and sequence goals for agents. Numerical results show that our new algorithm can solve the multi-agent problem with 20 agents and 50 goals in a minute of CPU time on a standard laptop.
Multi-agent path finding (MAPF) determines an ensemble of collision-free paths for multiple agents between their respective start and goal locations. Among the available MAPF planners for workspaces modeled as a graph, A*-based approaches have been widely investigated and have demonstrated their efficiency in numerous scenarios. However, almost all of these A*-based approaches assume that each agent executes an action concurrently in that all agents start and stop together. This article presents a natural generalization of MAPF with asynchronous actions where agents do not necessarily start and stop concurrently. The main contribution of the work is a proposed approach called Loosely Synchronized Search (LSS) that extends A*-based MAPF planners to handle asynchronous actions. We show LSS is complete and finds an optimal solution if one exists. We also combine LSS with other existing MAPF methods that aims to trade-off optimality for computational efficiency. Extensive numerical results are presented to corroborate the performance of the proposed approaches. Finally, we also verify the applicability of our method in the Robotarium, a remotely accessible swarm robotics research platform.
Conventional multi-agent path planners typically determine a path that optimizes a single objective, such as path length. Many applications, however, may require multiple objectives, say time-to-completion and fuel use, to be simultaneously optimized in the planning process. Often, these criteria may not be readily compared and sometimes lie in competition with each other. Simply applying standard multi-objective search algorithms to multi-agent path finding may prove to be inefficient because the size of the space of possible solutions, i.e., the Pareto-optimal set, can grow exponentially with the number of agents (the dimension of the search space). This paper presents an approach that bypasses this so-called curse of dimensionality by leveraging our prior multi-agent work with a framework called subdimensional expansion. One example of subdimensional expansion, when applied to A*, is called M* and M* was limited to a single objective function. We combine principles of dominance and subdimensional expansion to create a new algorithm named multi-objective M* (MOM*), which dynamically couples agents for planning only when those agents have to "interact" with each other. MOM* computes the complete Pareto-optimal set for multiple agents efficiently and naturally trades off sub-optimal approximations of the Pareto-optimal set and computational efficiency. Our approach is able to find the complete Pareto-optimal set for problem instances with hundreds of solutions which the standard multi-objective A* algorithms could not find within a bounded time.
Quadrotors can achieve aggressive flight by tracking complex maneuvers and rapidly changing directions. Planning for aggressive flight with trajectory optimization could be incredibly fast, even in higher dimensions, and can account for dynamics of the quadrotor, however, only provides a locally optimal solution. On the other hand, planning with discrete graph search can handle non-convex spaces to guarantee optimality but suffers from exponential complexity with the dimension of search. We introduce a framework for aggressive quadrotor trajectory generation with global reasoning capabilities that combines the best of trajectory optimization and discrete graph search. Specifically, we develop a novel algorithmic framework that \textit{interleaves} these two methods to complement each other and generate trajectories with provable guarantees on completeness up to discretization. We demonstrate and quantitatively analyze the performance of our algorithm in challenging simulation environments with narrow gaps that create severe attitude constraints and push the dynamic capabilities of the quadrotor. Experiments show the benefits of the proposed algorithmic framework over standalone trajectory optimization and graph search-based planning techniques for aggressive quadrotor flight.
Conventional multi-agent path planners typically compute an ensemble of paths while optimizing a single objective, such as path length. However, many applications may require multiple objectives, say fuel consumption and completion time, to be simultaneously optimized during planning and these criteria may not be readily compared and sometimes lie in competition with each other. Naively applying existing multi-objective search algorithms to multi-agent path finding may prove to be inefficient as the size of the space of possible solutions, i.e., the Pareto-optimal set, can grow exponentially with the number of agents (the dimension of the search space). This article presents an approach named Multi-objective Conflict-based Search (MO-CBS) that bypasses this so-called curse of dimensionality by leveraging prior Conflict-based Search (CBS), a well-known algorithm for single-objective multi-agent path finding, and principles of dominance from multi-objective optimization literature. We prove that MO-CBS is able to compute the entire Pareto-optimal set. Our results show that MO-CBS can solve problem instances with hundreds of Pareto-optimal solutions which the standard multi-objective A* algorithms could not find within a bounded time.
Snake robots composed of alternating single-axis pitch and yaw joints have many internal degrees of freedom, which make them capable of versatile three-dimensional locomotion. Often, snake robot motions are planned kinematically by a chronological sequence of continuous backbone curves that capture desired macroscopic shapes of the robot. However, as the geometric arrangement of single-axis rotary joints creates constraints on the rotations in the robot, it is challenging for the robot to reconstruct an arbitrary 3-D curve. When the robot configuration does not accurately achieve the desired shapes defined by these backbone curves, the robot can have undesired contact with the environment, such that the robot does not achieve the desired motion. In this work, we propose a method for snake robots to reconstruct desired backbone curves by posing an optimization problem that exploits the robot's geometric structure. We verified that our method enables accurate curve-configuration conversions through its applications to commonly used 3-D gaits. We also demonstrated via robot experiments that 1) our method results in smooth locomotion on the robot; 2) our method allows the robot to approach the numerically predicted locomotive performance of a sequence of continuous backbone curve.
Identifying landmarks in the femoral area is crucial for ultrasound (US) -based robot-guided catheter insertion, and their presentation varies when imaged with different scanners. As such, the performance of past deep learning-based approaches is also narrowly limited to the training data distribution; this can be circumvented by fine-tuning all or part of the model, yet the effects of fine-tuning are seldom discussed. In this work, we study the US-based segmentation of multiple classes through transfer learning by fine-tuning different contiguous blocks within the model, and evaluating on a gamut of US data from different scanners and settings. We propose a simple method for predicting generalization on unseen datasets and observe statistically significant differences between the fine-tuning methods while working towards domain generalization.
This paper presents a novel factor graph-based approach to solve the discrete-time finite-horizon Linear Quadratic Regulator problem subject to auxiliary linear equality constraints within and across time steps. We represent such optimal control problems using constrained factor graphs and optimize the factor graphs to obtain the optimal trajectory and the feedback control policies using the variable elimination algorithm with a modified Gram-Schmidt process. We prove that our approach has the same order of computational complexity as the state-of-the-art dynamic programming approach. Furthermore, current dynamic programming approaches can only handle equality constraints between variables at the same time step, but ours can handle equality constraints among any combination of variables at any time step while maintaining linear complexity with respect to trajectory length. Our approach can be used to efficiently generate trajectories and feedback control policies to achieve periodic motion or repetitive manipulation.