Towards Efficient Full Pose Omnidirectionality with Overactuated MAVs

Omnidirectional MAVs are a growing field, with demonstrated advantages for aerial interaction and uninhibited observation. While systems with complete pose omnidirectionality and high hover efficiency have been developed independently, a robust system that combines the two has not been demonstrated to date. This paper presents VoliroX: a novel omnidirectional vehicle that can exert a wrench in any orientation while maintaining efficient flight configurations. The system design is presented, and a 6 DOF geometric control that is robust to singularities. Flight experiments further demonstrate and verify its capabilities.Comment: 10 pages, 6 figures, ISER 2018 conference submissio

On Time-optimal Trajectories for a Car-like Robot with One Trailer

In addition to the theoretical value of challenging optimal control problmes, recent progress in autonomous vehicles mandates further research in optimal motion planning for wheeled vehicles. Since current numerical optimal control techniques suffer from either the curse of dimens ionality, e.g. the Hamilton-Jacobi-Bellman equation, or the curse of complexity, e.g. pseudospectral optimal control and max-plus methods, analytical characterization of geodesics for wheeled vehicles becomes important not only from a theoretical point of view but also from a prac tical one. Such an analytical characterization provides a fast motion planning algorithm that can be used in robust feedback loops. In this work, we use the Pontryagin Maximum Principle to characterize extremal trajectories, i.e. candidate geodesics, for a car-like robot with one trailer. We use time as the distance function. In spite of partial progress, this problem has remained open in the past two decades. Besides straight motion and turn with maximum allowed curvature, we identify planar elastica as the third piece of motion that occurs along our extr emals. We give a detailed characterization of such curves, a special case of which, called \emph{merging curve}, connects maximum curvature turns to straight line segments. The structure of extremals in our case is revealed through analytical integration of the system and adjoint equations

A Real-Time Solver For Time-Optimal Control Of Omnidirectional Robots with Bounded Acceleration

We are interested in the problem of time-optimal control of omnidirectional robots with bounded acceleration (TOC-ORBA). While there exist approximate solutions for such robots, and exact solutions with unbounded acceleration, exact solvers to the TOC-ORBA problem have remained elusive until now. In this paper, we present a real-time solver for true time-optimal control of omnidirectional robots with bounded acceleration. We first derive the general parameterized form of the solution to the TOC-ORBA problem by application of Pontryagin's maximum principle. We then frame the boundary value problem of TOC-ORBA as an optimization problem over the parametrized control space. To overcome local minima and poor initial guesses to the optimization problem, we introduce a two-stage optimal control solver (TSOCS): The first stage computes an upper bound to the total time for the TOC-ORBA problem and holds the time constant while optimizing the parameters of the trajectory to approach the boundary value conditions. The second stage uses the parameters found by the first stage, and relaxes the constraint on the total time to solve for the parameters of the complete TOC-ORBA problem. We further implement TSOCS as a closed loop controller to overcome actuation errors on real robots in real-time. We empirically demonstrate the effectiveness of TSOCS in simulation and on real robots, showing that 1) it runs in real time, generating solutions in less than 0.5ms on average; 2) it generates faster trajectories compared to an approximate solver; and 3) it is able to solve TOC-ORBA problems with non-zero final velocities that were previously unsolvable in real-time

Spatio-Temporal Calibration for Omni-Directional Vehicle-Mounted

We present a solution to the problem of spatio-temporal calibration for event cameras mounted on an onmi-directional vehicle. Different from traditional methods that typically determine the camera's pose with respect to the vehicle's body frame using alignment of trajectories, our approach leverages the kinematic correlation of two sets of linear velocity estimates from event data and wheel odometers, respectively. The overall calibration task consists of estimating the underlying temporal offset between the two heterogeneous sensors, and furthermore, recovering the extrinsic rotation that defines the linear relationship between the two sets of velocity estimates. The first sub-problem is formulated as an optimization one, which looks for the optimal temporal offset that maximizes a correlation measurement invariant to arbitrary linear transformation. Once the temporal offset is compensated, the extrinsic rotation can be worked out with an iterative closed-form solver that incrementally registers associated linear velocity estimates. The proposed algorithm is proved effective on both synthetic data and real data, outperforming traditional methods based on alignment of trajectories

Search-based Motion Planning for Aggressive Flight in SE(3)

Quadrotors with large thrust-to-weight ratios are able to track aggressive trajectories with sharp turns and high accelerations. In this work, we develop a search-based trajectory planning approach that exploits the quadrotor maneuverability to generate sequences of motion primitives in cluttered environments. We model the quadrotor body as an ellipsoid and compute its flight attitude along trajectories in order to check for collisions against obstacles. The ellipsoid model allows the quadrotor to pass through gaps that are smaller than its diameter with non-zero pitch or roll angles. Without any prior information about the location of gaps and associated attitude constraints, our algorithm is able to find a safe and optimal trajectory that guides the robot to its goal as fast as possible. To accelerate planning, we first perform a lower dimensional search and use it as a heuristic to guide the generation of a final dynamically feasible trajectory. We analyze critical discretization parameters of motion primitive planning and demonstrate the feasibility of the generated trajectories in various simulations and real-world experiments.Comment: 8 pages, submitted to RAL and ICRA 201

Design, Modeling, and Geometric Control on SE(3) of a Fully-Actuated Hexarotor for Aerial Interaction

In this work we present the optimization-based design and control of a fully-actuated omnidirectional hexarotor. The tilt angles of the propellers are designed by maximizing the control wrench applied by the propellers. This maximizes (a) the agility of the UAV, (b) the maximum payload the UAV can hover with at any orientation, and (c) the interaction wrench that the UAV can apply to the environment in physical contact. It is shown that only axial tilting of the propellers with respect to the UAV's body yields optimal results. Unlike the conventional hexarotor, the proposed hexarotor can generate at least 1.9 times the maximum thrust of one rotor in any direction, in addition to the higher control torque around the vehicle's upward axis. A geometric controller on SE(3) is proposed for the trajectory tracking problem for the class of fully actuated UAVs. The proposed controller avoids singularities and complexities that arise when using local parametrizations, in addition to being invariant to a change of inertial coordinate frame. The performance of the controller is validated in simulation.Comment: 9 pages, 9 figures, ICRA201

A Decomposition Approach to Multi-Vehicle Cooperative Control

We present methods that generate cooperative strategies for multi-vehicle control problems using a decomposition approach. By introducing a set of tasks to be completed by the team of vehicles and a task execution method for each vehicle, we decomposed the problem into a combinatorial component and a continuous component. The continuous component of the problem is captured by task execution, and the combinatorial component is captured by task assignment. In this paper, we present a solver for task assignment that generates near-optimal assignments quickly and can be used in real-time applications. To motivate our methods, we apply them to an adversarial game between two teams of vehicles. One team is governed by simple rules and the other by our algorithms. In our study of this game we found phase transitions, showing that the task assignment problem is most difficult to solve when the capabilities of the adversaries are comparable. Finally, we implement our algorithms in a multi-level architecture with a variable replanning rate at each level to provide feedback on a dynamically changing and uncertain environment.Comment: 36 pages, 19 figures, for associated web page see http://control.mae.cornell.edu/earl/decom