Doctor of Philosophy

dissertationThis dissertation solves the collision avoidance problem for single- and multi-robot systems where dynamic effects are significant. In many robotic systems (e.g., highly maneuverable and agile unmanned aerial vehicles) the dynamics cannot be ignored and collision avoidance schemes based on kinematic models can result in collisions or provide limited performance, especially at high operating speeds. Herein, real-time, model-based collision avoidance algorithms that explicitly consider the robots' dynamics and perform real-time input changes to alter the trajectory and steer the robot away from potential collisions are developed, implemented, and verified in simulations and physical experiments. Such algorithms are critical in applications where a high degree of autonomy and performance are needed, for example in robot-assisted first response where aerial and/or mobile ground robots are required to maneuver quickly through cluttered and dangerous environments in search of survivors. Firstly, the research extends reciprocal collision avoidance to robots with dynamics by unifying previous approaches to reciprocal collision avoidance under a single, generalized representation using control obstacles. In fact, it is shown how velocity obstacles, acceleration velocity obstacles, continuous control obstacles, and linear quadratic regulator (LQR)-obstacles are special instances of the generalized framework. Furthermore, an extension of control obstacles to general reciprocal collision avoidance for nonlinear, nonhomogeneous systems where the robots may have different state spaces and different nonlinear equations of motion from one another is described. Both simulations and physical experiments are provided for a combination of differential-drive, differential-drive with a trailer, and car-like robots to demonstrate that the approach is capable of letting a nonhomogeneous group of robots with nonlinear equations of motion safely avoid collisions at real-time computation rates. Secondly, the research develops a stochastic collision avoidance algorithm for a tele-operated unmanned aerial vehicle (UAV) that considers uncertainty in the robot's dynamics model and the obstacles' position as measured from sensors. The model-based automatic collision avoidance algorithm is implemented on a custom-designed quadcopter UAV system with on-board computation and the sensor data are processed using a split-and-merge segmentation algorithm and an approximate Minkowski difference. Flight tests are conducted to validate the algorithm's capabilities for providing tele-operated collision-free operation. Finally, a set of human subject studies are performed to quantitatively compare the performance between the model-based algorithm, the basic risk field algorithm (a variant on potential field), and full manual control. The results show that the model-based algorithm performs significantly better than manual control in both the number of collisions and the UAV's average speed, both of which are extremely vital, for example, for UAV-assisted search and rescue applications. Compared to the potential-field-based algorithm, the model-based algorithm allowed the pilot to operate the UAV with higher average speeds

Distributed Spacecraft Path Planning and Collision Avoidance via Reciprocal Velocity Obstacle Approach

This paper presents the development of a combined linear quadratic regulation and reciprocal velocity obstacle (LQR/RVO) control algorithm for multiple satellites during close proximity operations. The linear quadratic regulator (LQR) control effort drives the spacecraft towards their target position while the reciprocal velocity obstacle (RVO) provides collision avoidance capabilities. Each spacecraft maneuvers independently, without explicit communication or knowledge in term of collision avoidance decision making of the other spacecraft in the formation. To assess the performance of this novel controller different test cases are implemented. Numerical results show that this method guarantees safe and collision-free maneuvers for all the satellites in the formation and the control performance is presented in term of Δv and fuel consumption

Multi-agent Collision Avoidance Using Interval Analysis and Symbolic Modelling with its Application to the Novel Polycopter

Coordination is fundamental component of autonomy when a system is defined by multiple mobile agents. For unmanned aerial systems (UAS), challenges originate from their low-level systems, such as their flight dynamics, which are often complex. The thesis begins by examining these low-level dynamics in an analysis of several well known UAS using a novel symbolic component-based framework. It is shown how this approach is used effectively to define key model and performance properties necessary of UAS trajectory control. This is demonstrated initially under the context of linear quadratic regulation (LQR) and model predictive control (MPC) of a quadcopter. The symbolic framework is later extended in the proposal of a novel UAS platform, referred to as the ``Polycopter" for its morphing nature. This dual-tilt axis system has unique authority over is thrust vector, in addition to an ability to actively augment its stability and aerodynamic characteristics. This presents several opportunities in exploitative control design. With an approach to low-level UAS modelling and control proposed, the focus of the thesis shifts to investigate the challenges associated with local trajectory generation for the purpose of multi-agent collision avoidance. This begins with a novel survey of the state-of-the-art geometric approaches with respect to performance, scalability and tolerance to uncertainty. From this survey, the interval avoidance (IA) method is proposed, to incorporate trajectory uncertainty in the geometric derivation of escape trajectories. The method is shown to be more effective in ensuring safe separation in several of the presented conditions, however performance is shown to deteriorate in denser conflicts. Finally, it is shown how by re-framing the IA problem, three dimensional (3D) collision avoidance is achieved. The novel 3D IA method is shown to out perform the original method in three conflict cases by maintaining separation under the effects of uncertainty and in scenarios with multiple obstacles. The performance, scalability and uncertainty tolerance of each presented method is then examined in a set of scenarios resembling typical coordinated UAS operations in an exhaustive Monte-Carlo analysis

Downwash-Aware Trajectory Planning for Large Quadrotor Teams

We describe a method for formation-change trajectory planning for large quadrotor teams in obstacle-rich environments. Our method decomposes the planning problem into two stages: a discrete planner operating on a graph representation of the workspace, and a continuous refinement that converts the non-smooth graph plan into a set of C^k-continuous trajectories, locally optimizing an integral-squared-derivative cost. We account for the downwash effect, allowing safe flight in dense formations. We demonstrate the computational efficiency in simulation with up to 200 robots and the physical plausibility with an experiment with 32 nano-quadrotors. Our approach can compute safe and smooth trajectories for hundreds of quadrotors in dense environments with obstacles in a few minutes.Comment: 8 page

Stochastic Extended LQR for Optimization-Based Motion Planning Under Uncertainty

We introduce a novel optimization-based motion planner, Stochastic Extended LQR (SELQR), which computes a trajectory and associated linear control policy with the objective of minimizing the expected value of a user-defined cost function. SELQR applies to robotic systems that have stochastic non-linear dynamics with motion uncertainty modeled by Gaussian distributions that can be state- and control-dependent. In each iteration, SELQR uses a combination of forward and backward value iteration to estimate the cost-to-come and the cost-to-go for each state along a trajectory. SELQR then locally optimizes each state along the trajectory at each iteration to minimize the expected total cost, which results in smoothed states that are used for dynamics linearization and cost function quadratization. SELQR progressively improves the approximation of the expected total cost, resulting in higher quality plans. For applications with imperfect sensing, we extend SELQR to plan in the robot's belief space. We show that our iterative approach achieves fast and reliable convergence to high-quality plans in multiple simulated scenarios involving a car-like robot, a quadrotor, and a medical steerable needle performing a liver biopsy procedure