There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Today’s autonomous drones have reaction times of tens of milliseconds, which is not enough for navigating fast in complex dynamic environments. To safely avoid fast moving objects, drones need low-latency sensors and algorithms. We departed from state-of-the-art approaches by using event cameras, which are bioinspired sensors with reaction times of microseconds. Our approach exploits the temporal information contained in the event stream to distinguish between static and dynamic objects and leverages a fast strategy to generate the motor commands necessary to avoid the approaching obstacles. Standard vision algorithms cannot be applied to event cameras because the output of these sensors is not images but a stream of asynchronous events that encode per-pixel intensity changes. Our resulting algorithm has an overall latency of only 3.5 milliseconds, which is sufficient for reliable detection and avoidance of fast-moving obstacles. We demonstrate the effectiveness of our approach on an autonomous quadrotor using only onboard sensing and computation. Our drone was capable of avoiding multiple obstacles of different sizes and shapes, at relative speeds up to 10 meters/second, both indoors and outdoors.

/pdf/dynamic-obstacle-avoidance-for-quadrotors-with-event-cameras-3ynzhsbckd.pdf

Dynamic obstacle avoidance for quadrotors with event cameras

Augmented Reality for Robotics: A Review

Autonomous robot navigation through unknown, cluttered environments at high-speeds is still an open problem. Quadrotor platforms with this capability have only begun to emerge with the advancements in light-weight, small form factor sensing and computing. Many of the existing platforms, however, require excessive computation time to perform collision avoidance, which ultimately limits the vehicle's top speed. This work presents an efficient perception and planning approach that significantly reduces the computation time by using instantaneous perception data for collision avoidance. Minimum-time, state and input constrained motion primitives are generated by sampling terminal states until a collision-free path is found. The worst case performance of the Triple Integrator Planner (TIP) is nearly an order of magnitude faster than the state-of-the-art. Experimental results demonstrate the algorithm's ability to plan and execute aggressive collision avoidance maneuvers in highly cluttered environments.

Aggressive 3-D collision avoidance for high-speed navigation

High-speed trajectory planning through unknown environments requires algorithmic techniques that enable fast reaction times while maintaining safety as new information about the operating environment is obtained. The requirement of computational tractability typically leads to optimization problems that do not include the obstacle constraints (collision checks are done on the solutions) or use a convex decomposition of the free space and then impose an ad-hoc time allocation scheme for each interval of the trajectory. Moreover, safety guarantees are usually obtained by having a local planner that plans a trajectory with a final “stop” condition in the freeknown space. However, these two decisions typically lead to slow and conservative trajectories. We propose FASTER (Fast and Safe Trajectory Planner) to overcome these issues. FASTER obtains high-speed trajectories by enabling the local planner to optimize in both the free-known and unknown spaces. Safety guarantees are ensured by always having a feasible, safe back-up trajectory in the free-known space at the start of each replanning step. Furthermore, we present a Mixed Integer Quadratic Program formulation in which the solver can choose the trajectory interval allocation, and where a time allocation heuristic is computed efficiently using the result of the previous replanning iteration. This proposed algorithm is tested extensively both in simulation and in real hardware, showing agile flights in unknown cluttered environments with velocities up to 3.6 $\mathrm{m}/\mathrm{s}$.

FASTER: Fast and Safe Trajectory Planner for Flights in Unknown Environments

A new framework is developed for control of constrained nonlinear systems with structured parametric uncertainty. Forward invariance of a safe set is achieved through online parameter adaptation and data-driven model estimation. The new adaptive data-driven safety paradigm is merged with a recent adaptive controller for systems nominally contracting in closed-loop. This unification is more general than other safety controllers as contraction does not require the system be invertible or in a particular form. The method is tested on the pitch dynamics of an aircraft with uncertain nonlinear aerodynamics.

Robust Adaptive Control Barrier Functions: An Adaptive and Data-Driven Approach to Safety

Modeling error or external disturbances can severely degrade the performance of Model Predictive Control (MPC) in real-world scenarios. Robust MPC (RMPC) addresses this limitation by optimizing over feedback policies but at the expense of increased computational complexity. Tube MPC is an approximate solution strategy in which a robust controller, designed offline, keeps the system in an invariant tube around a desired nominal trajectory, generated online. Naturally, this decomposition is suboptimal, especially for systems with changing objectives or operating conditions. In addition, many tube MPC approaches are unable to capture state-dependent uncertainty due to the complexity of calculating invariant tubes, resulting in overly-conservative approximations. This work presents the Dynamic Tube MPC (DTMPC) framework for nonlinear systems where both the tube geometry and open-loop trajectory are optimized simultaneously. By using boundary layer sliding control, the tube geometry can be expressed as a simple relation between control parameters and uncertainty bound; enabling the tube geometry dynamics to be added to the nominal MPC optimization with minimal increase in computational complexity. In addition, DTMPC is able to leverage state-dependent uncertainty to reduce conservativeness and improve optimization feasibility. DTMPC is demonstrated to robustly perform obstacle avoidance and modify the tube geometry in response to obstacle proximity.

/pdf/dynamic-tube-mpc-for-nonlinear-systems-1cwadydl65.pdf

Brett T. Lopez

Papers

Aggressive 3-D collision avoidance for high-speed navigation

FASTER: Fast and Safe Trajectory Planner for Flights in Unknown Environments

Robust Adaptive Control Barrier Functions: An Adaptive and Data-Driven Approach to Safety

Dynamic Tube MPC for Nonlinear Systems

Dynamic Tube MPC for Nonlinear Systems