Gabriel M. Hoffmann

Stanley: The Robot That Won the DARPA Grand Challenge

This article describes the robot Stanley, which won the 2005 DARPA Grand Challenge. Stanley was developed for high-speed desert driving without human intervention. The robot’s software system relied predominately on state-of-the-art AI technologies, such as machine learning and probabilistic reasoning. This article describes the major components of this architecture, and discusses the results of the Grand Challenge race.

Aerodynamics and control of autonomous quadrotor helicopters in aggressive maneuvering

Quadrotor helicopters have become increasingly important in recent years as platforms for both research and commercial unmanned aerial vehicle applications. This paper extends previous work on several important aerodynamic effects impacting quadrotor flight in regimes beyond nominal hover conditions. The implications of these effects on quadrotor performance are investigated and control techniques are presented that compensate for them accordingly. The analysis and control systems are validated on the Stanford Testbed of Autonomous Rotorcraft for Multi-Agent Control quadrotor helicopter testbed by performing the quadrotor equivalent of the stall turn aerobatic maneuver. Flight results demonstrate the accuracy of the aerodynamic models and improved control performance with the proposed control schemes.

Quadrotor Helicopter Trajectory Tracking Control

The Stanford Testbed of Autonomous Rotorcraft for Multi-Agent Control (STARMAC), a eet of quadrotor helicopters, has been developed as a testbed for novel algorithms that enable autonomous operation of aerial vehicles. This paper develops an autonomous vehicle trajectory tracking algorithm through cluttered environments for the STARMAC platform. A system relying on a single optimization must trade o the complexity of the planned path with the rate of update of the control input. In this paper, a trajectory tracking controller for quadrotor helicopters is developed to decouple the two problems. By accepting as inputs a path of waypoints and desired velocities, the control input can be updated frequently to accurately track the desired path, while the path planning occurs as a separate process on a slower timescale. To enable the use of planning algorithms that do not consider dynamic feasibility or provide feedforward inputs, a computationally ecient algorithm using space-indexed waypoints is presented to modify the speed prole of input paths to guarantee feasibility of the planned trajectory and minimum time traversal of the planned. The algorithm is an ecient alternative to formulating a nonlinear optimization or mixed integer program. Both indoor and outdoor ight test results are presented for path tracking on the STARMAC vehicles.

Mobile Sensor Network Control Using Mutual Information Methods and Particle Filters

This paper develops a set of methods enabling an information-theoretic distributed control architecture to facilitate search by a mobile sensor network. Given a particular configuration of sensors, this technique exploits the structure of the probability distributions of the target state and of the sensor measurements to control the mobile sensors such that future observations minimize the expected future uncertainty of the target state. The mutual information between the sensors and the target state is computed using a particle filter representation of the posterior probability distribution, making it possible to directly use nonlinear and non-Gaussian target state and sensor models. To make the approach scalable to increasing network sizes, single-node and pairwise-node approximations to the mutual information are derived for general probability density models, with analytically bounded error. The pairwise-node approximation is proven to be a more accurate objective function than the single-node approximation. The mobile sensors are cooperatively controlled using a distributed optimization, yielding coordinated motion of the network. These methods are explored for various sensing modalities, including bearings-only sensing, range-only sensing, and magnetic field sensing, all with potential for search and rescue applications. For each sensing modality, the behavior of this non-parametric method is compared and contrasted with the results of linearized methods, and simulations are performed of a target search using the dynamics of actual vehicles. Monte Carlo results demonstrate that as network size increases, the sensors more quickly localize the target, and the pairwise-node approximation provides superior performance to the single-node approximation. The proposed methods are shown to produce similar results to linearized methods in particular scenarios, yet they capture effects in more general scenarios that are not possible with linearized methods.

Multi-agent quadrotor testbed control design: integral sliding mode vs. reinforcement learning

The Stanford Testbed of Autonomous Rotorcraft for Multi-Agent Control (STARMAC) is a multi-vehicle testbed currently comprised of two quadrotors, also called X4-flyers, with capacity for eight. This paper presents a comparison of control design techniques, specifically for outdoor altitude control, in and above ground effect, that accommodate the unique dynamics of the aircraft. Due to the complex airflow induced by the four interacting rotors, classical linear techniques failed to provide sufficient stability. Integral sliding mode and reinforcement learning control are presented as two design techniques for accommodating the nonlinear disturbances. The methods both result in greatly improved performance over classical control techniques.

Applications of hybrid reachability analysis to robotic aerial vehicles

The control of complex non-linear systems can be aided by modeling each system as a collection of simplified hybrid modes, with each mode representing a particular operating regime defined by the system dynamics or by a region of the state space in which the system operates. Guarantees on the safety and performance of such hybrid systems can still be challenging to generate, however. Reachability analysis using a dynamic game formulation with Hamilton—Jacobi methods provides a useful way to generate these types of guarantees, and the technique is flexible enough to analyze a wide variety of systems. This paper presents two applications of reachable sets, both focused on guaranteeing the safety and performance of robotic aerial vehicles. In the first example, reachable sets are used to design and implement a backflip maneuver for a quadrotor helicopter. In the second, reachability analysis is used to design a decentralized collision avoidance algorithm for multiple quadrotors. The theory for both examples is explained, and successful experimental results are presented from flight tests on the STARMAC quadrotor helicopter platform.

Distributed Cooperative Search using Information-Theoretic Costs for Particle Filters, with Quadrotor Applications ∗

Search and rescue missions can be efficiently and automatically performed by small, highly maneuverable unmanned aerial vehicle (UAV) teams. The search problem is complicated by a lack of prior information, nonlinear mapping between sensor observations and the physical world, and potentially non-Gaussian sensor noise models. To address these problems, a distributed control algorithm is proposed, using information theoretic methods with particle filters, to compute optimal control inputs for a multi-vehicle, coordinated localization of a stationary target. This technique exploits the structure of the probability distributions of the target state and of the sensor measurements to compute the control inputs that maneuver the UAVs to make observations that minimize the expected future uncertainty of the target state. Because the method directly uses the particle filter state and an accurate sensor noise model to compute the mutual information, it is no longer necessary to discard information by using linear and Gaussian approximations. To ensure safety of the vehicles, the algorithm incorporates collision avoidance and control authority constraints. The resulting information theoretic cost calculation is coupled amongst the vehicles and becomes prohibitive as the size of the UAV team becomes large. Therefore, single vehicle and pairwise approximations to the cost function are used that greatly reduce the computational burden and allow for development of a distributed algorithm for real-time optimization of vehicle trajectories. Simulation results are shown for a bearings-only sensor model with multiple vehicles. Initial flight tests of the Stanford Testbed of Autonomous Rotorcraft for Multi-Agent Control (STARMAC) show the feasibility of implementation of this algorithm on the quadrotor testbed and in real world situations.

Tunnel-MILP: Path Planning with Sequential Convex Polytopes

This paper focuses on optimal path planning for vehicles in known environments. Previous work has presented mixed integer linear programming (MILP) formulations, which suer from scalability issues as the number of obstacles, and hence the number of integer variables, increases. In order to address MILP scalability, a novel three-stage algorithm is presented which rst computes a desirable path through the environment without considering dynamics, then generates a sequence of convex polytopes containing the desired path, and nally poses a MILP to identify a suitable dynamically feasible path. The sequence of polytopes form a safe tunnel through the environment, and integer decision variables are restricted to deciding when to enter and exit each region of the tunnel. Simulation results for this approach are presented and reveal a signicant increase in the size and complexity of the environment that can be solved.

Decentralized cooperative collision avoidance for acceleration constrained vehicles

Safety must be ensured in the deployment of multi-agent vehicle systems. This paper presents decentralized collision avoidance algorithms for systems with second order dynamics and acceleration constraints, using a switching control law. The technique augments existing multi-agent control laws with the capability to switch to provably safe collision avoidance maneuvers when required. Two algorithms with low computational cost are presented, one for two vehicles and one for more vehicles. In both methods, each vehicle computes avoid sets with respect to every other vehicle. When one or more vehicles are on the boundary of their avoid sets, collision avoidance action is taken. These algorithms are applied in simulation scenarios for which existing techniques either fail or are computationally expensive, and used for information theoretic control of a mobile sensor network to reduce the computational complexity. Finally, they are demonstrated in quadrotor helicopter flight experiments.

Mutual Information Methods with Particle Filters for Mobile Sensor Network Control

This paper develops a set of methods enabling an information-theoretic distributed control architecture based on particle filters to facilitate search by a mobile sensor network, permitting the use of nonlinear and non-Gaussian sensor models. Given a particular configuration sensors, this technique exploits the structure of the probability distributions of the target state and of the sensor measurements to compute the control inputs to the mobile sensors leading to future observations that minimize, in expectation, the future uncertainty of the target state. We compute the mutual information using a particle set representation of the posterior distribution. In order to control a large number of mobile sensors as a network, single-node and pairwise-node approximation schemes are presented, with analytically bounded error, making the approach scalable to increasing network sizes, while still planning cooperatively. The methods are applied in simulation to bearings-only sensing, and to localizing an avalanche rescue beacon of a buried victim, using transceivers on quadrotor aircraft to measure the magnetic field. Monte Carlo simulations also demonstrate that as network size increases, the sensors more quickly localize the target, and the pairwise-node approximation results in superior performance to the single-node approximation