This paper presents control and coordination algorithms for groups of vehicles. The focus is on autonomous vehicle networks performing distributed sensing tasks where each vehicle plays the role of a mobile tunable sensor. The paper proposes gradient descent algorithms for a class of utility functions which encode optimal coverage and sensing policies. The resulting closed-loop behavior is adaptive, distributed, asynchronous, and verifiably correct.

Coverage control for mobile sensing networks

We address the controller design and the trajectory generation for a quadrotor maneuvering in three dimensions in a tightly constrained setting typical of indoor environments. In such settings, it is necessary to allow for significant excursions of the attitude from the hover state and small angle approximations cannot be justified for the roll and pitch. We develop an algorithm that enables the real-time generation of optimal trajectories through a sequence of 3-D positions and yaw angles, while ensuring safe passage through specified corridors and satisfying constraints on velocities, accelerations and inputs. A nonlinear controller ensures the faithful tracking of these trajectories. Experimental results illustrate the application of the method to fast motion (5–10 body lengths/second) in three-dimensional slalom courses.

Minimum snap trajectory generation and control for quadrotors

We study the problem of designing dynamically feasible trajectories and controllers that drive a quadrotor to a desired state in state space. We focus on the development of a family of trajectories defined as a sequence of segments, each with a controller parameterized by a goal state or region in state space. Each controller is developed from the dynamic model of the robot and then iteratively refined through successive experimental trials in an automated fashion to account for errors in the dynamic model and noise in the actuators and sensors. We show that this approach permits the development of trajectories and controllers enabling such aggressive maneuvers as flying through narrow, vertical gaps and perching on inverted surfaces with high precision and repeatability.

Trajectory generation and control for precise aggressive maneuvers with quadrotors

Existing high-dimensional motion planning algorithms are simultaneously overpowered and underpowered. In domains sparsely populated by obstacles, the heuristics used by sampling-based planners to navigate “narrow passages” can be needlessly complex; furthermore, additional post-processing is required to remove the jerky or extraneous motions from the paths that such planners generate. In this paper, we present CHOMP, a novel method for continuous path refinement that uses covariant gradient techniques to improve the quality of sampled trajectories. Our optimization technique both optimizes higher-order dynamics and is able to converge over a wider range of input paths relative to previous path optimization strategies. In particular, we relax the collision-free feasibility prerequisite on input paths required by those strategies. As a result, CHOMP can be used as a standalone motion planner in many real-world planning queries. We demonstrate the effectiveness of our proposed method in manipulation planning for a 6-DOF robotic arm as well as in trajectory generation for a walking quadruped robot.

/pdf/chomp-gradient-optimization-techniques-for-efficient-motion-we8unveh3b.pdf

CHOMP: Gradient optimization techniques for efficient motion planning

Model predictive control (MPC) has demonstrated exceptional success for the high-performance control of complex systems [1], [2]. The conceptual simplicity of MPC as well as its ability to effectively cope with the complex dynamics of systems with multiple inputs and outputs, input and state/output constraints, and conflicting control objectives have made it an attractive multivariable constrained control approach [1]. MPC (a.k.a. receding-horizon control) solves an open-loop constrained optimal control problem (OCP) repeatedly in a receding-horizon manner [3]. The OCP is solved over a finite sequence of control actions {u0,u1,f,uN- 1} at every sampling time instant that the current state of the system is measured. The first element of the sequence of optimal control actions is applied to the system, and the computations are then repeated at the next sampling time. Thus, MPC replaces a feedback control law p(m), which can have formidable offline computation, with the repeated solution of an open-loop OCP [2]. In fact, repeated solution of the OCP confers an "implicit" feedback action to MPC to cope with system uncertainties and disturbances. Alternatively, explicit MPC approaches circumvent the need to solve an OCP online by deriving relationships for the optimal control actions in terms of an "explicit" function of the state and reference vectors. However, explicit MPC is not typically intended to replace standard MPC but, rather, to extend its area of application [4]-[6].

/pdf/stochastic-model-predictive-control-an-overview-and-1kyy9166uh.pdf

Stochastic Model Predictive Control: An Overview and Perspectives for Future Research

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 Hamiltonâ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.

Applications of hybrid reachability analysis to robotic aerial vehicles

For many applications, the control of a complex nonlinear system can be made easier by modeling the system as a collection of simplified hybrid modes, each representing a particular operating regime. An example of this is the decomposition of complex aerobatic flights into sequences of discrete maneuvers, an approach that has proven very successful for both human piloted and autonomously controlled aircraft. However, a critical step when designing such control systems is to ensure the safety and feasibility of transitions between these maneuvers. This work presents a hybrid dynamics framework for the design of guaranteed safe switching regions and is applied to a quadrotor helicopter performing an autonomous backflip. The regions are constructed using reachable sets calculated via a Hamilton-Jacobi differential game formulation, and experimental results are presented from flight tests on the STARMAC quadrotor platform.

/pdf/design-of-guaranteed-safe-maneuvers-using-reachable-sets-on1wc53bqm.pdf

Design of guaranteed safe maneuvers using reachable sets: Autonomous quadrotor aerobatics in theory and practice

On efficient sensor scheduling for linear dynamical systems

https://www.cs.ox.ac.uk/people/alessandro.abate/publications/ZAHV09.pdf

Exponential stabilization of discrete-time switched linear systems ☆

Consider a set of sensors estimating the state of a process in which only one of these sensors can operate at each time-step due to constraints on the overall system. The problem addressed here is to choose which sensor should operate at each time-step to minimize a weighted function of the error covariance of the state estimation at each time-step. This work investigates the development of tractable algorithms to solve for the optimal and suboptimal sensor schedule. First, a condition on the non-optimality of an initialization of the schedule is presented. Second, using this condition, both an optimal and a suboptimal algorithm are devised to prune the search tree of all possible sensor schedules. This pruning enables the solution of larger systems and longer time horizons than with enumeration alone. The suboptimal algorithm trades off the quality of the solution and the complexity of the problem through a tuning parameter. Third, a hierarchical algorithm is formulated to decrease the computation time of the suboptimal algorithm by using results from a low complexity solution to further prune the tree. Numerical simulations are performed to demonstrate the performance of the proposed algorithms.

/pdf/on-efficient-sensor-scheduling-for-linear-dynamical-systems-3ommpx1fap.pdf

Michael P. Vitus

Papers

Applications of hybrid reachability analysis to robotic aerial vehicles

Design of guaranteed safe maneuvers using reachable sets: Autonomous quadrotor aerobatics in theory and practice

On efficient sensor scheduling for linear dynamical systems

Exponential stabilization of discrete-time switched linear systems ☆

On efficient sensor scheduling for linear dynamical systems