642 research outputs found
Reachability as a Unifying Framework for Computing Helicopter Safe Operating Conditions and Autonomous Emergency Landing
We present a numeric method to compute the safe operating flight conditions
for a helicopter such that we can ensure a safe landing in the event of a
partial or total engine failure. The unsafe operating region is the complement
of the backwards reachable tube, which can be found as the sub-zero level set
of the viscosity solution of a Hamilton-Jacobi (HJ) equation. Traditionally,
numerical methods used to solve the HJ equation rely on a discrete grid of the
solution space and exhibit exponential scaling with dimension, which is
problematic for the high-fidelity dynamics models required for accurate
helicopter modeling. We avoid the use of spatial grids by formulating a
trajectory optimization problem, where the solution at each initial condition
can be computed in a computationally efficient manner. The proposed method is
shown to compute an autonomous landing trajectory from any operating condition,
even in non-cruise flight conditions.Comment: Accepted for publication in the proceedings of the 2020 IFAC World
Congres
Reactive Task and Motion Planning for Robust Whole-Body Dynamic Locomotion in Constrained Environments
Contact-based decision and planning methods are becoming increasingly
important to endow higher levels of autonomy for legged robots. Formal
synthesis methods derived from symbolic systems have great potential for
reasoning about high-level locomotion decisions and achieving complex
maneuvering behaviors with correctness guarantees. This study takes a first
step toward formally devising an architecture composed of task planning and
control of whole-body dynamic locomotion behaviors in constrained and
dynamically changing environments. At the high level, we formulate a two-player
temporal logic game between the multi-limb locomotion planner and its dynamic
environment to synthesize a winning strategy that delivers symbolic locomotion
actions. These locomotion actions satisfy the desired high-level task
specifications expressed in a fragment of temporal logic. Those actions are
sent to a robust finite transition system that synthesizes a locomotion
controller that fulfills state reachability constraints. This controller is
further executed via a low-level motion planner that generates feasible
locomotion trajectories. We construct a set of dynamic locomotion models for
legged robots to serve as a template library for handling diverse environmental
events. We devise a replanning strategy that takes into consideration sudden
environmental changes or large state disturbances to increase the robustness of
the resulting locomotion behaviors. We formally prove the correctness of the
layered locomotion framework guaranteeing a robust implementation by the motion
planning layer. Simulations of reactive locomotion behaviors in diverse
environments indicate that our framework has the potential to serve as a
theoretical foundation for intelligent locomotion behaviors.Comment: 47 pages, 23 figures, 1 tabl
Safe Robot Navigation in Cluttered Environments using Invariant Ellipsoids and a Reference Governor
This paper considers the problem of safe autonomous navigation in unknown
environments, relying on local obstacle sensing. We consider a control-affine
nonlinear robot system subject to bounded input noise and rely on feedback
linearization to determine ellipsoid output bounds on the closed-loop robot
trajectory under stabilizing control. A virtual governor system is developed to
adaptively track a desired navigation path, while relying on the robot
trajectory bounds to slow down if safety is endangered and speed up otherwise.
The main contribution is the derivation of theoretical guarantees for safe
nonlinear system path-following control and its application to autonomous robot
navigation in unknown environments
On optimal multiplexing of an ensemble of discrete-time constrained control systems on matrix Lie groups
We study a constrained optimal control problem for an ensemble of control
systems. Each sub-system (or plant) evolves on a matrix Lie group, and must
satisfy given state and control action constraints pointwise in time. In
addition, certain multiplexing requirement is imposed: the controller must be
shared between the plants in the sense that at any time instant the control
signal may be sent to only one plant. We provide first-order necessary
conditions for optimality in the form of suitable Pontryagin maximum principle
in this problem. Detailed numerical experiments are presented for a system of
two satellites performing energy optimal maneuvers under the preceding family
of constraints.Comment: 29 pages, 7 figure
Funnel Libraries for Real-Time Robust Feedback Motion Planning
We consider the problem of generating motion plans for a robot that are
guaranteed to succeed despite uncertainty in the environment, parametric model
uncertainty, and disturbances. Furthermore, we consider scenarios where these
plans must be generated in real-time, because constraints such as obstacles in
the environment may not be known until they are perceived (with a noisy sensor)
at runtime. Our approach is to pre-compute a library of "funnels" along
different maneuvers of the system that the state is guaranteed to remain within
(despite bounded disturbances) when the feedback controller corresponding to
the maneuver is executed. We leverage powerful computational machinery from
convex optimization (sums-of-squares programming in particular) to compute
these funnels. The resulting funnel library is then used to sequentially
compose motion plans at runtime while ensuring the safety of the robot. A major
advantage of the work presented here is that by explicitly taking into account
the effect of uncertainty, the robot can evaluate motion plans based on how
vulnerable they are to disturbances.
We demonstrate and validate our method using extensive hardware experiments
on a small fixed-wing airplane avoiding obstacles at high speed (~12 mph),
along with thorough simulation experiments of ground vehicle and quadrotor
models navigating through cluttered environments. To our knowledge, these
demonstrations constitute one of the first examples of provably safe and robust
control for robotic systems with complex nonlinear dynamics that need to plan
in real-time in environments with complex geometric constraints.Comment: International Journal of Robotics Research (To Appear
Improved Optimization of Motion Primitives for Motion Planning in State Lattices
In this paper, we propose a framework for generating motion primitives for
lattice-based motion planners automatically. Given a family of systems, the
user only needs to specify which principle types of motions, which are here
denoted maneuvers, that are relevant for the considered system family. Based on
the selected maneuver types and a selected system instance, the algorithm not
only automatically optimizes the motions connecting pre-defined boundary
conditions, but also simultaneously optimizes the end-point boundary conditions
as well. This significantly reduces the time consuming part of manually
specifying all boundary value problems that should be solved, and no exhaustive
search to generate feasible motions is required. In addition to handling static
a priori known system parameters, the framework also allows for fast automatic
re-optimization of motion primitives if the system parameters change while the
system is in use, e.g, if the load significantly changes or a trailer with a
new geometry is picked up by an autonomous truck. We also show in several
numerical examples that the framework can enhance the performance of the motion
planner in terms of total cost for the produced solution.Comment: Manuscript updated after reviewer comments and submitted to IV 201
Constraints on Nonlinear Finite Dimensional Flat Systems
This chapter presents an approach to embed the input/state/output constraints
in a unified manner into the trajectory design for differentially flat systems.
To that purpose, we specialize the flat outputs (or the reference trajectories)
as Bezier curves. Using the flatness property, the system's inputs/states can
be expressed as a combination of Bezier curved flat outputs and their
derivatives. Consequently, we explicitly obtain the expressions of the control
points of the inputs/states Bezier curves as a combination of the control
points of the flat outputs. By applying desired constraints to the latter
control points, we find the feasible regions for the output Bezier control
points i.e. a set of feasible reference trajectories.Comment: 53 pages, 24 figures. The second chapter of the PhD thesis of the
autho
Safe Learning of Quadrotor Dynamics Using Barrier Certificates
To effectively control complex dynamical systems, accurate nonlinear models
are typically needed. However, these models are not always known. In this
paper, we present a data-driven approach based on Gaussian processes that
learns models of quadrotors operating in partially unknown environments. What
makes this challenging is that if the learning process is not carefully
controlled, the system will go unstable, i.e., the quadcopter will crash. To
this end, barrier certificates are employed for safe learning. The barrier
certificates establish a non-conservative forward invariant safe region, in
which high probability safety guarantees are provided based on the statistics
of the Gaussian Process. A learning controller is designed to efficiently
explore those uncertain states and expand the barrier certified safe region
based on an adaptive sampling scheme. In addition, a recursive Gaussian Process
prediction method is developed to learn the complex quadrotor dynamics in
real-time. Simulation results are provided to demonstrate the effectiveness of
the proposed approach.Comment: Submitted to ICRA 2018, 8 page
Robust Trajectory Planning for Autonomous Parafoils under Wind Uncertainty
A key challenge facing modern airborne delivery systems, such as parafoils, is the ability to accurately and consistently deliver supplies into di cult, complex terrain. Robustness is a primary concern, given that environmental wind disturbances are often highly uncertain and time-varying, coupled with under-actuated dynamics and potentially narrow drop zones. This paper presents a new on-line trajectory planning algorithm that enables a large, autonomous parafoil to robustly execute collision avoidance and precision landing on mapped terrain, even with signi cant wind uncertainties. This algorithm is designed to handle arbitrary initial altitudes, approach geometries, and terrain surfaces, and is robust to wind disturbances which may be highly dynamic throughout the terminal approach. Explicit, real-time wind modeling and classi cation is used to anticipate future disturbances, while a novel uncertainty-sampling technique ensures that robustness to possible future variation is e ciently maintained. The designed cost-to-go function enables selection of partial paths which intelligently trade o between current and reachable future states. Simulation results demonstrate that the proposed algorithm reduces the worst-case impact of wind disturbances relative to state-of-the-art approaches.Charles Stark Draper Laborator
Robust Trajectory Planning for Autonomous Parafoils under Wind Uncertainty
A key challenge facing modern airborne delivery systems, such as parafoils, is the ability to accurately and consistently deliver supplies into di cult, complex terrain. Robustness is a primary concern, given that environmental wind disturbances are often highly uncertain and time-varying, coupled with under-actuated dynamics and potentially narrow drop zones. This paper presents a new on-line trajectory planning algorithm that enables a large, autonomous parafoil to robustly execute collision avoidance and precision landing on mapped terrain, even with signi cant wind uncertainties. This algorithm is designed to handle arbitrary initial altitudes, approach geometries, and terrain surfaces, and is robust to wind disturbances which may be highly dynamic throughout the terminal approach. Explicit, real-time wind modeling and classi cation is used to anticipate future disturbances, while a novel uncertainty-sampling technique ensures that robustness to possible future variation is e ciently maintained. The designed cost-to-go function enables selection of partial paths which intelligently trade o between current and reachable future states. Simulation results demonstrate that the proposed algorithm reduces the worst-case impact of wind disturbances relative to state-of-the-art approaches.Charles Stark Draper Laborator
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