2,685 research outputs found
Fast, Safe, and Propellant-Efficient Spacecraft Planning under Clohessy-Wiltshire-Hill Dynamics
This paper presents a sampling-based motion planning algorithm for real-time
and propellant-optimized autonomous spacecraft trajectory generation in
near-circular orbits. Specifically, this paper leverages recent algorithmic
advances in the field of robot motion planning to the problem of
impulsively-actuated, propellant-optimized rendezvous and proximity operations
under the Clohessy-Wiltshire-Hill (CWH) dynamics model. The approach calls upon
a modified version of the Fast Marching Tree (FMT*) algorithm to grow a set of
feasible trajectories over a deterministic, low-dispersion set of sample points
covering the free state space. To enforce safety, the tree is only grown over
the subset of actively-safe samples, from which there exists a feasible
one-burn collision avoidance maneuver that can safely circularize the
spacecraft orbit along its coasting arc under a given set of potential thruster
failures. Key features of the proposed algorithm include: (i) theoretical
guarantees in terms of trajectory safety and performance, (ii) amenability to
real-time implementation, and (iii) generality, in the sense that a large class
of constraints can be handled directly. As a result, the proposed algorithm
offers the potential for widespread application, ranging from on-orbit
satellite servicing to orbital debris removal and autonomous inspection
missions.Comment: Submitted to the AIAA Journal of Guidance, Control, and Dynamics
(JGCD) special issue entitled "Computational Guidance and Control". This
submission is the journal version corresponding to the conference manuscript
"Real-Time, Propellant-Efficient Spacecraft Planning under
Clohessy-Wiltshire-Hill Dynamics" accepted to the 2016 IEEE Aerospace
Conference in Big Sky, MT, US
Safe non-smooth black-box optimization with application to policy search
For safety-critical black-box optimization tasks, observations of the
constraints and the objective are often noisy and available only for the
feasible points. We propose an approach based on log barriers to find a local
solution of a non-convex non-smooth black-box optimization problem subject to , at the same time,
guaranteeing constraint satisfaction while learning an optimal solution with
high probability. Our proposed algorithm exploits noisy observations to
iteratively improve on an initial safe point until convergence. We derive the
convergence rate and prove safety of our algorithm. We demonstrate its
performance in an application to an iterative control design problem
Real-Time Stochastic Kinodynamic Motion Planning via Multiobjective Search on GPUs
In this paper we present the PUMP (Parallel Uncertainty-aware Multiobjective
Planning) algorithm for addressing the stochastic kinodynamic motion planning
problem, whereby one seeks a low-cost, dynamically-feasible motion plan subject
to a constraint on collision probability (CP). To ensure exhaustive evaluation
of candidate motion plans (as needed to tradeoff the competing objectives of
performance and safety), PUMP incrementally builds the Pareto front of the
problem, accounting for the optimization objective and an approximation of CP.
This is performed by a massively parallel multiobjective search, here
implemented with a focus on GPUs. Upon termination of the exploration phase,
PUMP searches the Pareto set of motion plans to identify the lowest cost
solution that is certified to satisfy the CP constraint (according to an
asymptotically exact estimator). We introduce a novel particle-based CP
approximation scheme, designed for efficient GPU implementation, which accounts
for dependencies over the history of a trajectory execution. We present
numerical experiments for quadrotor planning wherein PUMP identifies solutions
in ~100 ms, evaluating over one hundred thousand partial plans through the
course of its exploration phase. The results show that this multiobjective
search achieves a lower motion plan cost, for the same CP constraint, compared
to a safety buffer-based search heuristic and repeated RRT trials
Continuous-Time Gaussian Process Motion Planning via Probabilistic Inference
We introduce a novel formulation of motion planning, for continuous-time
trajectories, as probabilistic inference. We first show how smooth
continuous-time trajectories can be represented by a small number of states
using sparse Gaussian process (GP) models. We next develop an efficient
gradient-based optimization algorithm that exploits this sparsity and GP
interpolation. We call this algorithm the Gaussian Process Motion Planner
(GPMP). We then detail how motion planning problems can be formulated as
probabilistic inference on a factor graph. This forms the basis for GPMP2, a
very efficient algorithm that combines GP representations of trajectories with
fast, structure-exploiting inference via numerical optimization. Finally, we
extend GPMP2 to an incremental algorithm, iGPMP2, that can efficiently replan
when conditions change. We benchmark our algorithms against several
sampling-based and trajectory optimization-based motion planning algorithms on
planning problems in multiple environments. Our evaluation reveals that GPMP2
is several times faster than previous algorithms while retaining robustness. We
also benchmark iGPMP2 on replanning problems, and show that it can find
successful solutions in a fraction of the time required by GPMP2 to replan from
scratch.Comment: The International Journal of Robotics Research (IJRR), 2018, Volume
37, Issue 1
An Accelerated Linearized Alternating Direction Method of Multipliers
We present a novel framework, namely AADMM, for acceleration of linearized
alternating direction method of multipliers (ADMM). The basic idea of AADMM is
to incorporate a multi-step acceleration scheme into linearized ADMM. We
demonstrate that for solving a class of convex composite optimization with
linear constraints, the rate of convergence of AADMM is better than that of
linearized ADMM, in terms of their dependence on the Lipschitz constant of the
smooth component. Moreover, AADMM is capable to deal with the situation when
the feasible region is unbounded, as long as the corresponding saddle point
problem has a solution. A backtracking algorithm is also proposed for practical
performance
The Convex Feasible Set Algorithm for Real Time Optimization in Motion Planning
With the development of robotics, there are growing needs for real time
motion planning. However, due to obstacles in the environment, the planning
problem is highly non-convex, which makes it difficult to achieve real time
computation using existing non-convex optimization algorithms. This paper
introduces the convex feasible set algorithm (CFS) which is a fast algorithm
for non-convex optimization problems that have convex costs and non-convex
constraints. The idea is to find a convex feasible set for the original problem
and iteratively solve a sequence of subproblems using the convex constraints.
The feasibility and the convergence of the proposed algorithm are proved in the
paper. The application of this method on motion planning for mobile robots is
discussed. The simulations demonstrate the effectiveness of the proposed
algorithm.Comment: in SIAM Journal on Control and Optimizatio
Zeroth-order Nonconvex Stochastic Optimization: Handling Constraints, High-Dimensionality and Saddle-Points
In this paper, we propose and analyze zeroth-order stochastic approximation
algorithms for nonconvex and convex optimization, with a focus on addressing
constrained optimization, high-dimensional setting and saddle-point avoiding.
To handle constrained optimization, we first propose generalizations of the
conditional gradient algorithm achieving rates similar to the standard
stochastic gradient algorithm using only zeroth-order information. To
facilitate zeroth-order optimization in high-dimensions, we explore the
advantages of structural sparsity assumptions. Specifically, (i) we highlight
an implicit regularization phenomenon where the standard stochastic gradient
algorithm with zeroth-order information adapts to the sparsity of the problem
at hand by just varying the step-size and (ii) propose a truncated stochastic
gradient algorithm with zeroth-order information, whose rate of convergence
depends only poly-logarithmically on the dimensionality. We next focus on
avoiding saddle-points in non-convex setting. Towards that, we interpret the
Gaussian smoothing technique for estimating gradient based on zeroth-order
information as an instantiation of first-order Stein's identity. Based on this,
we provide a novel linear-(in dimension) time estimator of the Hessian matrix
of a function using only zeroth-order information, which is based on
second-order Stein's identity. We then provide an algorithm for avoiding
saddle-points, which is based on a zeroth-order cubic regularization Newton's
method and discuss its convergence rates
Projection Neural Network for a Class of Sparse Regression Problems with Cardinality Penalty
In this paper, we consider a class of sparse regression problems, whose
objective function is the summation of a convex loss function and a cardinality
penalty. By constructing a smoothing function for the cardinality function, we
propose a projected neural network and design a correction method for solving
this problem. The solution of the proposed neural network is unique, global
existent, bounded and globally Lipschitz continuous. Besides, we prove that all
accumulation points of the proposed neural network have a common support set
and a unified lower bound for the nonzero entries. Combining the proposed
neural network with the correction method, any corrected accumulation point is
a local minimizer of the considered sparse regression problem. Moreover, we
analyze the equivalent relationship on the local minimizers between the
considered sparse regression problem and another regression sparse problem.
Finally, some numerical experiments are provided to show the efficiency of the
proposed neural networks in solving some sparse regression problems in
practice
SERoCS: Safe and Efficient Robot Collaborative Systems for Next Generation Intelligent Industrial Co-Robots
Human-robot collaborations have been recognized as an essential component for
future factories. It remains challenging to properly design the behavior of
those co-robots. Those robots operate in dynamic uncertain environment with
limited computation capacity. The design objective is to maximize their task
efficiency while guaranteeing safety. This paper discusses a set of design
principles of a safe and efficient robot collaboration system (SERoCS) for the
next generation co-robots, which consists of robust cognition algorithms for
environment monitoring, efficient task planning algorithms for reference
generations, and safe motion planning and control algorithms for safe
human-robot interactions. The proposed SERoCS will address the design
challenges and significantly expand the skill sets of the co-robots to allow
them to work safely and efficiently with their human counterparts. The
development of SERoCS will create a significant advancement toward adoption of
co-robots in various industries. The experiments validate the effectiveness of
SERoCS.Comment: 19 page
Monte Carlo Motion Planning for Robot Trajectory Optimization Under Uncertainty
This article presents a novel approach, named MCMP (Monte Carlo Motion
Planning), to the problem of motion planning under uncertainty, i.e., to the
problem of computing a low-cost path that fulfills probabilistic collision
avoidance constraints. MCMP estimates the collision probability (CP) of a given
path by sampling via Monte Carlo the execution of a reference tracking
controller (in this paper we consider LQG). The key algorithmic contribution of
this paper is the design of statistical variance-reduction techniques, namely
control variates and importance sampling, to make such a sampling procedure
amenable to real-time implementation. MCMP applies this CP estimation procedure
to motion planning by iteratively (i) computing an (approximately) optimal path
for the deterministic version of the problem (here, using the FMT* algorithm),
(ii) computing the CP of this path, and (iii) inflating or deflating the
obstacles by a common factor depending on whether the CP is higher or lower
than a target value. The advantages of MCMP are threefold: (i) asymptotic
correctness of CP estimation, as opposed to most current approximations, which,
as shown in this paper, can be off by large multiples and hinder the
computation of feasible plans; (ii) speed and parallelizability, and (iii)
generality, i.e., the approach is applicable to virtually any planning problem
provided that a path tracking controller and a notion of distance to obstacles
in the configuration space are available. Numerical results illustrate the
correctness (in terms of feasibility), efficiency (in terms of path cost), and
computational speed of MCMP
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