3,067 research outputs found
Exact robot navigation in geometrically complicated but topologically simple spaces
A navigation function is an artificial potential energy function on a robot configuration space (C-space) which encodes the task of moving to an arbitrary destination without hitting any obstacle. In particular, such a function possesses no spurious local minima. In this paper we construct navigation functions on forests of stars: geometrically complicated C-spaces that are topologically indistinguishable from a simple disc punctured by disjoint smaller discs, representing model obstacles. For reasons of mathematical tractability we approximate each C-space obstacle by a Boolean combination of linear and quadratic polynomial inequalities (with sharp corners allowed), and use a calculus of implicit representations to effectively represent such obstacles. We provide evidence of the effectiveness of this technology of implicit representations in the form of several simulation studies illustrated at the end of the paper
Optimal Navigation Functions for Nonlinear Stochastic Systems
This paper presents a new methodology to craft navigation functions for
nonlinear systems with stochastic uncertainty. The method relies on the
transformation of the Hamilton-Jacobi-Bellman (HJB) equation into a linear
partial differential equation. This approach allows for optimality criteria to
be incorporated into the navigation function, and generalizes several existing
results in navigation functions. It is shown that the HJB and that existing
navigation functions in the literature sit on ends of a spectrum of
optimization problems, upon which tradeoffs may be made in problem complexity.
In particular, it is shown that under certain criteria the optimal navigation
function is related to Laplace's equation, previously used in the literature,
through an exponential transform. Further, analytical solutions to the HJB are
available in simplified domains, yielding guidance towards optimality for
approximation schemes. Examples are used to illustrate the role that noise, and
optimality can potentially play in navigation system design.Comment: Accepted to IROS 2014. 8 Page
Safe Multi-Agent Interaction through Robust Control Barrier Functions with Learned Uncertainties
Robots operating in real world settings must navigate and maintain safety while interacting with many heterogeneous agents and obstacles. Multi-Agent Control Barrier Functions (CBF) have emerged as a computationally efficient tool to guarantee safety in multi-agent environments, but they assume perfect knowledge of both the robot dynamics and other agents' dynamics. While knowledge of the robot's dynamics might be reasonably well known, the heterogeneity of agents in real-world environments means there will always be considerable uncertainty in our prediction of other agents' dynamics. This work aims to learn high-confidence bounds for these dynamic uncertainties using Matrix-Variate Gaussian Process models, and incorporates them into a robust multi-agent CBF framework. We transform the resulting min-max robust CBF into a quadratic program, which can be efficiently solved in real time. We verify via simulation results that the nominal multi-agent CBF is often violated during agent interactions, whereas our robust formulation maintains safety with a much higher probability and adapts to learned uncertainties
Fast Second-order Cone Programming for Safe Mission Planning
This paper considers the problem of safe mission planning of dynamic systems
operating under uncertain environments. Much of the prior work on achieving
robust and safe control requires solving second-order cone programs (SOCP).
Unfortunately, existing general purpose SOCP methods are often infeasible for
real-time robotic tasks due to high memory and computational requirements
imposed by existing general optimization methods. The key contribution of this
paper is a fast and memory-efficient algorithm for SOCP that would enable
robust and safe mission planning on-board robots in real-time. Our algorithm
does not have any external dependency, can efficiently utilize warm start
provided in safe planning settings, and in fact leads to significant speed up
over standard optimization packages (like SDPT3) for even standard SOCP
problems. For example, for a standard quadrotor problem, our method leads to
speedup of 1000x over SDPT3 without any deterioration in the solution quality.
Our method is based on two insights: a) SOCPs can be interpreted as
optimizing a function over a polytope with infinite sides, b) a linear function
can be efficiently optimized over this polytope. We combine the above
observations with a novel utilization of Wolfe's algorithm to obtain an
efficient optimization method that can be easily implemented on small embedded
devices. In addition to the above mentioned algorithm, we also design a
two-level sensing method based on Gaussian Process for complex obstacles with
non-linear boundaries such as a cylinder
Adaptive Robot Navigation with Collision Avoidance subject to 2nd-order Uncertain Dynamics
This paper considers the problem of robot motion planning in a workspace with
obstacles for systems with uncertain 2nd-order dynamics. In particular, we
combine closed form potential-based feedback controllers with adaptive control
techniques to guarantee the collision-free robot navigation to a predefined
goal while compensating for the dynamic model uncertainties. We base our
findings on sphere world-based configuration spaces, but extend our results to
arbitrary star-shaped environments by using previous results on configuration
space transformations. Moreover, we propose an algorithm for extending the
control scheme to decentralized multi-robot systems. Finally, extensive
simulation results verify the theoretical findings
Neural Network Memory Architectures for Autonomous Robot Navigation
This paper highlights the significance of including memory structures in
neural networks when the latter are used to learn perception-action loops for
autonomous robot navigation. Traditional navigation approaches rely on global
maps of the environment to overcome cul-de-sacs and plan feasible motions. Yet,
maintaining an accurate global map may be challenging in real-world settings. A
possible way to mitigate this limitation is to use learning techniques that
forgo hand-engineered map representations and infer appropriate control
responses directly from sensed information. An important but unexplored aspect
of such approaches is the effect of memory on their performance. This work is a
first thorough study of memory structures for deep-neural-network-based robot
navigation, and offers novel tools to train such networks from supervision and
quantify their ability to generalize to unseen scenarios. We analyze the
separation and generalization abilities of feedforward, long short-term memory,
and differentiable neural computer networks. We introduce a new method to
evaluate the generalization ability by estimating the VC-dimension of networks
with a final linear readout layer. We validate that the VC estimates are good
predictors of actual test performance. The reported method can be applied to
deep learning problems beyond robotics
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