29,314 research outputs found
Motion Planning of Uncertain Ordinary Differential Equation Systems
This work presents a novel motion planning framework, rooted in nonlinear programming theory, that treats uncertain fully and under-actuated dynamical systems described by ordinary differential equations. Uncertainty in multibody dynamical systems comes from various sources, such as: system parameters, initial conditions, sensor and actuator noise, and external forcing. Treatment of uncertainty in design is of paramount practical importance because all real-life systems are affected by it, and poor robustness and suboptimal performance result if itâs not accounted for in a given design. In this work uncertainties are modeled using Generalized Polynomial Chaos and are solved quantitatively using a least-square collocation method. The computational efficiency of this approach enables the inclusion of uncertainty statistics in the nonlinear programming optimization process. As such, the proposed framework allows the user to pose, and answer, new design questions related to uncertain dynamical systems.
Specifically, the new framework is explained in the context of forward, inverse, and hybrid dynamics formulations. The forward dynamics formulation, applicable to both fully and under-actuated systems, prescribes deterministic actuator inputs which yield uncertain state trajectories. The inverse dynamics formulation is the dual to the forward dynamic, and is only applicable to fully-actuated systems; deterministic state trajectories are prescribed and yield uncertain actuator inputs. The inverse dynamics formulation is more computationally efficient as it requires only algebraic evaluations and completely avoids numerical integration. Finally, the hybrid dynamics formulation is applicable to under-actuated systems where it leverages the benefits of inverse dynamics for actuated joints and forward dynamics for unactuated joints; it prescribes actuated state and unactuated input trajectories which yield uncertain unactuated states and actuated inputs.
The benefits of the ability to quantify uncertainty when planning the motion of multibody dynamic systems are illustrated through several case-studies. The resulting designs determine optimal motion plansâsubject to deterministic and statistical constraintsâfor all possible systems within the probability space
Tracking moving optima using Kalman-based predictions
The dynamic optimization problem concerns finding an optimum in a changing environment. In the field of evolutionary algorithms, this implies dealing with a timechanging fitness landscape. In this paper we compare different techniques for integrating motion information into an evolutionary algorithm, in the case it has to follow a time-changing optimum, under the assumption that the changes follow a nonrandom law. Such a law can be estimated in order to improve the optimum tracking capabilities of the algorithm. In particular, we will focus on first order dynamical laws to track moving objects. A vision-based tracking robotic application is used as testbed for experimental comparison
Automatic Differentiation of Rigid Body Dynamics for Optimal Control and Estimation
Many algorithms for control, optimization and estimation in robotics depend
on derivatives of the underlying system dynamics, e.g. to compute
linearizations, sensitivities or gradient directions. However, we show that
when dealing with Rigid Body Dynamics, these derivatives are difficult to
derive analytically and to implement efficiently. To overcome this issue, we
extend the modelling tool `RobCoGen' to be compatible with Automatic
Differentiation. Additionally, we propose how to automatically obtain the
derivatives and generate highly efficient source code. We highlight the
flexibility and performance of the approach in two application examples. First,
we show a Trajectory Optimization example for the quadrupedal robot HyQ, which
employs auto-differentiation on the dynamics including a contact model. Second,
we present a hardware experiment in which a 6 DoF robotic arm avoids a randomly
moving obstacle in a go-to task by fast, dynamic replanning
Disparity and Optical Flow Partitioning Using Extended Potts Priors
This paper addresses the problems of disparity and optical flow partitioning
based on the brightness invariance assumption. We investigate new variational
approaches to these problems with Potts priors and possibly box constraints.
For the optical flow partitioning, our model includes vector-valued data and an
adapted Potts regularizer. Using the notation of asymptotically level stable
functions we prove the existence of global minimizers of our functionals. We
propose a modified alternating direction method of minimizers. This iterative
algorithm requires the computation of global minimizers of classical univariate
Potts problems which can be done efficiently by dynamic programming. We prove
that the algorithm converges both for the constrained and unconstrained
problems. Numerical examples demonstrate the very good performance of our
partitioning method
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