Abstract:This article reports on recent progress in robot perception and control methods developed by taking the symmetry of the problem into account. Inspired by existing mathematical tools for studying the symmetry structures of geometric spaces, geometric sensor registration, state estimator, and control methods provide indispensable insights into the problem formulations and generalization of robotics algorithms to challenging unknown environments. When combined with computational methods for learning hard-to-measu… Show more
“…Nonholonomic systems can also be modeled by LGVI, while the discretization of nonholonomic constraints needs more attention [73,74]. More generally, LGVI is aligned with symmetry-preserving methods in robotics [75] and its applications in various robot perception and control problems from a promising research direction. The memory and time cost of the proposed algorithm is still high for real-time applications.…”
This paper reports a novel result: with proper robot models on matrix Lie groups, one can formulate the kinodynamic motion planning problem for rigid body systems as exact polynomial optimization problems that can be relaxed as semidefinite programming (SDP). Due to the nonlinear rigid body dynamics, the motion planning problem for rigid body systems is nonconvex. Existing global optimization-based methods do not properly deal with the configuration space of the 3D rigid body; thus, they do not scale well to long-horizon planning problems. We use Lie groups as the configuration space in our formulation and apply the variational integrator to formulate the forced rigid body systems as quadratic polynomials. Then we leverage Lasserre's hierarchy to obtain the globally optimal solution via SDP. By constructing the motion planning problem in a sparse manner, the results show that the proposed algorithm has linear complexity with respect to the planning horizon. This paper demonstrates the proposed method can provide rank-one optimal solutions at relaxation order two for most of the testing cases of 1) 3D drone landing using the full dynamics model and 2) inverse kinematics for serial manipulators.
“…Nonholonomic systems can also be modeled by LGVI, while the discretization of nonholonomic constraints needs more attention [73,74]. More generally, LGVI is aligned with symmetry-preserving methods in robotics [75] and its applications in various robot perception and control problems from a promising research direction. The memory and time cost of the proposed algorithm is still high for real-time applications.…”
This paper reports a novel result: with proper robot models on matrix Lie groups, one can formulate the kinodynamic motion planning problem for rigid body systems as exact polynomial optimization problems that can be relaxed as semidefinite programming (SDP). Due to the nonlinear rigid body dynamics, the motion planning problem for rigid body systems is nonconvex. Existing global optimization-based methods do not properly deal with the configuration space of the 3D rigid body; thus, they do not scale well to long-horizon planning problems. We use Lie groups as the configuration space in our formulation and apply the variational integrator to formulate the forced rigid body systems as quadratic polynomials. Then we leverage Lasserre's hierarchy to obtain the globally optimal solution via SDP. By constructing the motion planning problem in a sparse manner, the results show that the proposed algorithm has linear complexity with respect to the planning horizon. This paper demonstrates the proposed method can provide rank-one optimal solutions at relaxation order two for most of the testing cases of 1) 3D drone landing using the full dynamics model and 2) inverse kinematics for serial manipulators.
“…Another possible extension of MKF is to apply it to the belief space planning problem. Finally, an attractive research direction is an extension of the moment-based approach to symmetrypreserving estimation and control methods [32]- [39].…”
Section: B Simulation With Real Robot Datamentioning
This paper develops a new nonlinear filter, called Moment-based Kalman Filter (MKF), using the exact moment propagation method. Existing state estimation methods use linearization techniques or sampling points to compute approximate values of moments. However, moment propagation of probability distributions of random variables through nonlinear process and measurement models play a key role in the development of state estimation and directly affects their performance. The proposed moment propagation procedure can compute exact moments for non-Gaussian as well as non-independent Gaussian random variables. Thus, MKF can propagate exact moments of uncertain state variables up to any desired order. MKF is derivative-free and does not require tuning parameters. Moreover, MKF has the same computation time complexity as the extended or unscented Kalman filters, i.e., EKF and UKF. The experimental evaluations show that MKF is the preferred filter in comparison to EKF and UKF and outperforms both filters in non-Gaussian noise regimes.
“…This suggests that symmetry-breaking events (or the preservation of symmetry) are responsible for the developmental origins for intelligent behaviour emerging through a combination of cell differentiation, changes in connectivity [18] and the differential effects of embodiment (electronic supplementary material, SF1). This theoretical model will be useful for understanding the process of embodied cognitive morphogenesis and cognition in single-cell organisms, animal species with small nervous system networks and bioinspired computational agents [19]. Figure 14E cognition in the context of agent development (generic embryo).…”
The embryological view of development is that coordinated gene expression, cellular physics and migration provides the basis for phenotypic complexity. This stands in contrast with the prevailing view of embodied cognition, which claims that informational feedback between organisms and their environment is key to the emergence of intelligent behaviours. We aim to unite these two perspectives as
embodied cognitive morphogenesis
, in which morphogenetic symmetry breaking produces specialized organismal subsystems which serve as a substrate for the emergence of autonomous behaviours. As embodied cognitive morphogenesis produces fluctuating phenotypic asymmetry and the emergence of information processing subsystems, we observe three distinct properties: acquisition, generativity and transformation. Using a generic organismal agent, such properties are captured through models such as tensegrity networks, differentiation trees and embodied hypernetworks, providing a means to identify the context of various symmetry-breaking events in developmental time. Related concepts that help us define this phenotype further include concepts such as modularity, homeostasis and 4E (embodied, enactive, embedded and extended) cognition. We conclude by considering these autonomous developmental systems as a process called connectogenesis, connecting various parts of the emerged phenotype into an approach useful for the analysis of organisms and the design of bioinspired computational agents.
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