The Experts below are selected from a list of 3366 Experts worldwide ranked by ideXlab platform
Scaramuzza Davide - One of the best experts on this subject based on the ideXlab platform.
-
Fisher Information Field: an Efficient and Differentiable Map for Perception-aware Planning
2020Co-Authors: Zhang Zichao, Scaramuzza DavideAbstract:Considering visual localization accuracy at the planning time gives preference to robot motion that can be better localized and thus has the potential of improving vision-based navigation, especially in visually degraded environments. To integrate the knowledge about localization accuracy in motion planning algorithms, a central task is to quantify the amount of information that an image taken at a 6 degree-of-freedom pose brings for localization, which is often represented by the Fisher information. However, computing the Fisher information from a set of sparse landmarks (i.e., a point cloud), which is the most common Map for visual localization, is inefficient. This approach scales linearly with the number of landmarks in the environment and does not allow the reuse of the computed Fisher information. To overcome these drawbacks, we propose the first dedicated Map representation for evaluating the Fisher information of 6 degree-of-freedom visual localization for perception-aware motion planning. By formulating the Fisher information and sensor visibility carefully, we are able to separate the rotational invariant component from the Fisher information and store it in a voxel grid, namely the Fisher information field. This step only needs to be performed once for a known environment. The Fisher information for arbitrary poses can then be computed from the field in constant time, eliminating the need of costly iterating all the 3D landmarks at the planning time. Experimental results show that the proposed Fisher information field can be applied to different motion planning algorithms and is at least one order-of-magnitude faster than using the point cloud directly. Moreover,the proposed Map representation is Differentiable, resulting in better performance than the point cloud when used in trajectory optimization algorithms.Comment: 18 pages, 15 figure
Davide Scaramuzza - One of the best experts on this subject based on the ideXlab platform.
-
fisher information field an efficient and Differentiable Map for perception aware planning
arXiv: Robotics, 2020Co-Authors: Zichao Zhang, Davide ScaramuzzaAbstract:Considering visual localization accuracy at the planning time gives preference to robot motion that can be better localized and thus has the potential of improving vision-based navigation, especially in visually degraded environments. To integrate the knowledge about localization accuracy in motion planning algorithms, a central task is to quantify the amount of information that an image taken at a 6 degree-of-freedom pose brings for localization, which is often represented by the Fisher information. However, computing the Fisher information from a set of sparse landmarks (i.e., a point cloud), which is the most common Map for visual localization, is inefficient. This approach scales linearly with the number of landmarks in the environment and does not allow the reuse of the computed Fisher information. To overcome these drawbacks, we propose the first dedicated Map representation for evaluating the Fisher information of 6 degree-of-freedom visual localization for perception-aware motion planning. By formulating the Fisher information and sensor visibility carefully, we are able to separate the rotational invariant component from the Fisher information and store it in a voxel grid, namely the Fisher information field. This step only needs to be performed once for a known environment. The Fisher information for arbitrary poses can then be computed from the field in constant time, eliminating the need of costly iterating all the 3D landmarks at the planning time. Experimental results show that the proposed Fisher information field can be applied to different motion planning algorithms and is at least one order-of-magnitude faster than using the point cloud directly. Moreover,the proposed Map representation is Differentiable, resulting in better performance than the point cloud when used in trajectory optimization algorithms.
Zhang Zichao - One of the best experts on this subject based on the ideXlab platform.
-
Fisher Information Field: an Efficient and Differentiable Map for Perception-aware Planning
2020Co-Authors: Zhang Zichao, Scaramuzza DavideAbstract:Considering visual localization accuracy at the planning time gives preference to robot motion that can be better localized and thus has the potential of improving vision-based navigation, especially in visually degraded environments. To integrate the knowledge about localization accuracy in motion planning algorithms, a central task is to quantify the amount of information that an image taken at a 6 degree-of-freedom pose brings for localization, which is often represented by the Fisher information. However, computing the Fisher information from a set of sparse landmarks (i.e., a point cloud), which is the most common Map for visual localization, is inefficient. This approach scales linearly with the number of landmarks in the environment and does not allow the reuse of the computed Fisher information. To overcome these drawbacks, we propose the first dedicated Map representation for evaluating the Fisher information of 6 degree-of-freedom visual localization for perception-aware motion planning. By formulating the Fisher information and sensor visibility carefully, we are able to separate the rotational invariant component from the Fisher information and store it in a voxel grid, namely the Fisher information field. This step only needs to be performed once for a known environment. The Fisher information for arbitrary poses can then be computed from the field in constant time, eliminating the need of costly iterating all the 3D landmarks at the planning time. Experimental results show that the proposed Fisher information field can be applied to different motion planning algorithms and is at least one order-of-magnitude faster than using the point cloud directly. Moreover,the proposed Map representation is Differentiable, resulting in better performance than the point cloud when used in trajectory optimization algorithms.Comment: 18 pages, 15 figure
Zichao Zhang - One of the best experts on this subject based on the ideXlab platform.
-
fisher information field an efficient and Differentiable Map for perception aware planning
arXiv: Robotics, 2020Co-Authors: Zichao Zhang, Davide ScaramuzzaAbstract:Considering visual localization accuracy at the planning time gives preference to robot motion that can be better localized and thus has the potential of improving vision-based navigation, especially in visually degraded environments. To integrate the knowledge about localization accuracy in motion planning algorithms, a central task is to quantify the amount of information that an image taken at a 6 degree-of-freedom pose brings for localization, which is often represented by the Fisher information. However, computing the Fisher information from a set of sparse landmarks (i.e., a point cloud), which is the most common Map for visual localization, is inefficient. This approach scales linearly with the number of landmarks in the environment and does not allow the reuse of the computed Fisher information. To overcome these drawbacks, we propose the first dedicated Map representation for evaluating the Fisher information of 6 degree-of-freedom visual localization for perception-aware motion planning. By formulating the Fisher information and sensor visibility carefully, we are able to separate the rotational invariant component from the Fisher information and store it in a voxel grid, namely the Fisher information field. This step only needs to be performed once for a known environment. The Fisher information for arbitrary poses can then be computed from the field in constant time, eliminating the need of costly iterating all the 3D landmarks at the planning time. Experimental results show that the proposed Fisher information field can be applied to different motion planning algorithms and is at least one order-of-magnitude faster than using the point cloud directly. Moreover,the proposed Map representation is Differentiable, resulting in better performance than the point cloud when used in trajectory optimization algorithms.
Takeshi Miura - One of the best experts on this subject based on the ideXlab platform.
-
on the hyers ulam stability of the banach space valued differential equation y λy
Bulletin of The Korean Mathematical Society, 2002Co-Authors: Sinei Takahasi, Takeshi Miura, Shizuo MiyajimaAbstract:Let I be an open interval and X a complex Banach space. Let a non-zero complex number with Re . If is a strongly Differentiable Map from I to X with , then we show that the distance between and the set of all solutions to the differential equation y'=y is at most $\varepsilon/Re\lambda$.
-
on the hyers ulam stability of real continuous function valued Differentiable Map
Tokyo Journal of Mathematics, 2001Co-Authors: Takeshi Miura, Sinei Takahasi, Hisashi ChodaAbstract:We consider a Differentiable Map $f$ from an open interval to a real Banach space of all bounded continuous real-valued functions on a topological space. We show that $f$ can be approximated by the solution to the differential equation $x'(t)=\lambda x(t)$, if $||f'(t)-\lambda f(t)||_\infty\leq\varepsilon$ holds.