Academia.eduAcademia.edu

Figure 8 – uploaded by Antonis Dimitriou

See full PDFdownloadDownload figure
CORRIDOR pose errors per feedback method Fig. 8 The distribution of the mean 2-norm total pose error of MCL (to the left of each indicated feedback method) and of the compound system’s (to the right of each indicated feedback method) across N = 100 simulations according to feedback method in environment CORRIDOR. Signifier “open” is shorthand for open-loop, meaning that no particle of the overall system is fed back to the particle filter, “soft-1” for the configuration where the overall system’s output is fed back to the particle filter in the form of one particle, “soft-50” for that where it is fed back in the form of as many particles as half of the population’s size, and “hard” for the configuration where the particle filter is initialised around the pose calculated after scan-matching

Figure 8 CORRIDOR pose errors per feedback method Fig. 8 The distribution of the mean 2-norm total pose error of MCL (to the left of each indicated feedback method) and of the compound system’s (to the right of each indicated feedback method) across N = 100 simulations according to feedback method in environment CORRIDOR. Signifier “open” is shorthand for open-loop, meaning that no particle of the overall system is fed back to the particle filter, “soft-1” for the configuration where the overall system’s output is fed back to the particle filter in the form of one particle, “soft-50” for that where it is fed back in the form of as many particles as half of the population’s size, and “hard” for the configuration where the particle filter is initialised around the pose calculated after scan-matching

Related Figures (13)

Fig. 1 The robot is initially posed at time ¢ = fo at x(x, y,9), and captures a range scan z. Then, at time fj > fg, it is posed at x'(x’, y’, 0), from where it captures a second range scan 2’. Scan- matching between z (the reference scan) and 2’ (the input, or “data” scan) produces the rigid-body transform q(Ax, Ay, A@). Information pertaining to the first scan is denoted with red, while that pertaining to the second with blue. The red and blue arrows denote the robot’s pose and orientation. Dashed lines depict the angular range of the scans, while dotted lines depict the parts of the environment that are visible by each scan. The colour orange is used to denote parts of the environment that are visible from both poses. The green vector depicts the translational part of q, the result of scan-matching z and 2’
Fig. 1 The robot is initially posed at time ¢ = fo at x(x, y,9), and captures a range scan z. Then, at time fj > fg, it is posed at x'(x’, y’, 0), from where it captures a second range scan 2’. Scan- matching between z (the reference scan) and 2’ (the input, or “data” scan) produces the rigid-body transform q(Ax, Ay, A@). Information pertaining to the first scan is denoted with red, while that pertaining to the second with blue. The red and blue arrows denote the robot’s pose and orientation. Dashed lines depict the angular range of the scans, while dotted lines depict the parts of the environment that are visible by each scan. The colour orange is used to denote parts of the environment that are visible from both poses. The green vector depicts the translational part of q, the result of scan-matching z and 2’
Fig. 2. The overall system in block structure. Blocks indicate sub- systems, while ellipses indicate their inputs. The colour red is used to identify the contributions of our approach to the state-of-the-art in tandem systems of particle filters and scan-matching. Here, scan- matching is treated as a prosthesis of MCL. MCL’s population P; is subject to weight-based selection at time t > 0. The selected particles are weight-averaged and the resulting pose is used as the origin of a virtual scan across the map. The real and virtual scans are then matched using PL-ICP. The output of scan-matching %} is, in principle, more accurate than that of MCL, x;, which means that it could be used to serve in assistance to MCL’s localisation by feeding it back to it. See text for the three ways that feedback can be introduced in particle filters The proposed feedback strategy will be referred to hereafter as soft-p loop-closure, where p is expressed in percentage terms (e.g. in the regime of soft-50 loop-closure, every time MCL outputs a result to PL-ICP, the latter improves its estimate and introduces — and possibly deletes — as many particles as needed so that the final proportion of copies of its output is 50% of the particle filter’s final total population; the term soft-1 loop-closure will be reserved for reference to the original idea of inserting only one particle to the filter’s population).
Fig. 2. The overall system in block structure. Blocks indicate sub- systems, while ellipses indicate their inputs. The colour red is used to identify the contributions of our approach to the state-of-the-art in tandem systems of particle filters and scan-matching. Here, scan- matching is treated as a prosthesis of MCL. MCL’s population P; is subject to weight-based selection at time t > 0. The selected particles are weight-averaged and the resulting pose is used as the origin of a virtual scan across the map. The real and virtual scans are then matched using PL-ICP. The output of scan-matching %} is, in principle, more accurate than that of MCL, x;, which means that it could be used to serve in assistance to MCL’s localisation by feeding it back to it. See text for the three ways that feedback can be introduced in particle filters The proposed feedback strategy will be referred to hereafter as soft-p loop-closure, where p is expressed in percentage terms (e.g. in the regime of soft-50 loop-closure, every time MCL outputs a result to PL-ICP, the latter improves its estimate and introduces — and possibly deletes — as many particles as needed so that the final proportion of copies of its output is 50% of the particle filter’s final total population; the term soft-1 loop-closure will be reserved for reference to the original idea of inserting only one particle to the filter’s population).
In Algorithm 2, if hard-closed-loop is selected as the method of feedback, the particle set is filled with Ninax copies of the system’s output at the previous timestep and then each component of each particle’s pose hypothesis is subject to minor disturbance according to parameters
In Algorithm 2, if hard-closed-loop is selected as the method of feedback, the particle set is filled with Ninax copies of the system’s output at the previous timestep and then each component of each particle’s pose hypothesis is subject to minor disturbance according to parameters
Fig. 3 Internal to the modified version of MCL, there are 4 distinct and mutually exclusive modes of feedback. Denoting by *’ the output of the scan-matching process, by P the filter’s population at the time of feedback execution, and by P’ the population output by feedback: (a) hard loop-closure, where the population of MCL is initialised anew, with P’ comprised of particles spread around <’, (b) soft-1 loop-closure, where &’ is introduced into P in the form of one discrete particle, (c) soft-p loop-closure, where p% of P’ is comprised of clones of one particle with pose equal to #’ and (100 — p)% is comprised by the corresponding in number heavy-most particles of P, and (d) no feedback at all. The colour red is used to identify the contribution of our approach with respect to feedback methods to the state-of-the-art in tandem systems of particle filters and scan-matching. Feedback modes are immutable and set a priori
Fig. 3 Internal to the modified version of MCL, there are 4 distinct and mutually exclusive modes of feedback. Denoting by *’ the output of the scan-matching process, by P the filter’s population at the time of feedback execution, and by P’ the population output by feedback: (a) hard loop-closure, where the population of MCL is initialised anew, with P’ comprised of particles spread around <’, (b) soft-1 loop-closure, where &’ is introduced into P in the form of one discrete particle, (c) soft-p loop-closure, where p% of P’ is comprised of clones of one particle with pose equal to #’ and (100 — p)% is comprised by the corresponding in number heavy-most particles of P, and (d) no feedback at all. The colour red is used to identify the contribution of our approach with respect to feedback methods to the state-of-the-art in tandem systems of particle filters and scan-matching. Feedback modes are immutable and set a priori
Fig. 4 The map of environment CORRIDOR, Mc. The initial configuration of the robot is seen in green colour, while its goal one in red. The size of the environment is 10 x 7m? The two environments are dubbed CORRIDOR, denoted by Mc and presented in Fig. 4, of size 10 x 7 m’, and WAREHOUSE, denoted by My and presented in Fig. 5, of size 20 x 42 m*. The resolution of both maps is 0.01mx0.01m/cell. The former is used to illustrate the efficacy of the proposed system in non-complex environments, where all of its boundaries are within the range of the robot’s 2D range sensor at all times. By contrast, the latter is a large warehouse, —the natural habitat of RFID-tagged objects in industry— intended to put more strain on the system and thus its performance: obstacles are further apart than in CORRIDOR, which means that either not all rays of the sensor carry valuable and usable information, or they are more corrupted by noise, as the range error increases with the sensed distance, or both. The first challenge affects MCL, in that it has to rely more on its odometry, which is prone to error accumulation, and less on precise range measurements, and scan-matching, as there are less measured scan-points, therefore greater insufficiency of information in pairing the virtual scan taken across the map to the reference real laser surface. The second challenge affects MCL, in that the pose estimate is disturbed by noise, and scan-matching, in that noise raises the probability of false correspondences and, in general, erroneous alignment altogether. To this end, we configured the virtual range sensor to operate at a maximum range of 10.0 meters.
Fig. 4 The map of environment CORRIDOR, Mc. The initial configuration of the robot is seen in green colour, while its goal one in red. The size of the environment is 10 x 7m? The two environments are dubbed CORRIDOR, denoted by Mc and presented in Fig. 4, of size 10 x 7 m’, and WAREHOUSE, denoted by My and presented in Fig. 5, of size 20 x 42 m*. The resolution of both maps is 0.01mx0.01m/cell. The former is used to illustrate the efficacy of the proposed system in non-complex environments, where all of its boundaries are within the range of the robot’s 2D range sensor at all times. By contrast, the latter is a large warehouse, —the natural habitat of RFID-tagged objects in industry— intended to put more strain on the system and thus its performance: obstacles are further apart than in CORRIDOR, which means that either not all rays of the sensor carry valuable and usable information, or they are more corrupted by noise, as the range error increases with the sensed distance, or both. The first challenge affects MCL, in that it has to rely more on its odometry, which is prone to error accumulation, and less on precise range measurements, and scan-matching, as there are less measured scan-points, therefore greater insufficiency of information in pairing the virtual scan taken across the map to the reference real laser surface. The second challenge affects MCL, in that the pose estimate is disturbed by noise, and scan-matching, in that noise raises the probability of false correspondences and, in general, erroneous alignment altogether. To this end, we configured the virtual range sensor to operate at a maximum range of 10.0 meters.
Fig. 5 The map of environment WAREHOUSE, My. The initial configuration of the robot is seen in green colour, while its goal one in red. The size of the environment is 20 x 42m?
Fig. 5 The map of environment WAREHOUSE, My. The initial configuration of the robot is seen in green colour, while its goal one in red. The size of the environment is 20 x 42m?
CORRIDOR pose errors per pose selection method Fig.6 The distribution of the mean 2-norm total pose error of open- loop-MCL (to the left of each indicated selection method) and of the compound system’s (to the right of each indicated selection method) across N = 100 simulations according to population selection method in environment CORRIDOR. Signifier “100%” denotes the configuration where all particles of the population set were chosen in the process of weight-averaging for extracting the system’s pose estimate, “> W” that where only those particles whose weight was greater than the particle population’s mean weight were selected, “10%” that where only the top 10% of heaviest particles were selected, and “top” the configuration where only the particle with the highest weight among all those in the population was selected as the system’s estimate
CORRIDOR pose errors per pose selection method Fig.6 The distribution of the mean 2-norm total pose error of open- loop-MCL (to the left of each indicated selection method) and of the compound system’s (to the right of each indicated selection method) across N = 100 simulations according to population selection method in environment CORRIDOR. Signifier “100%” denotes the configuration where all particles of the population set were chosen in the process of weight-averaging for extracting the system’s pose estimate, “> W” that where only those particles whose weight was greater than the particle population’s mean weight were selected, “10%” that where only the top 10% of heaviest particles were selected, and “top” the configuration where only the particle with the highest weight among all those in the population was selected as the system’s estimate
WAREHOUSE pose errors per pose selection method Fig. 7 The distribution of the mean 2-norm total pose error of open- loop-MCL (to the left of each indicated selection method) and of the compound system’s (to the right of each indicated selection method) across N = 100 simulations according to population selection method in environment WAREHOUSE. Signifier “100%” denotes the configuration where all particles of the population set were chosen in the process of weight-averaging for extracting the system’s pose estimate, “> W” that where only those particles whose weight was greater than the particle population’s mean weight were selected, “10%” that where only the top 10% of heaviest particles were selected, and “top” the configuration where only the particle with the highest weight among all those in the population was selected as the system’s estimate
WAREHOUSE pose errors per pose selection method Fig. 7 The distribution of the mean 2-norm total pose error of open- loop-MCL (to the left of each indicated selection method) and of the compound system’s (to the right of each indicated selection method) across N = 100 simulations according to population selection method in environment WAREHOUSE. Signifier “100%” denotes the configuration where all particles of the population set were chosen in the process of weight-averaging for extracting the system’s pose estimate, “> W” that where only those particles whose weight was greater than the particle population’s mean weight were selected, “10%” that where only the top 10% of heaviest particles were selected, and “top” the configuration where only the particle with the highest weight among all those in the population was selected as the system’s estimate
Fig.9 The distribution of the mean 2-norm total pose error of MCL (to the left of each indicated feedback method) and of the compound system’s (to the right of each indicated feedback method) across N = 100 simulations according to feedback method in environment WAREHOUSE. Signifier “open” is shorthand for open-loop, meaning that no particle of the overall system is fed back to the particle filter, “soft-1” for the configuration where the overall system’s output is fed back to the particle filter in the form of one particle, “soft-50” for that where it is fed back in the form of as many particles as half of the population’s size, and “hard” for the configuration where the particle filter is initialised around the pose calculated after scan-matching
Fig.9 The distribution of the mean 2-norm total pose error of MCL (to the left of each indicated feedback method) and of the compound system’s (to the right of each indicated feedback method) across N = 100 simulations according to feedback method in environment WAREHOUSE. Signifier “open” is shorthand for open-loop, meaning that no particle of the overall system is fed back to the particle filter, “soft-1” for the configuration where the overall system’s output is fed back to the particle filter in the form of one particle, “soft-50” for that where it is fed back in the form of as many particles as half of the population’s size, and “hard” for the configuration where the particle filter is initialised around the pose calculated after scan-matching
CORRIDOR pose errors per pose selection method Fig.11 The distribution of the mean 2-norm total pose error of open- loop-MCL (to the left of each indicated selection method) and of the compound system’s (to the right of each indicated selection method) across N = 100 simulations according to population selection method in environment CORRIDOR, focused for clarity of comparison
CORRIDOR pose errors per pose selection method Fig.11 The distribution of the mean 2-norm total pose error of open- loop-MCL (to the left of each indicated selection method) and of the compound system’s (to the right of each indicated selection method) across N = 100 simulations according to population selection method in environment CORRIDOR, focused for clarity of comparison
Fig. 13. The distribution of the mean 2-norm total pose error of MCL (to the left of each indicated feedback method) and of the compound system’s (to the right of each indicated feedback method) across N = 100 simulations according to feedback method in environment CORRIDOR, focused for clarity of comparison
Fig. 13. The distribution of the mean 2-norm total pose error of MCL (to the left of each indicated feedback method) and of the compound system’s (to the right of each indicated feedback method) across N = 100 simulations according to feedback method in environment CORRIDOR, focused for clarity of comparison
WAREHOUSE pose errors per feedback method Fig. 14 The distribution of the mean 2-norm total pose error of MCL (to the left of each indicated feedback method) and of the compound system’s (to the right of each indicated feedback method) across N = 100 simulations according to feedback method in environment WAREHOUSE, focused for clarity of comparison
WAREHOUSE pose errors per feedback method Fig. 14 The distribution of the mean 2-norm total pose error of MCL (to the left of each indicated feedback method) and of the compound system’s (to the right of each indicated feedback method) across N = 100 simulations according to feedback method in environment WAREHOUSE, focused for clarity of comparison
References WAREHOUSE pose errors per pose selection method Fig. 12 The distribution of the mean 2-norm total pose error of open- loop-MCL (to the left of each indicated selection method) and of the compound system’s (to the right of each indicated selection method) across N = 100 simulations according to population selection method in environment WAREHOUSE, focused for clarity of comparison
References WAREHOUSE pose errors per pose selection method Fig. 12 The distribution of the mean 2-norm total pose error of open- loop-MCL (to the left of each indicated selection method) and of the compound system’s (to the right of each indicated selection method) across N = 100 simulations according to population selection method in environment WAREHOUSE, focused for clarity of comparison
Related topics:
Cognitive ScienceComputer ScienceArtificial IntelligenceMobile RobotMatching statistics
580 California St., Suite 400
San Francisco, CA, 94104
© 2025 Academia. All rights reserved