confidence-aware motion prediction for real-time collision ...prediction for real-time collision...
TRANSCRIPT
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Confidence-aware motion prediction for real-time collision avoidance
Andrea Bajcsy
Long-term Human Motion Prediction Workshop
ICRA 2019
Work with Sylvia Herbert, Jaime Fisac, David Fridovich-Keil, Steven Wang, Sampada Deglurkar, Claire Tomlin and Anca Dragan
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When robots observe behavior that is not well explained by their predictive models, how do
they produce safe but efficient motions?
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Connections to reachability analysis
Confidence-aware prediction & planning
Scaling up to multi-robot, multi-human scenarios
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Confidence-aware prediction & planning
Scaling up to multi-robot, multi-human scenarios
Connections to reachability analysis
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Low probabilityHigh probability
𝑃 𝑢𝐻 𝑥𝐻; 𝜃, 𝛽) ∝ 𝑒𝛽𝑄(𝑥𝐻,𝑢𝐻;𝜃)
Noisily-Rational Human Motion Prediction
ሶ𝑥𝐻 = 𝑓𝐻(𝑥𝐻 , 𝑢𝐻)
[Luce, 1959]
[Baker et al., 2007][Ziebart et al., AAAI 2008]
[Ramachandran et al., IJCAI 2007]
[Finn et al., ICML 2016]
[Pfeiffer et al., IROS 2016]
[Herman et al., ICRA 2015]
[Schultz et al., ICRA 2017]
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Robust Robot Planning with Human Predictions
𝑥𝑅𝑔
ሶ𝑥𝑅 = 𝑓𝑅(𝑥𝑅 , 𝑢𝑅)
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Robust Robot Planning with Human Predictions
𝑥𝑅𝑔
ሶ𝑥𝑅 = 𝑓𝑅(𝑥𝑅 , 𝑢𝑅)
ሶ𝑠𝑅 = ሚ𝑓𝑅(𝑠𝑅 , 𝑎𝑅)
vs.
[Herbert, 2017]
[Mitchell, 2005]
[Lygeros, 2005]
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Hamilton-Jacobi Reachability Analysis
Robust Robot Planning with Human Predictions
𝑥𝑅𝑔
ሶ𝑥𝑅 = 𝑓𝑅(𝑥𝑅 , 𝑢𝑅)
ሶ𝑠𝑅 = ሚ𝑓𝑅(𝑠𝑅 , 𝑎𝑅)
vs.
[Herbert, 2017]
𝑉 𝑟, 𝑇 = sup𝑎[𝑢](∙)
inf𝑢(∙)
{ sup𝑡∈[0,𝑇]
𝑐𝑜𝑠𝑡(𝜉𝑟𝑢,𝑎(𝑡))}
ሶ𝑟 = 𝑓𝑅 𝑥𝑅 , 𝑢𝑅 − 𝜙( ሚ𝑓𝑅 𝑠𝑅 , 𝑎𝑅 )
[Mitchell, 2005]
[Lygeros, 2005]
[Herbert*, Chen*, Han, Bansal, Fisac, Tomlin. "FaSTrack: a Modular Framework for Fast and Guaranteed Safe Motion Planning." CDC, 2017.]
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Robust Robot Planning with Human Predictions
𝑥𝑅𝑔
Error bound𝑉 𝑟, 𝑇 = sup
𝑎[𝑢](∙)inf𝑢(∙)
{ sup𝑡∈[0,𝑇]
𝑐𝑜𝑠𝑡(𝜉𝑟𝑢,𝑎(𝑡))}
ሶ𝑟 = 𝑓𝑅 𝑥𝑅 , 𝑢𝑅 − 𝜙( ሚ𝑓𝑅 𝑠𝑅 , 𝑎𝑅 )
[Mitchell, 2005]
[Lygeros, 2005]
Hamilton-Jacobi Reachability Analysis
[Herbert*, Chen*, Han, Bansal, Fisac, Tomlin. "FaSTrack: a Modular Framework for Fast and Guaranteed Safe Motion Planning." CDC, 2017.]
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Robust Robot Planning with Human Predictions
𝑥𝑅𝑔
[Herbert, 2017]
[Fisac, 2018]
𝑉 𝑟, 𝑇 = sup𝑎[𝑢](∙)
inf𝑢(∙)
{ sup𝑡∈[0,𝑇]
𝑐𝑜𝑠𝑡(𝜉𝑟𝑢,𝑎(𝑡))}
ሶ𝑟 = 𝑓𝑅 𝑥𝑅 , 𝑢𝑅 − 𝜙( ሚ𝑓𝑅 𝑠𝑅 , 𝑎𝑅 )
[Mitchell, 2005]
[Lygeros, 2005]
Hamilton-Jacobi Reachability Analysis
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𝑃 Crash > 𝑐𝑜𝑙𝑙𝑖𝑠𝑖𝑜𝑛𝑡ℎ𝑟𝑒𝑠ℎ
Robust Robot Planning with Human Predictions
𝑥𝑅𝑔
[Herbert, 2017]
[Mitchell, 2005]
[Fisac, 2018]
[Lygeros, 2005]
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Robust Robot Planning with Human Predictions
[Mitchell, 2008]
𝑥𝑅𝑔
[Herbert, 2017]
[Fisac, 2018]
[Lygeros, 2005]
𝑃 Crash > 𝑐𝑜𝑙𝑙𝑖𝑠𝑖𝑜𝑛𝑡ℎ𝑟𝑒𝑠ℎ
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What if the predictive model is wrong?
Modeled human goal
UnmodeledObstacle
Robot goal
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High Confidence Low Confidence
UnmodeledObstacle
UnmodeledGoal
human goal
human goal 1
human goal 2
robot goal
robot goal 1
robot goal 2
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𝑃 𝑢𝐻 𝑥𝐻; 𝜃, 𝛽) ∝ 𝑒𝛽𝑄(𝑥𝐻,𝑢𝐻;𝜃)
Bayesian Model Confidence
ሶ𝑥𝐻 = 𝑓𝐻(𝑥𝐻 , 𝑢𝐻)
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𝑃 𝑢𝐻 𝑥𝐻; 𝜃, 𝛽) ∝ 𝑒𝛽𝑄(𝑥𝐻,𝑢𝐻;𝜃)
Bayesian Model Confidence
ሶ𝑥𝐻 = 𝑓𝐻(𝑥𝐻 , 𝑢𝐻)
𝛽
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𝑃 𝑢𝐻 𝑥𝐻; 𝜃, 𝛽) ∝ 𝑒𝛽𝑄(𝑥𝐻,𝑢𝐻;𝜃)
Bayesian Model Confidence
ሶ𝑥𝐻 = 𝑓𝐻(𝑥𝐻 , 𝑢𝐻)
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𝑃 𝑢𝐻 𝑥𝐻; 𝜃, 𝛽) ∝ 𝑒𝛽𝑄(𝑥𝐻,𝑢𝐻;𝜃)
Bayesian Model Confidence
ሶ𝑥𝐻 = 𝑓𝐻(𝑥𝐻 , 𝑢𝐻)
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Bayesian Model Confidence
ሶ𝑥𝐻 = 𝑓𝐻(𝑥𝐻 , 𝑢𝐻)
𝑏𝑡 𝛽 ∝ 𝑃 𝑢𝐻𝑡 𝑥𝐻
𝑡 ; 𝜃, 𝛽)𝑏𝑡−1(𝛽)
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Bayesian Model Confidence
𝑏𝑡 𝛽 ∝ 𝑃 𝑢𝐻𝑡 𝑥𝐻
𝑡 ; 𝜃, 𝛽)𝑏𝑡−1(𝛽)
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Fixed confidence Bayesian confidence𝛽
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Less confident!
More confident!
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Confidence-aware prediction Scaling up to multi-robot, multi-human scenarios
Connections to reachability analysis
Robust motion planning
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Confidence-aware prediction Scaling up to multi-robot, multi-human scenarios
Connections to reachability analysis
Robust motion planning
![Page 25: Confidence-aware motion prediction for real-time collision ...prediction for real-time collision avoidance Andrea Bajcsy Long-term Human Motion Prediction Workshop ICRA 2019 Work with](https://reader034.vdocuments.us/reader034/viewer/2022042809/5f92ff5281df236d870067fb/html5/thumbnails/25.jpg)
Forward Reachable Set
ሶ𝑥𝐻 = 𝑓𝐻(𝑥𝐻 , 𝑢𝐻)
𝐹𝑅𝑆 𝑥𝐻 , 𝑡 ≔ {𝑥′: ∃𝑢𝐻(∙), 𝑥′ = 𝜉(𝑥𝐻 , 𝑡, 𝑢𝐻(∙))}
𝜉(𝑥𝐻(0), 𝑡, 𝑢𝐻(∙))
𝑥𝐻(0)
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Forward Reachable Set
ሶℎ𝑥 = 𝑣𝐻cos(𝑢𝐻)ሶℎ𝑦 = 𝑣𝐻sin(𝑢𝐻)
Δ𝑡 ∗ 𝑣𝐻
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Forward Reachable Set
ሶℎ𝑥 = 𝑣𝐻cos(𝑢𝐻)ሶℎ𝑦 = 𝑣𝐻sin(𝑢𝐻)
Δ𝑡 ∗ 𝑣𝐻
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Forward Reachable Set
ሶℎ𝑥 = 𝑣𝐻cos(𝑢𝐻)ሶℎ𝑦 = 𝑣𝐻sin(𝑢𝐻)
𝟏 𝒔𝒆𝒄 ∗ 𝑣𝐻
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Forward Reachable Set
ሶℎ𝑥 = 𝑣𝐻cos(𝑢𝐻)ሶℎ𝑦 = 𝑣𝐻sin(𝑢𝐻)
𝟏 𝒔𝒆𝒄 ∗ 𝑣𝐻
𝑃𝑐𝑜𝑙𝑙 ≫ 0
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Forward Reachable Set
ሶℎ𝑥 = 𝑣𝐻cos(𝑢𝐻)ሶℎ𝑦 = 𝑣𝐻sin(𝑢𝐻)
𝟏 𝒔𝒆𝒄 ∗ 𝑣𝐻
𝑃𝑐𝑜𝑙𝑙 > 0
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Forward Reachable Set
ሶℎ𝑥 = 𝑣𝐻cos(𝑢𝐻)ሶℎ𝑦 = 𝑣𝐻sin(𝑢𝐻)
𝟏 𝒔𝒆𝒄 ∗ 𝑣𝐻
𝑃𝑐𝑜𝑙𝑙 → 0
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Forward Reachable Set
ሶℎ𝑥 = 𝑣𝐻cos(𝑢𝐻)ሶℎ𝑦 = 𝑣𝐻sin(𝑢𝐻)
2 𝒔 ∗ 𝑣𝐻 3 𝒔 ∗ 𝑣𝐻𝟏 𝒔𝒆𝒄 ∗ 𝑣𝐻
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Forward Reachable Set
ሶℎ𝑥 = 𝑣𝐻cos(𝑢𝐻)ሶℎ𝑦 = 𝑣𝐻sin(𝑢𝐻)
2 𝒔 ∗ 𝑣𝐻 3 𝒔 ∗ 𝑣𝐻𝟏 𝒔𝒆𝒄 ∗ 𝑣𝐻
modeled goal
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Scaling up to multi-robot, multi-human scenarios
Connections between predictions and FRS
Confidence-aware prediction
Robust motion planning
Confidently determining subsets of the FRS to avoid
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Scaling up to multi-robot, multi-human scenarios
Connections between predictions and FRS
Confidence-aware prediction
Robust motion planning
Determining subsets of the FRS to avoid
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1000 x 1000 x 1000 = 1B 1000 x 1000 x 1000 x 1000 = 1T
1000
1000 x 1000 = 1M
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1000
1000
[Bajcsy, 2019]
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Hardware Demonstration
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Hardware Demonstration
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Confidence-aware predictions offer promising directions for scaling
Connections between predictions and FRS
Confidence-aware prediction
Robust motion planning
Determining subsets of the FRS to avoid
1000
1000
1000 x 1000 = 1M
1000 x 1000 x 1000 = 1B
1000 x 1000 x 1000 x 1000 = 1T
1000
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Confidence-aware predictions offer promising directions for scaling
Connections between predictions and FRS
Confidence-aware prediction
Robust motion planning
Determining subsets of the FRS to avoid
1000
1000
1000 x 1000 = 1M
1000 x 1000 x 1000 = 1B
1000 x 1000 x 1000 x 1000 = 1T
1000
![Page 42: Confidence-aware motion prediction for real-time collision ...prediction for real-time collision avoidance Andrea Bajcsy Long-term Human Motion Prediction Workshop ICRA 2019 Work with](https://reader034.vdocuments.us/reader034/viewer/2022042809/5f92ff5281df236d870067fb/html5/thumbnails/42.jpg)
Papers
Herbert*, Chen*, Han, Bansal, Fisac, Tomlin. "FaSTrack: a Modular Framework for Fast and Guaranteed Safe Motion Planning." CDC, 2017.
Fisac*, Bajcsy*, Herbert, Fridovich-Keil, Wang, Tomlin, and Dragan. "Probabilistically Safe Robot Planning with Confidence-Based Human Predictions." RSS, 2018.
Fridovich-Keil*, Bajcsy*, Fisac, Herbert, Wang, Dragan, and Tomlin. “Confidence-Aware Motion Prediction for Real-Time Collision Avoidance.” IJRR, 2019
Bajcsy*, Herbert*, Fridovich-Keil, Fisac, Deglurkar, Dragan, and Tomlin, “A Scalable Framework for Real-Time Multi-Robot, Multi-Human Collision Avoidance.” ICRA, 2019.
Multi-robot, multi-human planning: https://github.com/HJReachability/faSTPeople
Code
Fast and safe robot tracking: https://github.com/HJReachability/fastrack
Pedestrian prediction: https://github.com/shwang/pedestrian_prediction
ROS wrapper for pedestrian prediction: https://github.com/abajcsy/crazyflie_human