Optimization-Based Cooperative Multi-Robot Target Tracking with Reasoning about Occlusions Karol Hausman, Gregory Kahn, Sachin Patil, Joerg Mueller, Ken.

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Presentation transcript:

Optimization-Based Cooperative Multi-Robot Target Tracking with Reasoning about Occlusions Karol Hausman, Gregory Kahn, Sachin Patil, Joerg Mueller, Ken Goldberg, Pieter Abbeel, Gaurav Sukhatme University of Southern California, University of California Berkeley

Optimization-Based Cooperative Multi-Robot Target Tracking with Reasoning about Occlusions

Belief Space Planning Perception Action Belief Space Planning State space plan start goal Problem settingBelief space plan [Example from Platt et al., 2010] This is a Partially Observable Markov Decision Process (POMDP) – in general intractable

Optimization-Based Cooperative Multi-Robot Target Tracking with Reasoning about Occlusions Belief Space Planning State space plan start goal Problem settingBelief space plan [Example from Platt et al., 2010]

Optimization-Based Cooperative Multi-Robot Target Tracking with Reasoning about Occlusions Belief Space Planning Nonlinear stochastic motion and observation models Belief space: Convert underlying dynamics to belief space dynamics Bayesian filter (e.g., Extended Kalman Filter (EKF)) (state space) x (belief space)

Optimization-Based Cooperative Multi-Robot Target Tracking with Reasoning about Occlusions Belief Space Planning Minimize Constraints: = goal Measurements?

Optimization-Based Cooperative Multi-Robot Target Tracking with Reasoning about Occlusions Belief Space Planning Minimize Constraints: = goal Maximum likelihood measurements

Optimization-Based Cooperative Multi-Robot Target Tracking with Reasoning about Occlusions Level -1 Level 0 Level 1 Level 2 [Hausman et al., ISER 2014, IJRR 2015] Occlusions

Optimization-Based Cooperative Multi-Robot Target Tracking with Reasoning about Occlusions Occlusions Field of view (FOV) discontinuity Occlusion discontinuity

Optimization-Based Cooperative Multi-Robot Target Tracking with Reasoning about Occlusions Occlusions : Binary variable {0,1} 0 -> No measurement 1 -> Measurement Modified Kalman Gain in EKF: [Patil et al. ICRA 2014] Binary non-convex optimization problem – difficult to solve!

Optimization-Based Cooperative Multi-Robot Target Tracking with Reasoning about Occlusions Occlusions ≈

Optimization-Based Cooperative Multi-Robot Target Tracking with Reasoning about Occlusions Occlusions Increasing difficulty [Patil et al. ICRA 2014]

Optimization-Based Cooperative Multi-Robot Target Tracking with Reasoning about Occlusions Occlusions Outside camera FOV Occlusions due to other quadrotors [Hausman et al., ICRA 2016]

Optimization-Based Cooperative Multi-Robot Target Tracking with Reasoning about Occlusions Consider nonlinear stochastic dynamics and measurement models Dynamics: Measurement: Problem formulation

Optimization-Based Cooperative Multi-Robot Target Tracking with Reasoning about Occlusions Problem formulation Cost terms:

Optimization-Based Cooperative Multi-Robot Target Tracking with Reasoning about Occlusions Results

Optimization-Based Cooperative Multi-Robot Target Tracking with Reasoning about Occlusions Results Thank you How does the optimization time horizon affect tracking performance? 2 time steps5 time steps10 time steps Avg. over 10 runs

Optimization-Based Cooperative Multi-Robot Target Tracking with Reasoning about Occlusions Results Thank you How does number of quadrotors affect tracking performance? 1 quadrotor3 quadrotors5 quadrotors

Optimization-Based Cooperative Multi-Robot Target Tracking with Reasoning about Occlusions Results Thank you How does optimization compare to random sampling or lattice based sampling in terms of tracking performance? Random samplingLattice samplingOptimization 3 Quadrotors

Optimization-Based Cooperative Multi-Robot Target Tracking with Reasoning about Occlusions Results How does explicit consideration of occlusions affect tracking performance? Does not consider occlusions during planning Consider occlusions during planning

Optimization-Based Cooperative Multi-Robot Target Tracking with Reasoning about Occlusions Results Multi-level topology approach (Hausman et al, 2014) Optimization Comparison of topology approach vs. optimization

Optimization-Based Cooperative Multi-Robot Target Tracking with Reasoning about Occlusions Insights

Optimization-Based Cooperative Multi-Robot Target Tracking with Reasoning about Occlusions Summary 3D Tracking Approach: considers onboard sensing and does not need to explicitly reason about sensing topologies is probabilistic and takes into account motion and sensing uncertainties provides locally optimal control in 3D

Questions?