1. 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

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

3. 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

4. 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]

5. 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)

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

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

8. 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

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

10. 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!

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

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

13. 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]

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

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

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

17. 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

18. 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

19. 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

20. 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

21. 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

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

23. 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

24. Questions?