4._CRD Simulation_NN1 results_NN2 
The_AT0 risk-reward_AJ0 optimization_NN1 problem_NN1 (_PUL 8_CRD )_PUR for_PRP human-robot_NN1 collaboration_NN1 is_VBZ analyzed_VVN for_PRP robotic_AJ0 citrus_AJ0 harvesting_NN1 in_PRP Florida_NP0 ,_PUN USA_NP0 ._SENT However_AV0 ,_PUN we_PNP emphasize_VVB that_CJT this_DT0 framework_NN1 is_VBZ not_XX0 restrictive_AJ0 to_PRP the_AT0 presented_AJ0 application_NN1 ,_PUN and_CJC it_PNP can_VM0 be_VBI suitably_AV0 modified_VVN for_PRP use_NN1 in_PRP other_AJ0 agricultural_AJ0 operations_NN2 requiring_VVG human-robot_NN1 collaboration_NN1 ._SENT 
4.1_CRD ._SENT Experimental_AJ0 setup_NN1 
The_AT0 developed_AJ0 framework_NN1 is_VBZ validated_VVN in_PRP a_AT0 simulated_AJ0 grove_NN1 environment_NN1 using_VVG citrus_AJ0 production_NN1 data_NN0 for_PRP 2016_CRD –_PUN 17_CRD obtained_VVN from_PRP the_AT0 United_NP0 States_NP0 Department_NN1 of_PRF Agriculture_NN1 (_PUL USDA_NP0 )_PUR ,_PUN National_AJ0 Agricultural_AJ0 Statistics_NN0 Service_NN1 ,_PUN Southern_AJ0 Region_NN1 ,_PUN Florida_NP0 Field_NP0 Office_NN1 ._SENT Relevant_AJ0 to_PRP the_AT0 problem_NN1 in_PRP hand_NN1 ,_PUN data_NN0 shown_VVN in_PRP Table_NN1 1_CRD was_VBD obtained_VVN for_PRP Valencia_NP0 ,_PUN Navel_NN1 ,_PUN Early-midseason_NP0 ,_PUN white_AJ0 grapefruit_NN0 ,_PUN and_CJC red_AJ0 grapefruit_NN0 ._SENT The_AT0 results_NN2 presented_VVN in_PRP this_DT0 section_NN1 consider_VVB simulated_AJ0 citrus_AJ0 groves_NN2 of_PRF 100_CRD acres_NN2 for_PRP fresh_AJ0 fruit_NN0 production_NN1 for_PRP the_AT0 above_AJ0 fruit_NN0 varieties_NN2 ._SENT Based_VVN on_PRP the_AT0 USDA_NP0 statistics_NN0 ,_PUN we_PNP obtain_VVB production_NN1 parameters_NN2 for_PRP the_AT0 simulated_AJ0 groves_NN2 as_CJS shown_VVN in_PRP Table_NN1 2._CRD The_AT0 production_NN1 data_NN0 in_PRP Table_NN1 2_CRD can_VM0 be_VBI directly_AV0 obtained_VVN by_PRP scaling_VVG down_AVP the_AT0 data_NN0 in_PRP Table_NN1 1_CRD for_PRP the_AT0 simulated_AJ0 groves_NN2 of_PRF 100_CRD acres_NN2 ._SENT The_AT0 remainder_NN1 of_PRF this_DT0 section_NN1 provides_VVZ values_NN2 of_PRF the_AT0 parameters_NN2 used_VVN in_PRP model_NN1 (_PUL 8_CRD )_PUR and_CJC discusses_VVZ the_AT0 experimental_AJ0 setup_NN1 for_PRP the_AT0 presented_AJ0 human-robot_NN1 collaboration_NN1 framework_NN1 ._SENT 
During_PRP the_AT0 harvesting_NN1 operation_NN1 ,_PUN any_DT0 loss_NN1 in_PRP efficiency_NN1 at_PRP early_AJ0 stages_NN2 of_PRF the_AT0 operation_NN1 can_VM0 result_VVI in_PRP higher_AJC economic_AJ0 losses_NN2 because_CJS the_AT0 number_NN1 of_PRF fruit_NN0 that_CJT may_VM0 not_XX0 get_VVI harvested_VVN will_VM0 be_VBI higher_AJC if_CJS the_AT0 system_NN1 continues_VVZ to_TO0 operate_VVI at_PRP reduced_AJ0 efficiency_NN1 ._SENT Subsequently_AV0 ,_PUN human_AJ0 collaboration_NN1 can_VM0 be_VBI economically_AV0 beneficial_AJ0 at_PRP early_AJ0 stages_NN2 ._SENT However_AV0 ,_PUN at_PRP later_AJC stages_NN2 of_PRF the_AT0 operation_NN1 ,_PUN i.e._AV0 ,_PUN when_CJS the_AT0 number_NN1 of_PRF fruit_NN0 remained_VVD to_TO0 be_VBI harvested_VVN is_VBZ lower_AJC ,_PUN it_PNP is_VBZ not_XX0 certain_AJ0 whether_CJS human_AJ0 collaboration_NN1 will_VM0 always_AV0 be_VBI economically_AV0 beneficial_AJ0 ._SENT Specifically_AV0 ,_PUN the_AT0 labor_NN1 cost_NN1 associated_VVN with_PRP human_AJ0 collaboration_NN1 may_VM0 offset_VVI any_DT0 economical_AJ0 advantage_NN1 gained_VVN through_PRP improved_AJ0 production_NN1 ._SENT Therefore_AV0 ,_PUN to_TO0 gain_VVI insights_NN2 into_PRP the_AT0 question_NN1 of_PRF when_AVQ should_VM0 a_AT0 human_AJ0 collaborator_NN1 interact_VVB with_PRP a_AT0 robotic_AJ0 system_NN1 that_CJT will_VM0 be_VBI economically_AV0 beneficial_AJ0 to_PRP the_AT0 co-robotic_AJ0 operation_NN1 ,_PUN different_AJ0 stages_NN2 of_PRF the_AT0 harvesting_NN1 operation_NN1 are_VBB considered_VVN ._SENT The_AT0 stages_NN2 correspond_VVB to_PRP the_AT0 percentage_NN1 of_PRF fruit_NN0 remaining_VVG to_TO0 be_VBI harvested_VVN ,_PUN namely_AV0 ,_PUN we_PNP consider_VVB stages_NN2 with_PRP 100_CRD %_NN0 ,_PUN 75_CRD %_NN0 ,_PUN 50_CRD %_NN0 ,_PUN 25_CRD %_NN0 and_CJC 15_CRD %_NN0 fruit_NN0 remaining_AJ0 to_TO0 be_VBI harvested_VVN ._SENT The_AT0 parameter_NN1 ci_CRD ,_PUN i.e._AV0 ,_PUN the_AT0 cost_NN1 of_PRF reduced_AJ0 production_NN1 due_AJ0 to_PRP unit_NN1 loss_NN1 in_PRP efficiency_NN1 of_PRF i_CRD ,_PUN in_PRP (_PUL 6_CRD )_PUR and_CJC (_PUL 8_CRD )_PUR can_VM0 be_VBI obtained_VVN from_PRP the_AT0 value_NN1 of_PRF production_NN1 in_PRP Table_NN1 2_CRD for_PRP each_DT0 fruit_NN0 variety_NN1 ._SENT The_AT0 values_NN2 of_PRF ci_CRD corresponding_AJ0 to_PRP different_AJ0 stages_NN2 of_PRF harvesting_VVG for_PRP the_AT0 considered_AJ0 fruit_NN0 varieties_NN2 are_VBB shown_VVN in_PRP Table_NN1 3._CRD The_AT0 presented_AJ0 results_NN2 assume_VVB that_CJT ci_CRD is_VBZ constant_AJ0 across_PRP all_DT0 the_AT0 components_NN2 ,_PUN i.e._AV0 ,_PUN ci_CRD =_NP0 cj_NP0 ,_PUN ∀i_NP0 =_NP0 ∕_NP0 j_ZZ0 and_CJC i_ZZ0 ,_PUN j_ZZ0 ∈_VVB I_PNP ._SENT In_PRP other_AJ0 words_NN2 ,_PUN the_AT0 loss_NN1 in_PRP efficiency_NN1 of_PRF each_DT0 component_NN1 contributes_VVZ equally_AV0 to_PRP reduction_NN1 in_PRP the_AT0 value_NN1 of_PRF production_NN1 ._SENT This_DT0 is_VBZ a_AT0 mild_AJ0 assumption_NN1 since_PRP the_AT0 loss_NN1 function_NN1 in_PRP (_PUL 6_CRD )_PUR is_VBZ designed_VVN to_TO0 accommodate_VVI differences_NN2 in_PRP ci_CRD ._SENT Also_AV0 ,_PUN it_PNP is_VBZ to_TO0 be_VBI noted_VVN that_CJT ci_CRD is_VBZ directly_AV0 proportional_AJ0 to_PRP the_AT0 value_NN1 of_PRF production_NN1 and_CJC thus_AV0 the_AT0 orchard_NN1 size_NN1 ;_PUN the_AT0 cost_NN1 of_PRF reduced_AJ0 production_NN1 per_PRP unit_NN1 loss_NN1 in_PRP efficiency_NN1 is_VBZ higher_AJC for_PRP larger_AJC orchards_NN2 ._SENT 
The_AT0 total_AJ0 service_NN1 time_NN1 in_PRP (_PUL 8f_CRD )_PUR was_VBD chosen_VVN to_TO0 be_VBI T_ZZ0 =_NN1 20_CRD minutes_NN2 ,_PUN and_CJC the_AT0 prescribed_AJ0 return_NN1 λ_NN1 in_PRP (_PUL 8d_NN0 )_PUR was_VBD selected_VVN to_TO0 be_VBI 100_CRD dollars_NN2 ,_PUN which_DTQ accounts_VVZ for_PRP the_AT0 labor_NN1 cost_NN1 expended_VVN in_PRP servicing_VVG the_AT0 harvester_NN1 for_PRP time_NN1 T_ZZ0 ._SENT From_PRP (_PUL 8d_NN0 )_PUR ,_PUN since_CJS λ_NP0 is_VBZ a_AT0 lower_AJC bound_NN1 on_PRP the_AT0 expected_AJ0 return_NN1 ,_PUN human_AJ0 collaboration_NN1 is_VBZ economically_AV0 beneficial_AJ0 only_AV0 when_CJS the_AT0 expected_AJ0 reward_NN1 ,_PUN i.e._AV0 ,_PUN the_AT0 increase_NN1 in_PRP the_AT0 value_NN1 of_PRF production_NN1 after_PRP human_AJ0 collaboration_NN1 ,_PUN is_VBZ greater_AJC than_CJS or_CJC equal_AJ0 to_PRP 100_CRD dollars_NN2 ._SENT Net_AJ0 profit_NN1 is_VBZ obtained_VVN as_PRP the_AT0 difference_NN1 between_PRP the_AT0 increase_NN1 in_PRP the_AT0 value_NN1 of_PRF production_NN1 and_CJC the_AT0 cost_NN1 of_PRF labor_NN1 for_PRP time_NN1 T_ZZ0 ,_PUN where_AVQ the_AT0 labor_NN1 rate_NN1 was_VBD considered_VVN to_TO0 be_VBI 30_CRD dollars_NN2 per_PRP hour_NN1 ._SENT The_AT0 parameter_NN1 λ_NN1 may_VM0 also_AV0 be_VBI chosen_VVN to_TO0 include_VVI economic_AJ0 losses_NN2 as_PRP a_AT0 result_NN1 of_PRF downtime_NN1 in_PRP other_AJ0 operations_NN2 when_CJS the_AT0 human_AJ0 collaborator_NN1 services_NN2 the_AT0 harvester_NN1 ._SENT In_PRP general_AJ0 ,_PUN larger_AJC values_NN2 of_PRF λ_NN1 can_VM0 be_VBI selected_VVN to_TO0 achieve_VVI higher_AJC expected_AJ0 reward_NN1 ,_PUN which_DTQ ,_PUN however_AV0 ,_PUN may_VM0 reduce_VVI human_AJ0 involvement_NN1 if_CJS the_AT0 increase_NN1 in_PRP the_AT0 value_NN1 of_PRF production_NN1 is_VBZ less_AV0 than_CJS the_AT0 prescribed_AJ0 λ_NN1 ._SENT 
The_AT0 confidence_NN1 level_NN1 α_NN1 in_PRP the_AT0 objective_AJ0 function_NN1 of_PRF (_PUL 8_CRD )_PUR was_VBD selected_VVN to_TO0 be_VBI 0.9_CRD ._SENT As_CJS described_VVN earlier_AV0 ,_PUN the_AT0 risk_NN1 measure_NN1 HMCR_NN1 in_PRP (_PUL 4_CRD )_PUR is_VBZ considered_VVN with_PRP p_ZZ0 =_NP0 {_PUL 1_CRD ,_PUN 2_CRD ,_PUN 3_CRD }_PUR ._SENT For_PRP the_AT0 selected_AJ0 value_NN1 of_PRF α_NN1 ,_PUN the_AT0 case_NN1 of_PRF p_ZZ0 =_NN1 1_CRD relates_VVZ to_PRP reducing_VVG the_AT0 expected_AJ0 losses_NN2 in_PRP 10_CRD %_NN0 worst-case_AJ0 operating_NN1 scenarios_NN2 ,_PUN while_CJS the_AT0 loss_NN1 is_VBZ calculated_VVN via_PRP higher_AJC moments_NN2 when_CJS p_ZZ0 =_NN1 2_CRD ,_PUN 3._CRD 
The_AT0 robotic_AJ0 harvesting_NN1 operation_NN1 is_VBZ considered_VVN to_TO0 be_VBI comprised_VVN of_PRF the_AT0 following_AJ0 seven_CRD components_NN2 :_PUN Fruit_NN0 detection_NN1 ,_PUN fruit_NN0 localization_NN1 ,_PUN 3D_NN0 mapping_NN1 ,_PUN robot_NN1 path_NN1 planning_NN1 ,_PUN visual_AJ0 servo_NN1 control_NN1 ,_PUN fruit_NN0 detachment_NN1 ,_PUN and_CJC fruit_NN0 storage_NN1 ,_PUN which_DTQ constitute_VVB set_VVB I_PNP ._SENT In_PRP practice_NN1 ,_PUN as_CJS stated_VVN in_PRP Assumption_NN1 1_CRD ,_PUN the_AT0 probability_NN1 distribution_NN1 of_PRF the_AT0 nominal_AJ0 efficiency_NN1 ηi_NN1 ,_PUN i_CRD =_NP0 1_CRD ,_PUN ⋯_NP0 ,_PUN 7_CRD ,_PUN of_PRF these_DT0 components_NN2 can_VM0 be_VBI obtained_VVN for_PRP a_AT0 given_AJ0 robotic_AJ0 harvester_NN1 and_CJC a_AT0 fruit_NN0 variety_NN1 using_VVG the_AT0 harvester_NN1 's_POS historical_AJ0 performance_NN1 data_NN0 ._SENT However_AV0 ,_PUN as_CJS the_AT0 robotic_AJ0 citrus_AJ0 harvesting_NN1 systems_NN2 are_VBB still_AV0 being_VBG investigated_VVN and_CJC no_AT0 commercial_AJ0 solutions_NN2 are_VBB available_AJ0 ,_PUN such_DT0 probability_NN1 distribution_NN1 functions_NN2 of_PRF component_NN1 efficiencies_NN2 cannot_NN1 be_VBI found_VVN in_PRP literature_NN1 ._SENT Therefore_AV0 ,_PUN the_AT0 presented_AJ0 results_NN2 employ_VVB the_AT0 best_AJS estimates_NN2 of_PRF the_AT0 component_NN1 efficiencies_NN2 based_VVN on_PRP the_AT0 data_NN0 available_AJ0 in_PRP the_AT0 current_AJ0 state_NN1 of_PRF knowledge_NN1 and_CJC the_AT0 authors_NN2 '_POS experience_NN1 to_TO0 make_VVI the_AT0 model_NN1 as_CJS realistic_AJ0 as_CJS possible_AJ0 ._SENT Fig._NN1 2_CRD shows_VVZ the_AT0 assumed_AJ0 probability_NN1 distributions_NN2 of_PRF the_AT0 nominal_AJ0 efficiencies_NN2 ηi_NP0 ,_PUN ∀i_NP0 =_NP0 1_CRD ,_PUN ⋯_NP0 ,_PUN 7_CRD ,_PUN of_PRF the_AT0 components_NN2 modeled_VVN as_PRP lognormal_AJ0 distributions_NN2 ,_PUN which_DTQ are_VBB commonly_AV0 used_VVN in_PRP reliability_NN1 analysis_NN1 to_PRP model_NN1 uncertainties_NN2 in_PRP the_AT0 system_NN1 behavior_NN1 ._SENT In_PRP (_PUL 8_CRD )_PUR ,_PUN N_ZZ0 =_NN1 10000_CRD operating_NN1 scenarios_NN2 are_VBB generated_VVN by_PRP randomly_AV0 drawing_VVG samples_NN2 ηik_NP0 ,_PUN k_ZZ0 =_NP0 1_CRD ,_PUN ⋯_NP0 ,_PUN N_NP0 ,_PUN from_PRP the_AT0 distributions_NN2 of_PRF ηi_NP0 ,_PUN ∀i_NP0 ._SENT For_PRP simplicity_NN1 ,_PUN the_AT0 same_DT0 N_ZZ0 scenarios_NN2 are_VBB used_VVN for_PRP the_AT0 different_AJ0 fruit_NN0 varieties_NN2 under_PRP consideration_NN1 ._SENT It_PNP is_VBZ to_TO0 be_VBI noted_VVN that_CJT the_AT0 mathematical_AJ0 formulation_NN1 presented_VVN in_PRP the_AT0 paper_NN1 does_VDZ not_XX0 make_VVI assumptions_NN2 with_PRP respect_NN1 to_PRP the_AT0 distribution_NN1 functions_NN2 of_PRF ηi_NP0 ,_PUN ∀i_NP0 ._SENT In_PRP other_AJ0 words_NN2 ,_PUN any_DT0 arbitrary_AJ0 distributions_NN2 of_PRF these_DT0 random_AJ0 variables_NN2 as_CJS observed_VVN in_PRP practice_NN1 can_VM0 be_VBI accommodated_VVN without_PRP any_DT0 change_NN1 in_PRP the_AT0 model_NN1 ._SENT 
We_PNP performed_VVD 10_CRD experiments_NN2 with_PRP different_AJ0 values_NN2 of_PRF the_AT0 component_NN1 efficiencies_NN2 ̂ηi_NP0 ,_PUN i_CRD =_NP0 1_CRD ,_PUN ⋯_NP0 ,_PUN 7_CRD ,_PUN as_CJS shown_VVN in_PRP Table_NN1 4_CRD to_TO0 determine_VVI whether_CJS human_AJ0 collaboration_NN1 is_VBZ economically_AV0 beneficial_AJ0 in_PRP the_AT0 given_AJ0 experiment_NN1 ,_PUN and_CJC ,_PUN if_CJS so_AV0 ,_PUN what_DTQ is_VBZ the_AT0 optimal_AJ0 servicing_NN1 policy_NN1 in_PRP terms_NN2 of_PRF servicing_VVG times_NN2 for_PRP each_DT0 component_NN1 ._SENT These_DT0 experiments_NN2 can_VM0 be_VBI viewed_VVN to_TO0 simulate_VVI different_AJ0 operating_NN1 points_NN2 of_PRF the_AT0 system_NN1 ,_PUN when_CJS the_AT0 components_NN2 are_VBB operating_VVG at_PRP various_AJ0 efficiency_NN1 levels_NN2 ._SENT For_PRP each_DT0 experiment_NN1 ,_PUN the_AT0 component_NN1 efficiencies_NN2 are_VBB obtained_VVN via_PRP simple_AJ0 random_AJ0 sampling_NN1 from_PRP the_AT0 corresponding_AJ0 probability_NN1 distributions_NN2 given_VVN in_PRP Fig._NN1 2_CRD ,_PUN where_AVQ the_AT0 drawn_VVN samples_NN2 ̂ηi_NP0 ,_PUN i_CRD =_NP0 1_CRD ,_PUN ⋯_NP0 ,_PUN 7_CRD ,_PUN represent_VVB an_AT0 operating_NN1 point_NN1 of_PRF the_AT0 system_NN1 ._SENT Ten_CRD such_DT0 operating_NN1 points_NN2 are_VBB obtained_VVN to_TO0 yield_VVI experimental_AJ0 configurations_NN2 given_VVN in_PRP Table_NN1 4_CRD ,_PUN such_DT0 that_CJT each_DT0 row_NN1 represents_VVZ an_AT0 experiment_NN1 with_PRP the_AT0 associated_AJ0 simulated_AJ0 efficiencies_NN2 of_PRF the_AT0 components_NN2 ._SENT 
Section_NN1 4.2_CRD describes_VVZ the_AT0 results_NN2 of_PRF the_AT0 risk-averse_AJ0 collaboration_NN1 model_NN1 presented_VVN in_PRP (_PUL 8_CRD )_PUR for_PRP the_AT0 10_CRD simulated_AJ0 experiments_NN2 for_PRP each_DT0 of_PRF the_AT0 five_CRD harvesting_NN1 stages_NN2 (_PUL corresponding_VVG to_PRP remaining_AJ0 harvest_NN1 of_PRF 100_CRD %_NN0 ,_PUN 75_CRD %_NN0 ,_PUN 50_CRD %_NN0 ,_PUN 25_CRD %_NN0 ,_PUN 15_CRD %_NN0 )_PUR and_CJC p_ZZ0 =_NP0 {_PUL 1_CRD ,_PUN 2_CRD ,_PUN 3_CRD }_PUR ._SENT The_AT0 model_NN1 in_PRP (_PUL 8_CRD )_PUR is_VBZ solved_VVN for_PRP each_DT0 configuration_NN1 of_PRF the_AT0 triplet_NN1 {_PUL experiment_NN1 ,_PUN harvesting_VVG stage_NN1 ,_PUN p_ZZ0 }_PUR ._SENT For_PRP any_DT0 instance_NN1 of_PRF model_NN1 (_PUL 8_CRD )_PUR solved_VVD ,_PUN the_AT0 parameter_NN1 values_NN2 used_VVN (_PUL 8_CRD )_PUR are_VBB given_VVN by_PRP :_PUN ci_CRD corresponding_VVG to_PRP the_AT0 harvesting_NN1 stage_NN1 and_CJC fruit_NN0 type_NN1 pro-_NN1 vided_AJ0 in_PRP Table_NN1 3_CRD ;_PUN the_AT0 corresponding_AJ0 experiment_NN1 row_NN1 in_PRP Table_NN1 4_CRD ;_PUN the_AT0 N_ZZ0 =_NN1 10000_CRD randomly_AV0 drawn_VVN operating_VVG scenario_NN1 values_NN2 for_PRP η_NN1 from_PRP the_AT0 probability_NN1 distributions_NN2 in_PRP Fig._NN1 2_CRD ;_PUN and_CJC values_NN2 for_PRP T_ZZ0 ,_PUN p_ZZ0 ,_PUN λ_NP0 ,_PUN α_NP0 provided_VVD in_PRP the_AT0 preceding_AJ0 discussion_NN1 ._SENT The_AT0 solution_NN1 algorithm_NN1 was_VBD implemented_VVN in_PRP C++_NP0 ,_PUN and_CJC CPLEX_NP0 12.6_CRD mixed-integer_NN1 programming_NN1 solver_NN1 was_VBD utilized_VVN to_TO0 solve_VVI problem_NN1 (_PUL 8_CRD )_PUR ._SENT The_AT0 computation_NN1 hardware_NN1 included_VVD an_AT0 Intel_NP0 Xeon_NN1 3.50_CRD GHz_NN0 PC_NN1 with_PRP 64_CRD GB_NP0 of_PRF RAM_NN1 ,_PUN and_CJC a_AT0 Windows_NN2 7_CRD 64-bit_AJ0 environment_NN1 ._SENT The_AT0 solution_NN1 of_PRF (_PUL 8_CRD )_PUR is_VBZ obtained_VVN for_PRP each_DT0 experiment_NN1 in_PRP terms_NN2 of_PRF the_AT0 optimal_AJ0 service_NN1 time_NN1 xi_NN1 and_CJC the_AT0 optimal_AJ0 objective_NN1 value_NN1 (_PUL i.e._AV0 ,_PUN the_AT0 risk_NN1 of_PRF economic_AJ0 loss_NN1 )_PUR ._SENT Also_AV0 ,_PUN the_AT0 expected_AJ0 reward_NN1 is_VBZ given_VVN by_PRP the_AT0 value_NN1 of_PRF the_AT0 left-hand-side_NN1 of_PRF constraint_NN1 (_PUL 8d_NN0 )_PUR ._SENT 
4.2_CRD ._SENT Results_NN2 
For_PRP brevity_NN1 ,_PUN we_PNP present_VVB in-depth_AJ0 results_NN2 and_CJC discussions_NN2 for_PRP the_AT0 Valencia_NP0 orange_NN1 while_CJS only_AV0 the_AT0 key_AJ0 results_NN2 pertaining_VVG to_PRP economic_AJ0 benefits_NN2 of_PRF human-robot_NN1 collaboration_NN1 are_VBB shown_VVN in_PRP Fig._NN1 8_CRD (_PUL a_AT0 )_PUR -_PUN (_PUL d_ZZ0 )_PUR for_PRP other_AJ0 citrus_AJ0 varieties_NN2 ._SENT It_PNP should_VM0 be_VBI noted_VVN that_CJT the_AT0 results_NN2 and_CJC discussions_NN2 for_PRP these_DT0 citrus_AJ0 varieties_NN2 are_VBB analogous_AJ0 to_PRP that_DT0 of_PRF the_AT0 Valencia_NP0 orange_NN1 ._SENT 
Fig._NN1 3_CRD shows_VVZ the_AT0 main_AJ0 result_NN1 of_PRF the_AT0 developed_AJ0 optimal_AJ0 collaboration_NN1 framework_NN1 for_PRP harvesting_VVG Valencia_NP0 oranges_NN2 for_PRP different_AJ0 experiments_NN2 when_CJS p_ZZ0 =_NN1 1_CRD and_CJC the_AT0 remaining_AJ0 harvest_NN1 is_VBZ 100_CRD %_NN0 ._SENT The_AT0 bar_NN1 graphs_NN2 in_PRP Fig._NN1 3_CRD show_VVB the_AT0 efficiency_NN1 of_PRF the_AT0 components_NN2 before_PRP and_CJC after_PRP human_AJ0 collaboration_NN1 along_AVP with_PRP the_AT0 obtained_VVN optimal_AJ0 service_NN1 time_NN1 for_PRP each_DT0 component_NN1 ._SENT Component_NN1 efficiencies_NN2 before_PRP human_AJ0 collaboration_NN1 are_VBB shown_VVN as_PRP gray_AJ0 bars_NN2 ,_PUN which_DTQ correspond_VVB to_PRP the_AT0 values_NN2 in_PRP Table_NN1 4._CRD As_CJS discussed_VVN in_PRP Section_NN1 3_CRD ,_PUN the_AT0 improvement_NN1 in_PRP efficiency_NN1 after_PRP servicing_VVG component_NN1 i_ZZ0 for_PRP time_NN1 xi_NN1 is_VBZ ̂ηi_NP0 γik_NP0 xi_NN1 ._SENT Since_PRP γik_NP0 in_PRP (_PUL 7_CRD )_PUR is_VBZ computed_VVN over_PRP N_ZZ0 operating_NN1 scenarios_NN2 ηik_NN1 ,_PUN we_PNP consider_VVB the_AT0 median_AJ0 increase_NN1 in_PRP ̂ηiγikxi_NP0 as_PRP a_AT0 measure_NN1 of_PRF improvement_NN1 in_PRP efficiency_NN1 ._SENT In_PRP Fig._NN1 3_CRD ,_PUN the_AT0 median_AJ0 improvement_NN1 in_PRP efficiency_NN1 ,_PUN median_NN1 (_PUL ̂ηiγikxi_NP0 )_PUR ,_PUN of_PRF each_DT0 component_NN1 is_VBZ shown_VVN as_PRP a_AT0 green_AJ0 bar_NN1 stacked_VVN on_PRP top_NN1 of_PRF the_AT0 measured_AJ0 component_NN1 efficiency_NN1 (_PUL gray_AJ0 bar_NN1 )_PUR ,_PUN thereby_AV0 the_AT0 aggregate_AJ0 (_PUL gray_AJ0 +_NN1 green_AJ0 bars_NN2 )_PUR visualizes_VVZ the_AT0 component_NN1 efficiencies_NN2 after_PRP human_AJ0 collaboration_NN1 ._SENT The_AT0 blue_AJ0 error_NN1 bars_NN2 show_VVB the_AT0 least_AV0 and_CJC the_AT0 largest_AJS efficiency_NN1 of_PRF the_AT0 components_NN2 in_PRP N_ZZ0 scenarios_NN2 after_PRP human_AJ0 collaboration_NN1 ._SENT It_PNP is_VBZ noteworthy_AJ0 that_CJT deterministic_AJ0 values_NN2 for_PRP improvement_NN1 in_PRP efficiency_NN1 of_PRF individual_AJ0 components_NN2 are_VBB intractable_AJ0 to_TO0 obtain_VVI ,_PUN since_CJS the_AT0 model_NN1 involves_VVZ finding_VVG optimal_AJ0 decision_NN1 over_PRP stochastic_AJ0 component_NN1 efficiencies_NN2 ,_PUN and_CJC the_AT0 objective_AJ0 function_NN1 involves_VVZ minimizing_VVG the_AT0 global_AJ0 economic_AJ0 loss_NN1 over_PRP all_DT0 the_AT0 components_NN2 ._SENT Consequently_AV0 ,_PUN the_AT0 results_NN2 provide_VVB median_AJ0 improvement_NN1 in_PRP efficiency_NN1 of_PRF each_DT0 component_NN1 ,_PUN and_CJC the_AT0 error_NN1 bars_NN2 indicate_VVB the_AT0 deviation_NN1 in_PRP the_AT0 aggregate_AJ0 efficiency_NN1 over_PRP N_ZZ0 random_AJ0 scenarios_NN2 after_PRP human_AJ0 collaboration_NN1 ._SENT 
The_AT0 function_NN1 γik_NN1 (_PUL ̂ηi_NP0 ,_PUN ηik_NP0 )_PUR in_PRP (_PUL 7_CRD )_PUR is_VBZ a_AT0 measure_NN1 of_PRF serviceability_NN1 of_PRF component_NN1 i_ZZ0 in_PRP scenario_NN1 k_ZZ0 ._SENT As_CJS such_DT0 ,_PUN γik_NP0 provides_VVZ insights_NN2 into_PRP which_DTQ components_NN2 to_PRP service_NN1 in_PRP the_AT0 limited_AJ0 time_NN1 T_ZZ0 to_TO0 realize_VVI the_AT0 maximum_AJ0 economic_AJ0 benefit_NN1 ._SENT Fig._NN1 4_CRD shows_VVZ the_AT0 average_AJ0 serviceability_NN1 ,_PUN E_NP0 (_PUL γik_NP0 (_PUL ̂ηi_NP0 ,_PUN ηik_NP0 )_PUR )_PUR ∈_NP0 [_PUL 0_CRD ,_PUN 1_CRD )_PUR ,_PUN of_PRF component_NN1 i_ZZ0 over_PRP N_ZZ0 scenarios_NN2 for_PRP the_AT0 case_NN1 when_AVQ p_ZZ0 =_NN1 1_CRD and_CJC the_AT0 remaining_AJ0 harvest_NN1 is_VBZ 100_CRD %_NN0 ._SENT By_PRP design_NN1 ,_PUN E_NP0 (_PUL γik_NP0 (_PUL ̂ηi_NP0 ,_PUN ηik_NP0 )_PUR )_PUR =_NN1 0_CRD corresponds_VVZ to_PRP no_AT0 serviceability_NN1 and_CJC the_AT0 serviceability_NN1 improves_VVZ as_PRP E_ZZ0 (_PUL γik_NP0 (_PUL ̂ηi_NP0 ,_PUN ηik_NP0 )_PUR )_PUR approaches_VVZ 1._CRD This_DT0 can_VM0 be_VBI verified_VVN by_PRP considering_VVG the_AT0 expression_NN1 for_PRP the_AT0 median_AJ0 improvement_NN1 in_PRP efficiency_NN1 median_NN1 (_PUL ̂ηiγikxi_NP0 )_PUR ._SENT A_AT0 given_AJ0 improvement_NN1 in_PRP efficiency_NN1 can_VM0 be_VBI obtained_VVN with_PRP less_DT0 service_NN1 time_NN1 xi_NN1 when_CJS E_NP0 (_PUL γik_NP0 (_PUL ̂ηi_NP0 ,_PUN ηik_NP0 )_PUR )_PUR is_VBZ large_AJ0 (_PUL i.e._AV0 ,_PUN the_AT0 component_NN1 is_VBZ easy_AJ0 to_PRP service_NN1 )_PUR ._SENT For_PRP a_AT0 component_NN1 with_PRP less_DT0 serviceability_NN1 ,_PUN i.e._AV0 ,_PUN smaller_AJC E_ZZ0 (_PUL γik_NP0 (_PUL ̂ηi_NP0 ,_PUN ηik_NP0 )_PUR )_PUR ,_PUN the_AT0 service_NN1 time_NN1 would_VM0 be_VBI higher_AJC to_TO0 achieve_VVI the_AT0 same_DT0 improvement_NN1 in_PRP efficiency_NN1 ._SENT The_AT0 limiting_AJ0 case_NN1 corresponds_VVZ to_PRP E_ZZ0 (_PUL γik_NP0 (_PUL ̂ηi_NP0 ,_PUN ηik_NP0 )_PUR )_PUR =_NN1 0_CRD (_PUL or_CJC γik_NP0 =_NP0 0_CRD ,_PUN due_AJ0 to_PRP positive_AJ0 semi-definiteness_NN1 )_PUR ,_PUN when_CJS no_AT0 improvement_NN1 in_PRP efficiency_NN1 can_VM0 be_VBI realized_VVN for_PRP any_DT0 arbitrarily_AV0 large_AJ0 service_NN1 time_NN1 ._SENT 
Fig._NN1 5_CRD shows_VVZ the_AT0 matrix_NN1 plot_NN1 of_PRF when_AVQ human_AJ0 collaboration_NN1 was_VBD sought_VVN in_PRP the_AT0 10_CRD experiments_NN2 during_PRP different_AJ0 stages_NN2 of_PRF the_AT0 harvesting_NN1 operation_NN1 ._SENT The_AT0 value_NN1 of_PRF 1_CRD indicates_VVZ that_CJT human_AJ0 collaboration_NN1 was_VBD economically_AV0 beneficial_AJ0 and_CJC sought_VVD ;_PUN 0_CRD indicates_VVZ that_CJT human_AJ0 collaboration_NN1 was_VBD not_XX0 sought_VVN ._SENT The_AT0 matrix_NN1 plot_NN1 is_VBZ shown_VVN for_PRP different_AJ0 values_NN2 of_PRF p_ZZ0 =_NP0 {_PUL 1_CRD ,_PUN 2_CRD ,_PUN 3_CRD }_PUR in_PRP Fig._NN1 5._CRD This_DT0 plot_NN1 provides_VVZ a_AT0 graphical_AJ0 answer_NN1 to_PRP when_AVQ should_VM0 a_AT0 human_AJ0 collaborator_NN1 interact_VVB with_PRP a_AT0 robotic_AJ0 system_NN1 that_CJT will_VM0 be_VBI economically_AV0 beneficial_AJ0 to_PRP the_AT0 co-robotic_AJ0 operation_NN1 ._SENT It_PNP can_VM0 be_VBI seen_VVN that_CJT the_AT0 need_NN1 for_PRP human_AJ0 collaboration_NN1 varies_VVZ with_PRP the_AT0 harvest_NN1 remaining_AJ0 as_CJS well_AV0 as_CJS the_AT0 experimental_AJ0 scenario_NN1 (_PUL i.e._AV0 ,_PUN component_NN1 efficiencies_NN2 )_PUR ._SENT 
The_AT0 risk_NN1 of_PRF economic_AJ0 loss_NN1 (_PUL dollars_NN2 )_PUR versus_PRP the_AT0 expected_AJ0 reward_NN1 (_PUL dollars_NN2 )_PUR is_VBZ shown_VVN in_PRP Fig._NN1 6_CRD for_PRP p_ZZ0 =_NP0 {_PUL 1_CRD ,_PUN 2_CRD ,_PUN 3_CRD }_PUR ._SENT Each_DT0 line_NN1 segment_NN1 corresponds_VVZ to_PRP an_AT0 experiment_NN1 and_CJC the_AT0 data_NN0 points_NN2 on_PRP each_DT0 line_NN1 correspond_VVB to_PRP the_AT0 harvesting_NN1 stages_NN2 ._SENT 
Fig._NN1 7_CRD shows_VVZ the_AT0 net_AJ0 profit_NN1 (_PUL dollars_NN2 )_PUR after_PRP human_AJ0 collaboration_NN1 in_PRP each_DT0 experiment_NN1 for_PRP various_AJ0 harvesting_NN1 stages_NN2 and_CJC the_AT0 case_NN1 when_AVQ p_ZZ0 =_NN1 1._CRD Fig._NN1 8_CRD shows_VVZ the_AT0 net_AJ0 profit_NN1 (_PUL dollars_NN2 )_PUR for_PRP Navel_NN1 ,_PUN Early-midseason_NP0 ,_PUN white_AJ0 grapefruit_NN0 ,_PUN and_CJC red_AJ0 grapefruit_NN0 ,_PUN respectively_AV0 ._SENT 
