| Task | z | wz | Phase | Gate Predicate ( z→z+1 or Success) | ϕz(s) |
| Pick & Place [2pt] obj(1) :Block obj(2) :Coaster | 1 | 0.10 | Reach | ∥ptcp−pobj(1)∥≤0.015 | 1−∥ptcp−pobj(1)∥/d1 |
| 2 | 0.25 | Grasp | dgrasp≤0.04∧Fgrasp>0 | 1−∣dgrasp−0.04∣/0.04 |
| 3 | 0.20 | Transit | G ∧∥ptcpxy−pobj(2)xy∥≤0.08∧robj(1)roll/pitch≤45∘ | 1−∥ptcpxy−pobj(2)xy∥/d3 |
| 4 | 0.45 | Place | Igoal:∥pobj(1)xy−pobj(2)xy∥≤0.025∧robj(1)roll/pitch≤5∘ | 1−∥pobj(1)z−0.025∥/d4 |
| Sweep [2pt] obj(1) :Broom obj(2) :Cube obj(3) :Dustpan | 1 | 0.08 | Reach | ∥ptcpyz−pobj(1)yz∥≤0.01∧∥ptcpx−pobj(1)x∥≤0.02 | 1−∥ptcpxyz−pobj(1)xyz∥/d1 |
| 2 | 0.20 | Grasp | dgrasp≤0.03∧Fgrasp>0 | 1−∣dgrasp−0.03∣/0.03 |