Reversible Dynamics, Asymmetric Actions: Parking as a Trajectory-Level Affordance
Overview
This research paper investigates the paradoxical advice of backing into parking spaces versus driving in nose first. The authors define three clearance metrics: static fit (F), eventual access (A_infinity), and resource-bounded access (A_K). Using certified arguments, they prove that while a car is dynamically reversible, forward-in and reverse-in tasks differ in the number of corrections required to maintain specific clearances under finite reversal budgets. The study proposes experiments to test if observers can distinguish these clearance types from simpler visual cues like body sweep.
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Event evidence and corrections
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Reported quantity · clearance: 0.5 other · Basis not reported · Differing source assertions
“orward and reverse. They satisfy $F\ge A_\infty\ge A_K$. In one fully specified scene (one car, bay, aisle and start), a certified argument proves $A_\infty=F=0.5000$ m for both tasks. In this scene, all certified forward/reverse asymmetry therefore arises at finite $K$: it lies in how many corrections each task needs, not in the clearance either can eventually keep. With one reversal, an explicit path gives reverse-”
Exact source · revision 1Source owner not reported
Reported quantity · clearance: 0.441 other · Basis not reported · Differing source assertions
“in at least $0.4410$ m clearance. A certified reachability argument caps forward-in's one-reversal clearance at $d_0<0.1720002$ m. With two reversals, forward-in gets at least $0.2833$ m. To keep a clearance strictly above any $d$ with $d_0\le d<0.2833$ m, reverse-in thus needs exactly one reversal and forward-in exactly two when both tasks move forward first. If both move in reverse first, the counts are two and thr”
Exact source · revision 1Source owner not reported
Reported quantity · clearance: 0.2833 other · Basis not reported · Differing source assertions
“in at least $0.4410$ m clearance. A certified reachability argument caps forward-in's one-reversal clearance at $d_0<0.1720002$ m. With two reversals, forward-in gets at least $0.2833$ m. To keep a clearance strictly above any $d$ with $d_0\le d<0.2833$ m, reverse-in thus needs exactly one reversal and forward-in exactly two when both tasks move forward first. If both move in reverse first, the counts are two and thr”
Exact source · revision 1Source owner not reported
Reported quantity · reversals: 1 other · Basis not reported · Differing source assertions
“in at least $0.4410$ m clearance. A certified reachability argument caps forward-in's one-reversal clearance at $d_0<0.1720002$ m. With two reversals, forward-in gets at least $0.2833$ m. To keep a clearance strictly above any $d$ with $d_0\le d<0.2833$ m, reverse-in thus needs exactly one reversal and forward-in exactly two when both tasks move forward first. If both move in reverse first, the counts are two and thr”
Exact source · revision 1Source owner not reported
Reported quantity · reversals: 2 other · Basis not reported · Differing source assertions
“in at least $0.4410$ m clearance. A certified reachability argument caps forward-in's one-reversal clearance at $d_0<0.1720002$ m. With two reversals, forward-in gets at least $0.2833$ m. To keep a clearance strictly above any $d$ with $d_0\le d<0.2833$ m, reverse-in thus needs exactly one reversal and forward-in exactly two when both tasks move forward first. If both move in reverse first, the counts are two and thr”
Exact source · revision 1Source owner not reported
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- arXiv Robotics — research abstractsSignalReversible Dynamics, Asymmetric Actions: Parking as a Trajectory-Level Affordance
This research paper investigates the paradoxical advice of backing into parking spaces versus driving in nose first. The authors define three clearance metrics: static fit (F), eventual access (A_infinity), and resource-bounded access (A_K). Using certified arguments, they prove that while a car is dynamically reversible, forward-in and reverse-in tasks differ in the number of corrections required to maintain specific clearances under finite reversal budgets. The study proposes experiments to test if observers can distinguish these clearance types from simpler visual cues like body sweep.
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