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Planning with Continuous Linear Change: COLIN

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Planning: How it all Started
(: action pickup_from_block (?b1 ?b2 – block)
:precondition (and (on ?b1 ?b2)
(arm_free))
:effect (and (holding ?b1)
(clear ?b2))
(not (arm_free))
(not (on ?b1 ?b2)))

Initial State: (on C A) (ontable B) (ontable A)
(arm_free) (clear B) (clear C)
Goal: (on B C) (on A B)
(: action put_down_on_block (?b1 ?b2 – block)
:precondition (and (holding ?b1)
(clear ?b2))
:effect (and (holding ?b1)
(clear ?b2))
(not (arm_free))
(not (on ?b1 ?b2)))

…And where it is Going
What Matters?
Time: Deadlines, Windows of Opportunity;
Numeric Quantities: Discrete and Continuous, Optimisation;
The environment: Uncertainty, Predictable Exogenous Change.

The Reality

Solar generation
State of Charge

Minimum state of charge at nightfall

Classical Planning as Forward Search

Classical Planning Gives Us:
Propositional Relaxation Heuristics: RPG, Causal Graph;
Search Guidance: Helpful Actions/Preferred Operators.
Search Techniques, Enforced Hill-Climbing, Multi Open List Search, Memoisation;

Continuous Linear Change
Numeric quantities so far we have seen change instantaneously:
e.g.(at end (decrease (battery) 1))
(at end (decrease (battery) (+ (*0.5 (temperature)) (*3 (?duration))))
V’ = W . V + C

In reality numeric values often change continuously, rather than discretely.
While the bus is running dbattery/dt = -40
(increase (battery) (*#t -40))
Of course change is not always linear, but that’s another lecture.
Today we will deal with linear changeonly.

battery’=

temperature
V’ = W. V+ C

Continuous Linear Change
Numeric quantities so far we have seen change instantaneously:
e.g.(at end (decrease (battery) 1))
(at end (decrease (battery) (+ (*0.5 (temperature)) (*3 (?duration))))
V’ = W . V + C

In reality numeric values often change continuously, rather than discretely.
While the bus is running dbattery/dt = -40
(increase (battery) (*#t -40))
Of course change is not always linear, but that’s another lecture.
Today we will deal with linear changeonly.

Continuous Linear Change: D1
Route1 D1 B1
duration = 2
Done Route1
Battery >= 10
Battery >= 30
dBattery/dt -=40
(increase (battery) (*#t -40))

“Temporal Planning in Domains with Linear Processes.” A. J. Coles, A. I. Coles, M. Fox, and D. Long. IJCAI (2009).
“COLIN: Planning with Continuous Linear Numeric Change.” A. J. Coles, A. I. Coles, M. Fox and D. Long. JAIR (44) (2013)

On Route B1
Run Engine B1
Battery <= 100dBattery/dt +=60dCost/dt +=1duration >= 0.25
EngineOff B1
¬EngineOff B1
EngineOff B1
Cost += 10

BR1⊣ >= 30

BE1 ⊢ >= 10
B’R1⊢ >= 10
B’E1⊢ >= 10
BE1⊣ >= 10
B’E1⊣ >= 10
BR1⊣ >= 10

B’E1⊢ <= 100BE1⊣ <= 100Continuous Linear Change:1 D1 B1duration = 2Battery >= 10
Battery >= 30
dBattery/dt -=40
Run Engine B1
Battery <= 100dBattery/dt +=60dCost/dt +=1duration >= 0.25
Constraints:
R1⊣– R⊢= 2
E1 ⊢ >=R1⊢ + ε
E1⊣– E1⊢>= 0.25
R1 ⊣ >=E1 ⊣ + ε

Cost += 10

BE1⊢= BR1 ⊢+ (E1⊢– R1⊢)*-40
BE1 ⊢ >= 10
CE1⊢ = C’R1⊢
B’E1⊢= BE1⊢
B’E1⊢ >= 10, <= 100C’E1⊢= CE1 ⊢+ 10BE1⊣= BE1⊢+ (E1⊣ – E1⊢)*20 BE1⊣ >= 10, <=100CE1⊣ = C’R1⊢ + (E1⊣- E1⊢) * 1 B’E1⊣= BE1 ⊣B’E1⊣ >= 10
C’E1⊣= CE1 ⊣

BR1⊣= BE1⊣ + (R1⊣ – E1⊣)*-40
BR1⊣ >= 10, >= 30
CR1⊣ = C’E1 ⊣
B’R1⊣= BE1 ⊣,
B’R1⊣ >= 10, <= 100C’R1⊣= CE1 ⊣”Temporal Planning in Domains with Linear Processes.” A. J. Coles, A. I. Coles, M. Fox, and D. Long. IJCAI (2009).”COLIN: Planning with Continuous Linear Numeric Change.” A. J. Coles, A. I. Coles, M. Fox and D. Long. JAIR (44) (2013)BR1⊢= 50B’R1⊢=BR1⊢ BE1⊢=B’R1⊢+(E1⊢-R1⊢)*-40B’E1⊢=BE1⊢Numeric Constraints:B’E1⊣= BE1⊣BR1⊣=B’E1⊣+(R1⊣-E1⊣)*-40 BE1⊣=B’E1⊢+(E1⊣-E1⊢)*20B’E1⊣= BE1 ⊣Continuous Linear Change:1 D1 B1duration = 2Battery >= 10
Battery >= 30
dBattery/dt -=40
Run Engine B1
Battery <= 100dBattery/dt +=60dCost/dt +=1duration >= 0.25
Constraints:
R1⊣– R⊢= 2
E1 ⊢ >=W⊢ + ε
E1⊣– E1⊢>= 0.25
R1 ⊢ >=E1⊢ + ε

Cost += 10

BE1⊢= BR1 ⊢+ (E1⊢– R1⊢)*-40
BE1 ⊢ >= 10
CE1⊢ = C’R1⊢
B’E1⊢= BE1⊢
B’E1⊢ >= 10, <= 100C’E1⊢= CE1 ⊢+ 10BE1⊣= BE1⊢+ (E1⊣ – E1⊢)*20 BE1⊣ >= 10, <=100CE1⊣ = C’R1⊢ + (E1⊣- E1⊢) * 1 B’E1⊣= BE1 ⊣B’E1⊣ >= 10
C’E1⊣= CE1 ⊣

BR1⊣= BE1⊣ + (R1⊣ – E1⊣)*-40
BR1⊣ >= 10, >= 30
CR1⊣ = C’E1 ⊣
B’R1⊣= BE1 ⊣,
B’R1⊣ >= 10, <= 100C’R1⊣= CE1 ⊣”Temporal Planning in Domains with Linear Processes.” A. J. Coles, A. I. Coles, M. Fox, and D. Long. IJCAI (2009).”COLIN: Planning with Continuous Linear Numeric Change.” A. J. Coles, A. I. Coles, M. Fox and D. Long. JAIR (44) (2013)C’R1⊢=CR1⊢ CE1⊢=C’R1⊢C’E1⊢=CE1⊢+10 Numeric Constraints:C’E1⊣= CE1⊣CR1⊣=C’E1⊣CE1⊣=C’E1⊢+(E1⊣-E1⊢)*1C’E1⊣= CE1 ⊣Linear ProgrammingGeneral form:Maximise: z = wz .v Subject to: w1 .v {≤, ≥, =} c1 w2 .v {≤, ≥, =} c2 wn .v {≤, ≥, =} cn/docProps/thumbnail.jpeg程序代写 CS代考加微信: assignmentchef QQ: 1823890830 Email: [email protected]