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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 thats 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 thats 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
BR1 >= 10
BE1 >= 10
BE1 >= 10
BE1 >= 10
BR1 >= 10

BE1 <= 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 +
E1 E1>= 0.25
R1 >=E1 +

Cost += 10

BE1= BR1 + (E1 R1)*-40
BE1 >= 10
CE1 = CR1
BE1= BE1
BE1 >= 10, <= 100CE1= CE1 + 10BE1= BE1+ (E1 – E1)*20 BE1 >= 10, <=100CE1 = CR1 + (E1- E1) * 1 BE1= BE1 BE1 >= 10
CE1= CE1

BR1= BE1 + (R1 E1)*-40
BR1 >= 10, >= 30
CR1 = CE1
BR1= BE1 ,
BR1 >= 10, <= 100CR1= 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= 50BR1=BR1 BE1=BR1+(E1-R1)*-40BE1=BE1Numeric Constraints:BE1= BE1BR1=BE1+(R1-E1)*-40 BE1=BE1+(E1-E1)*20BE1= 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 +
E1 E1>= 0.25
R1 >=E1 +

Cost += 10

BE1= BR1 + (E1 R1)*-40
BE1 >= 10
CE1 = CR1
BE1= BE1
BE1 >= 10, <= 100CE1= CE1 + 10BE1= BE1+ (E1 – E1)*20 BE1 >= 10, <=100CE1 = CR1 + (E1- E1) * 1 BE1= BE1 BE1 >= 10
CE1= CE1

BR1= BE1 + (R1 E1)*-40
BR1 >= 10, >= 30
CR1 = CE1
BR1= BE1 ,
BR1 >= 10, <= 100CR1= 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)CR1=CR1 CE1=CR1CE1=CE1+10 Numeric Constraints:CE1= CE1CR1=CE1CE1=CE1+(E1-E1)*1CE1= CE1 Linear ProgrammingGeneral form:Maximise: z = wz .v Subject to: w1 .v {, , =} c1 w2 .v {, , =} c2 wn .v {, , =} cn/docProps/thumbnail.jpeg CS: assignmentchef QQ: 1823890830 Email: [email protected]