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1/29
Motion PlanningViability
Contributions
Toward More Efficient Motion Planning withDifferential Constraints
Maciej Kalisiak
Final Oral ExamDecember 14th, 2007
Maciej Kalisiak Toward More Efficient MP w/Differential Constraints
2/29
Motion PlanningViability
Contributions
Outline
1 Motion Planning (MP)What is MP?Types of MP problemsMP is hard
2 Viability
3 ContributionsMP in highly constrained problemsMP w/viability filteringViability-based safety enforcement
4 Conclusion
Maciej Kalisiak Toward More Efficient MP w/Differential Constraints
3/29
Motion PlanningViability
Contributions
What is MP?Types of MP problemsMP is hard
Outline
1 Motion Planning (MP)What is MP?Types of MP problemsMP is hard
2 Viability
3 ContributionsMP in highly constrained problemsMP w/viability filteringViability-based safety enforcement
4 Conclusion
Maciej Kalisiak Toward More Efficient MP w/Differential Constraints
4/29
Motion PlanningViability
Contributions
What is MP?Types of MP problemsMP is hard
What is Motion Planning (MP)?
in a nutshell:“how to get from A to B?”
sometimes also:“... optimally?”
example problems
Maciej Kalisiak Toward More Efficient MP w/Differential Constraints
4/29
Motion PlanningViability
Contributions
What is MP?Types of MP problemsMP is hard
What is Motion Planning (MP)?
in a nutshell:“how to get from A to B?”
sometimes also:“... optimally?”
example problems
Maciej Kalisiak Toward More Efficient MP w/Differential Constraints
4/29
Motion PlanningViability
Contributions
What is MP?Types of MP problemsMP is hard
What is Motion Planning (MP)?
in a nutshell:“how to get from A to B?”
sometimes also:“... optimally?”
example problems
Maciej Kalisiak Toward More Efficient MP w/Differential Constraints
4/29
Motion PlanningViability
Contributions
What is MP?Types of MP problemsMP is hard
What is Motion Planning (MP)?
in a nutshell:“how to get from A to B?”
sometimes also:“... optimally?”
example problems
Maciej Kalisiak Toward More Efficient MP w/Differential Constraints
4/29
Motion PlanningViability
Contributions
What is MP?Types of MP problemsMP is hard
What is Motion Planning (MP)?
in a nutshell:“how to get from A to B?”
sometimes also:“... optimally?”
example problems
Maciej Kalisiak Toward More Efficient MP w/Differential Constraints
5/29
Motion PlanningViability
Contributions
What is MP?Types of MP problemsMP is hard
Approach
solved by converting to dual problem (agent → point)complication: often cannot manipulate agent directly
X = x × y × θx ∈ X
x = (x, y, θ)
Maciej Kalisiak Toward More Efficient MP w/Differential Constraints
5/29
Motion PlanningViability
Contributions
What is MP?Types of MP problemsMP is hard
Approach
solved by converting to dual problem (agent → point)complication: often cannot manipulate agent directly
Maciej Kalisiak Toward More Efficient MP w/Differential Constraints
5/29
Motion PlanningViability
Contributions
What is MP?Types of MP problemsMP is hard
Approach
solved by converting to dual problem (agent → point)complication: often cannot manipulate agent directly
Maciej Kalisiak Toward More Efficient MP w/Differential Constraints
6/29
Motion PlanningViability
Contributions
What is MP?Types of MP problemsMP is hard
Types of MP problems
common types:kinematicnonholonomickinodynamic
e.g., “Piano Mover’s Problem”
Maciej Kalisiak Toward More Efficient MP w/Differential Constraints
6/29
Motion PlanningViability
Contributions
What is MP?Types of MP problemsMP is hard
Types of MP problems
common types:kinematicnonholonomickinodynamic
e.g., agents w/rolling contacts
Maciej Kalisiak Toward More Efficient MP w/Differential Constraints
6/29
Motion PlanningViability
Contributions
What is MP?Types of MP problemsMP is hard
Types of MP problems
common types:kinematicnonholonomickinodynamic
e.g., inertia & balance play big role
Maciej Kalisiak Toward More Efficient MP w/Differential Constraints
6/29
Motion PlanningViability
Contributions
What is MP?Types of MP problemsMP is hard
Types of MP problems
common types:kinematicnonholonomickinodynamic
Differential Constraints (DC)DC: constraints on q′( d
dt of agent configuration)
nonholonomic kinodynamic
DC
DCs very common,but make MP more difficult
Maciej Kalisiak Toward More Efficient MP w/Differential Constraints
7/29
Motion PlanningViability
Contributions
What is MP?Types of MP problemsMP is hard
MP is hard
hardnessPiano Mover’s Problem:→ PSPACE-completeMP problems w/DC: at least as hard
why?“curse of dimensionality”real world problems often high-DDCs complicate search space further
300 S. M. LaValle: Planning Algorithms
P NP PSPACE EXPTIME
Figure 6.40: It is known that P ⊂ EXPTIME is a strict subset; however, it is notknown precisely how large NP and PSPACE are.
or EXPTIME. A language A is called X-hard if every language B in class X ispolynomial-time reducible to A. In short, this means that in polynomial time,any language in B can be translated into instances for language A, and then thedecisions for A can be correctly translated back in polynomial time to correctlydecide B. Thus, if A can be decided, then within a polynomial-time factor, everylanguage in X can be decided. The hardness concept can even be applied toa language (problem) that does not belong to the class. For example, we candeclare that a language A is NP-hard even if A 6∈NP (it could be harder and lie inEXPTIME, for example). If it is known that the language is both hard for someclass X and is also a member of X, then it is called X-complete (i.e., NP-complete,PSPACE-complete, etc.).8 Note that because of this uncertainty regarding P, NP,and PSPACE, one cannot say that a problem is intractable if it is NP-hard orPSPACE-hard, but one can, however, if the problem is EXPTIME-hard. Oneadditional remark: it is useful to remember that PSPACE-hard implies NP-hard.
Lower bounds for motion planning The general motion planning problem,Formulation 4.1, was shown in 1979 to be PSPACE-hard by Reif [819]. In fact, theproblem was restricted to polyhedral obstacles and a finite number of polyhedralrobot bodies attached by spherical joints. The coordinates of all polyhedra areassumed to be in Q (this enables a finite-length string encoding of the probleminstance). The proof introduces a fascinating motion planning instance that in-volves many attached, dangling robot parts that must work their way through acomplicated system of tunnels, which together simulates the operation of a sym-metric Turing machine. Canny later established that the problem in Formulation4.1 (expressed using polynomials that have rational coefficients) lies in PSPACE[175]. Therefore, the general motion planning problem is PSPACE-complete.
Many other lower bounds have been shown for a variety of planning problems.One famous example is the Warehouseman’s problem shown in Figure 6.41. This
8If you remember hearing that a planning problem is NP-something, but cannot rememberwhether it was NP-hard or NP-complete, then it is safe to say NP-hard because NP-completeimplies NP-hard. This can similarly be said for other classes, such as PSPACE-complete vs.PSPACE-hard.
Maciej Kalisiak Toward More Efficient MP w/Differential Constraints
7/29
Motion PlanningViability
Contributions
What is MP?Types of MP problemsMP is hard
MP is hard
hardnessPiano Mover’s Problem:→ PSPACE-completeMP problems w/DC: at least as hard
why?“curse of dimensionality”real world problems often high-DDCs complicate search space further
300 S. M. LaValle: Planning Algorithms
P NP PSPACE EXPTIME
Figure 6.40: It is known that P ⊂ EXPTIME is a strict subset; however, it is notknown precisely how large NP and PSPACE are.
or EXPTIME. A language A is called X-hard if every language B in class X ispolynomial-time reducible to A. In short, this means that in polynomial time,any language in B can be translated into instances for language A, and then thedecisions for A can be correctly translated back in polynomial time to correctlydecide B. Thus, if A can be decided, then within a polynomial-time factor, everylanguage in X can be decided. The hardness concept can even be applied toa language (problem) that does not belong to the class. For example, we candeclare that a language A is NP-hard even if A 6∈NP (it could be harder and lie inEXPTIME, for example). If it is known that the language is both hard for someclass X and is also a member of X, then it is called X-complete (i.e., NP-complete,PSPACE-complete, etc.).8 Note that because of this uncertainty regarding P, NP,and PSPACE, one cannot say that a problem is intractable if it is NP-hard orPSPACE-hard, but one can, however, if the problem is EXPTIME-hard. Oneadditional remark: it is useful to remember that PSPACE-hard implies NP-hard.
Lower bounds for motion planning The general motion planning problem,Formulation 4.1, was shown in 1979 to be PSPACE-hard by Reif [819]. In fact, theproblem was restricted to polyhedral obstacles and a finite number of polyhedralrobot bodies attached by spherical joints. The coordinates of all polyhedra areassumed to be in Q (this enables a finite-length string encoding of the probleminstance). The proof introduces a fascinating motion planning instance that in-volves many attached, dangling robot parts that must work their way through acomplicated system of tunnels, which together simulates the operation of a sym-metric Turing machine. Canny later established that the problem in Formulation4.1 (expressed using polynomials that have rational coefficients) lies in PSPACE[175]. Therefore, the general motion planning problem is PSPACE-complete.
Many other lower bounds have been shown for a variety of planning problems.One famous example is the Warehouseman’s problem shown in Figure 6.41. This
8If you remember hearing that a planning problem is NP-something, but cannot rememberwhether it was NP-hard or NP-complete, then it is safe to say NP-hard because NP-completeimplies NP-hard. This can similarly be said for other classes, such as PSPACE-complete vs.PSPACE-hard.
Maciej Kalisiak Toward More Efficient MP w/Differential Constraints
8/29
Motion PlanningViability
Contributions
Outline
1 Motion Planning (MP)What is MP?Types of MP problemsMP is hard
2 Viability
3 ContributionsMP in highly constrained problemsMP w/viability filteringViability-based safety enforcement
4 Conclusion
Maciej Kalisiak Toward More Efficient MP w/Differential Constraints
9/29
Motion PlanningViability
Contributions
What is Viability?
“definition”viable state: ∃ an evasive actionnonviable state: constraint violation unavoidable
Maciej Kalisiak Toward More Efficient MP w/Differential Constraints
9/29
Motion PlanningViability
Contributions
What is Viability?
“definition”viable state: ∃ an evasive actionnonviable state: constraint violation unavoidable
Maciej Kalisiak Toward More Efficient MP w/Differential Constraints
9/29
Motion PlanningViability
Contributions
What is Viability?
“definition”viable state: ∃ an evasive actionnonviable state: constraint violation unavoidable
why of interest?crops up in many contexts, usefulexploited throughout thesis:
to expedite MPto aid in user-control
Maciej Kalisiak Toward More Efficient MP w/Differential Constraints
10/29
Motion PlanningViability
Contributions
MP in highly constrained problemsMP w/viability filteringViability-based safety enforcement
Outline
1 Motion Planning (MP)What is MP?Types of MP problemsMP is hard
2 Viability
3 ContributionsMP in highly constrained problemsMP w/viability filteringViability-based safety enforcement
4 Conclusion
Maciej Kalisiak Toward More Efficient MP w/Differential Constraints
11/29
Motion PlanningViability
Contributions
MP in highly constrained problemsMP w/viability filteringViability-based safety enforcement
Overall goal of thesis
aim: explore some novel ideas in MPfocus: improving MP speedgrand vision: MP with motion “macro-primitives”
Maciej Kalisiak Toward More Efficient MP w/Differential Constraints
12/29
Motion PlanningViability
Contributions
MP in highly constrained problemsMP w/viability filteringViability-based safety enforcement
Outline
1 Motion Planning (MP)What is MP?Types of MP problemsMP is hard
2 Viability
3 ContributionsMP in highly constrained problemsMP w/viability filteringViability-based safety enforcement
4 Conclusion
Maciej Kalisiak Toward More Efficient MP w/Differential Constraints
13/29
Motion PlanningViability
Contributions
MP in highly constrained problemsMP w/viability filteringViability-based safety enforcement
MP in highly constrained problems
key idea: “any progress” is better than “no progress”
Maciej Kalisiak Toward More Efficient MP w/Differential Constraints
13/29
Motion PlanningViability
Contributions
MP in highly constrained problemsMP w/viability filteringViability-based safety enforcement
MP in highly constrained problems
improvement to RRT algorithmhighly-constrained problems:poor performanceproposed: RRT-Blossomresult: big speed ups (>10x)
Maciej Kalisiak Toward More Efficient MP w/Differential Constraints
13/29
Motion PlanningViability
Contributions
MP in highly constrained problemsMP w/viability filteringViability-based safety enforcement
MP in highly constrained problems
improvement to RRT algorithmhighly-constrained problems:poor performanceproposed: RRT-Blossomresult: big speed ups (>10x)
amount of constraint
runt
ime
ideal
RRT
Maciej Kalisiak Toward More Efficient MP w/Differential Constraints
13/29
Motion PlanningViability
Contributions
MP in highly constrained problemsMP w/viability filteringViability-based safety enforcement
MP in highly constrained problems
improvement to RRT algorithmhighly-constrained problems:poor performanceproposed: RRT-Blossomresult: big speed ups (>10x)
amount of constraint
runt
ime
ideal
RRT
Maciej Kalisiak Toward More Efficient MP w/Differential Constraints
14/29
Motion PlanningViability
Contributions
MP in highly constrained problemsMP w/viability filteringViability-based safety enforcement
RRT operation review
grows two trees(from qinit and qgoal)
each tree grows toward qtgt
Maciej Kalisiak Toward More Efficient MP w/Differential Constraints
14/29
Motion PlanningViability
Contributions
MP in highly constrained problemsMP w/viability filteringViability-based safety enforcement
RRT operation review
grows two trees(from qinit and qgoal)
each tree grows toward qtgt
Maciej Kalisiak Toward More Efficient MP w/Differential Constraints
14/29
Motion PlanningViability
Contributions
MP in highly constrained problemsMP w/viability filteringViability-based safety enforcement
RRT operation review
grows two trees(from qinit and qgoal)
each tree grows toward qtgt
Maciej Kalisiak Toward More Efficient MP w/Differential Constraints
14/29
Motion PlanningViability
Contributions
MP in highly constrained problemsMP w/viability filteringViability-based safety enforcement
RRT operation review
grows two trees(from qinit and qgoal)
each tree grows toward qtgt
Maciej Kalisiak Toward More Efficient MP w/Differential Constraints
15/29
Motion PlanningViability
Contributions
MP in highly constrained problemsMP w/viability filteringViability-based safety enforcement
RRT-Blossom
allow receding edges...but not if regressingfilter with regression testbottlenecks
key idea: “any progress” is better than “no progress”
Maciej Kalisiak Toward More Efficient MP w/Differential Constraints
15/29
Motion PlanningViability
Contributions
MP in highly constrained problemsMP w/viability filteringViability-based safety enforcement
RRT-Blossom
allow receding edges...but not if regressingfilter with regression testbottlenecks
regression if:∃other | ρ(parent, leaf ) > ρ(other , leaf )
key idea: “any progress” is better than “no progress”
Maciej Kalisiak Toward More Efficient MP w/Differential Constraints
15/29
Motion PlanningViability
Contributions
MP in highly constrained problemsMP w/viability filteringViability-based safety enforcement
RRT-Blossom
allow receding edges...but not if regressingfilter with regression testbottlenecks
21
key idea: “any progress” is better than “no progress”
Maciej Kalisiak Toward More Efficient MP w/Differential Constraints
16/29
Motion PlanningViability
Contributions
MP in highly constrained problemsMP w/viability filteringViability-based safety enforcement
Outline
1 Motion Planning (MP)What is MP?Types of MP problemsMP is hard
2 Viability
3 ContributionsMP in highly constrained problemsMP w/viability filteringViability-based safety enforcement
4 Conclusion
Maciej Kalisiak Toward More Efficient MP w/Differential Constraints
17/29
Motion PlanningViability
Contributions
MP in highly constrained problemsMP w/viability filteringViability-based safety enforcement
MP w/viability filtering
drawbacks of tree-based MP:tactile-only sensingsearch ignores prior attempts
general idea:“work smarter, not harder”add “sight” + “learning” → faster MP
Maciej Kalisiak Toward More Efficient MP w/Differential Constraints
17/29
Motion PlanningViability
Contributions
MP in highly constrained problemsMP w/viability filteringViability-based safety enforcement
MP w/viability filtering
drawbacks of tree-based MP:tactile-only sensingsearch ignores prior attempts
general idea:“work smarter, not harder”add “sight” + “learning” → faster MP
Maciej Kalisiak Toward More Efficient MP w/Differential Constraints
18/29
Motion PlanningViability
Contributions
MP in highly constrained problemsMP w/viability filteringViability-based safety enforcement
Key extensions
“sight”virtual sensors: distance along pathyield “locally situated” state
“learning”prior trajectories → viability modelsmodels parametrized using sensors→ local models→ transferrable
ideally: bootstrapping
Maciej Kalisiak Toward More Efficient MP w/Differential Constraints
18/29
Motion PlanningViability
Contributions
MP in highly constrained problemsMP w/viability filteringViability-based safety enforcement
Key extensions
“sight”virtual sensors: distance along pathyield “locally situated” state
“learning”prior trajectories → viability modelsmodels parametrized using sensors→ local models→ transferrable
ideally: bootstrapping
Maciej Kalisiak Toward More Efficient MP w/Differential Constraints
19/29
Motion PlanningViability
Contributions
MP in highly constrained problemsMP w/viability filteringViability-based safety enforcement
Exploiting viability
observationscurrently: search in all of Xfreebut Xfree includes Xricxgoal usually unreachable from x ∈ Xric
⇒ avoid futile searching!model agent viabilitykeep MP search within Viab(Xfree)observed: speed-up of up to 10x
Xobst
Xfree
Xric
Viab(Xfree)
Maciej Kalisiak Toward More Efficient MP w/Differential Constraints
19/29
Motion PlanningViability
Contributions
MP in highly constrained problemsMP w/viability filteringViability-based safety enforcement
Exploiting viability
observationscurrently: search in all of Xfreebut Xfree includes Xricxgoal usually unreachable from x ∈ Xric
⇒ avoid futile searching!model agent viabilitykeep MP search within Viab(Xfree)observed: speed-up of up to 10x
Xobst
Xfree
Xric
Viab(Xfree)
Maciej Kalisiak Toward More Efficient MP w/Differential Constraints
19/29
Motion PlanningViability
Contributions
MP in highly constrained problemsMP w/viability filteringViability-based safety enforcement
Exploiting viability
observationscurrently: search in all of Xfreebut Xfree includes Xricxgoal usually unreachable from x ∈ Xric
⇒ avoid futile searching!model agent viabilitykeep MP search within Viab(Xfree)observed: speed-up of up to 10x
Xobst
Xfree
Xric
Viab(Xfree)
Maciej Kalisiak Toward More Efficient MP w/Differential Constraints
19/29
Motion PlanningViability
Contributions
MP in highly constrained problemsMP w/viability filteringViability-based safety enforcement
Exploiting viability
observationscurrently: search in all of Xfreebut Xfree includes Xricxgoal usually unreachable from x ∈ Xric
⇒ avoid futile searching!model agent viabilitykeep MP search within Viab(Xfree)observed: speed-up of up to 10x
Xobst
Xfree
Xric
Viab(Xfree)
Maciej Kalisiak Toward More Efficient MP w/Differential Constraints
Results: model transfer
agent problem posed model trained on
problem algo. runtimes
RRT-CT 371.5sRRT-Blossom 21.0sRRT-Blossom-VF 5.6s
RRT-CT 209.9sRRT-Blossom 13.5sRRT-Blossom-VF 3.6s
RRT-CT 2148.6sRRT-Blossom 305.7sRRT-Blossom-VF 34.3s
20/29
Results: model transfer
agent problem posed model trained on
problem algo. runtimes
RRT-CT 371.5sRRT-Blossom 21.0sRRT-Blossom-VF 5.6s
RRT-CT 209.9sRRT-Blossom 13.5sRRT-Blossom-VF 3.6s
RRT-CT 2148.6sRRT-Blossom 305.7sRRT-Blossom-VF 34.3s
20/29
Results: tree structure
RRT-CT RRT-Blossom RRT-Blossom w/VF
no filtering viability filtering
21/29
22/29
Motion PlanningViability
Contributions
MP in highly constrained problemsMP w/viability filteringViability-based safety enforcement
Outline
1 Motion Planning (MP)What is MP?Types of MP problemsMP is hard
2 Viability
3 ContributionsMP in highly constrained problemsMP w/viability filteringViability-based safety enforcement
4 Conclusion
Maciej Kalisiak Toward More Efficient MP w/Differential Constraints
23/29
Motion PlanningViability
Contributions
MP in highly constrained problemsMP w/viability filteringViability-based safety enforcement
Viability-based safety enforcement
⇒ assisted control:inherently usefulfacilitates obtaining user-demonstrated training datahelpful in user-assisted MP (future work)
key idea: viability more reliable for detecting imminent danger
Maciej Kalisiak Toward More Efficient MP w/Differential Constraints
23/29
Motion PlanningViability
Contributions
MP in highly constrained problemsMP w/viability filteringViability-based safety enforcement
Viability-based safety enforcement
⇒ assisted control:inherently usefulfacilitates obtaining user-demonstrated training datahelpful in user-assisted MP (future work)
key idea: viability more reliable for detecting imminent danger
Maciej Kalisiak Toward More Efficient MP w/Differential Constraints
24/29
Motion PlanningViability
Contributions
MP in highly constrained problemsMP w/viability filteringViability-based safety enforcement
Collision avoidance
typical (collision-based)based on predictive lookahead (Th seconds)weakness: Th is finite
Th may be too smallsafety↑ as Th →∞
better: viability-based safety enforcementonly a minimal lookahead neededlonger lookaheads: milder corrections
Maciej Kalisiak Toward More Efficient MP w/Differential Constraints
24/29
Motion PlanningViability
Contributions
MP in highly constrained problemsMP w/viability filteringViability-based safety enforcement
Collision avoidance
typical (collision-based)based on predictive lookahead (Th seconds)weakness: Th is finite
Th may be too smallsafety↑ as Th →∞
better: viability-based safety enforcementonly a minimal lookahead neededlonger lookaheads: milder corrections
Maciej Kalisiak Toward More Efficient MP w/Differential Constraints
24/29
Motion PlanningViability
Contributions
MP in highly constrained problemsMP w/viability filteringViability-based safety enforcement
Collision avoidance
typical (collision-based)based on predictive lookahead (Th seconds)weakness: Th is finite
Th may be too smallsafety↑ as Th →∞
better: viability-based safety enforcementonly a minimal lookahead neededlonger lookaheads: milder corrections
Maciej Kalisiak Toward More Efficient MP w/Differential Constraints
24/29
Motion PlanningViability
Contributions
MP in highly constrained problemsMP w/viability filteringViability-based safety enforcement
Collision avoidance
typical (collision-based)based on predictive lookahead (Th seconds)weakness: Th is finite
Th may be too smallsafety↑ as Th →∞
better: viability-based safety enforcementonly a minimal lookahead neededlonger lookaheads: milder corrections
Maciej Kalisiak Toward More Efficient MP w/Differential Constraints
24/29
Motion PlanningViability
Contributions
MP in highly constrained problemsMP w/viability filteringViability-based safety enforcement
Collision avoidance
typical (collision-based)based on predictive lookahead (Th seconds)weakness: Th is finite
Th may be too smallsafety↑ as Th →∞
better: viability-based safety enforcementonly a minimal lookahead neededlonger lookaheads: milder corrections
Maciej Kalisiak Toward More Efficient MP w/Differential Constraints
24/29
Motion PlanningViability
Contributions
MP in highly constrained problemsMP w/viability filteringViability-based safety enforcement
Collision avoidance
typical (collision-based)based on predictive lookahead (Th seconds)weakness: Th is finite
Th may be too smallsafety↑ as Th →∞
better: viability-based safety enforcementonly a minimal lookahead neededlonger lookaheads: milder corrections
Maciej Kalisiak Toward More Efficient MP w/Differential Constraints
25/29
Motion PlanningViability
Contributions
MP in highly constrained problemsMP w/viability filteringViability-based safety enforcement
Operation
xk
xk
xkxk
F i(xk, vk)
L3
F i(xk, uj)
L2L1L0
Maciej Kalisiak Toward More Efficient MP w/Differential Constraints
26/29
Motion PlanningViability
Contributions
MP in highly constrained problemsMP w/viability filteringViability-based safety enforcement
Viability of control actions
U
ThTebTh
Teb
U
Maciej Kalisiak Toward More Efficient MP w/Differential Constraints
Experimentsag
ents
envi
ronm
ents
27/29
Results
environment
Viab(Xfree) model
enforcement
28/29
29/29
Motion PlanningViability
Contributions
Conclusion
contributionsbetter handling of constrained environments in RRTmore efficient MP by narrowing search to Viab(Xfree)more robust threat avoidance in computer-assisted control
future work:learning appropriate actions from motion dataMP w/motion “macro primitives”evaluate viability filtering with other MPslocal viability models for safety enforcement(near-)optimal solutions for MP w/DChuman-derived motion data (e.g., style content)human-guided MP: selection of style or topology
Maciej Kalisiak Toward More Efficient MP w/Differential Constraints
29/29
Motion PlanningViability
Contributions
Conclusion
contributionsbetter handling of constrained environments in RRTmore efficient MP by narrowing search to Viab(Xfree)more robust threat avoidance in computer-assisted control
future work:learning appropriate actions from motion dataMP w/motion “macro primitives”evaluate viability filtering with other MPslocal viability models for safety enforcement(near-)optimal solutions for MP w/DChuman-derived motion data (e.g., style content)human-guided MP: selection of style or topology
Maciej Kalisiak Toward More Efficient MP w/Differential Constraints
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