IP Library › Granted Patent US 12,204,336
Granted Patent B2
US 12,204,336 · App. 17/299,574 · Granted Jan 21, 2025

Apparatus, method and article to facilitate motion planning in an environment having dynamic objects

Inventors: Daniel Sorin (Durham, NC); William Floyd-Jones (Durham, NC); Sean Murray (Durham, NC); George Konidaris (Providence, RI); William Walker (Durham, NC)
Assignees: DUKE UNIVERSITY; BROWN UNIVERSITY
G05D1/0217G05D1/0088G05D1/0214G05D1/0219
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Quick Facts
Patent No.
US 12,204,336
App. No.
17/299,574
Filed
Jun 3, 2021
Granted
Jan 21, 2025
Kind
B2
Art Unit
3663
USPC
701/23
Abstract

A motion planner of a computer system of a primary agent, e.g., an autonomous vehicle, uses reconfigurable collision detection architecture hardware to perform a collision assessment on a planning graph for the primary agent prior to execution of a motion plan. For edges on the planning graph, which represent transitions in states of the primary agent, the system sets a probability of collision with another agent, e.g., a dynamic object, in the environment based at least in part on the collision assessment. Depending on whether the goal of the primary agent is to avoid or collide with a particular dynamic object in the environment, the system then performs an optimization to identify a path in the resulting planning graph with either a relatively low or relatively high potential of a collision with the particular dynamic object. The system then causes the actuator system of the primary agent to implement a motion plan with the applicable identified path based at least in part on the optimization.

Claims (97)

1. A motion planning method of operation in a processor-based system to perform motion planning via planning graphs, where each planning graph respectively comprises a plurality of nodes and edges, each node which represents, implicitly or explicitly, time and variables that characterize a state of a primary agent, which operates in an environment that includes one or more other agents, and each edge represents a transition between a respective pair of the nodes, the method comprising:

for a current node in a first planning graph,

for each trajectory in a set of trajectories that respectively represent actual or prospective trajectories of at least one of the one or more other agents,

determining which edges of the first planning graph collide with the respective trajectory, if any of the edges collide with the respective trajectory;

applying a cost function to one or more of the respective edges to reflect at least one of a determined collision or absence thereof; and

for each of a number of candidate nodes in the first planning graph, the candidate nodes being any node in the first planning graph that is directly coupled to the current node in the first planning graph by a respective single edge of the first planning graph, finding a least cost path from the current node to a goal node in the first planning graph that passes from the current node directly to the respective candidate node and then to the goal node, with or without a number of intervening nodes successively between the respective candidate node and the goal node along a corresponding path; and

after finding the least cost path for each of the candidate nodes with respect to the trajectories of the set of trajectories,

for each of the candidate nodes, computing a respective value based at least in part on a respective cost associated with each least cost path for the respective candidate node across all of the trajectories; and

selecting one of the candidate nodes based at least in part on the computed respective values.

2. The motion planning method of claim 1 wherein applying a cost function to one or more of the respective edges to reflect at least one of the determined collision or absence thereof includes:

for any of the edges that are determined to collide with at least one trajectory, increasing a cost of the respective edge to a relatively high magnitude to reflect the determined collision, wherein the relatively high magnitude is relatively higher than a relatively low magnitude that reflects an absence of collision for at least one other edge.

3. The motion planning method of claim 1 wherein applying a cost function to one or more of the respective edges to reflect at least one of the determined collision or absence thereof includes:

for any of the edges that are determined not to collide with at least one trajectory, increasing a cost of the respective edge to a relatively high magnitude to reflect the determined absence of collision, wherein the relatively high magnitude is relatively higher than a relatively low magnitude that reflects a collision for at least one other edge.

4. The motion planning method of claim 1 , further comprising:

for each of at least one of the other agents in the environment, sampling to determine the respective prospective trajectory of the other agent; and

forming the set of trajectories from the determined respective actual or prospective trajectory of each of the other agents.

5. The motion planning method of claim 1 , further comprising:

selecting the candidate nodes in the first planning graph from the other nodes of the first planning graph based on the candidate nodes being any node in the first planning graph that is directly coupled to the current node in the first planning graph by a respective single edge of the first planning graph.

6. The motion planning method of claim 1 wherein computing a respective value based at least in part on a respective cost associated with each least cost path for the respective candidate node across all of the trajectories, includes computing an average value of the respective cost associated with each least cost path that extends from the current node to the goal node via the respective candidate node and via all of the intervening nodes, if any.

7. The motion planning method of claim 1 wherein selecting one of the candidate nodes based at least in part on the computed respective values includes selecting the one of the candidate nodes which has the respective computed value that is a smallest of all of the computed values.

8. The motion planning method of claim 1 , further comprising: updating a trajectory of the primary agent based on the selected one of the candidate nodes.

9. The method of claim 1 , further comprising:

initializing the first planning graph before applying the cost function to the respective edges to reflect the determined collisions.

10. The method of claim 9 wherein initializing the first planning graph includes:

for each edge in the first planning graph performing a collision assessment for the edge relative to each of a number of static objects in the environment to identify collisions, if any, between the respective edge and the static objects.

11. The method of claim 10 wherein initializing the first planning graph further includes:

for each edge that is assessed as colliding with at least one of the static objects, applying a cost function to the respective edge to reflect the assessed collision or removing the edge from the first planning graph.

12. The method of claim 9 wherein initializing the first planning graph further includes:

for each node in the first planning graph, computing a cost to the goal node from the node; and

logically associating the computed cost with the respective node.

13. The method of claim 1 , further comprising:

assigning the selected one of the candidate nodes to be a new current node in the first planning graph;

for the new current node in a first planning graph,

for each trajectory in a set of trajectories that respectively represent actual or prospective trajectories of at least one of the one or more other agents,

determining which edges of the first planning graph collide with the respective trajectory, if any of the edges collide with the respective trajectory;

applying a cost function to one or more of the respective edges to reflect at least one of the determined collision or absence thereof; and

for each of a number of new candidate nodes in the first planning graph, the new candidate nodes being any node in the first planning graph that is directly coupled to the new current node in the first planning graph by a respective single edge of the first planning graph, finding a least cost path from the new current node to a goal node in the first planning graph that passes from the new current node directly to the respective new candidate node and then to the goal node, with or without a number of intervening nodes successively between the respective new candidate node and the goal node along a corresponding path; and

after finding the least cost path for each of the new candidate nodes with respect to the trajectories of the set of trajectories,

for each of the new candidate nodes, computing a respective value based at least in part on a respective cost associated with each least cost path for the respective new candidate node across all of the trajectories; and

selecting one of the new candidate nodes based at least in part on the computed respective values.

14. A processor-based system to perform motion planning via planning graphs, where each planning graph respectively comprises a plurality of nodes and edges, each node which represents, implicitly or explicitly, time and variables that characterize a state of a primary agent, which operates in an environment that includes one or more other agents, and each edge represents a transition between a respective pair of the nodes, the system comprising:

at least one processor; and

at least one nontransitory processor-readable medium that stores at least one of processor-executable instructions or data which, when executed by the at least one processor, causes the at least one processor to:

for a current node in a first planning graph,

for each trajectory in a set of trajectories that respectively represent actual or prospective trajectories of at least one of the one or more other agents,

determine which edges of the first planning graph collide with the respective trajectory, if any of the edges collide with the respective trajectory;

apply a cost function to one or more of the respective edges to reflect at least one of a determined collision or absence thereof; and

for each of a number of candidate nodes in the first planning graph, the candidate nodes being any node in the first planning graph that is directly coupled to the current node in the first planning graph by a respective single edge of the first planning graph, find a least cost path from the current node to a goal node in the first planning graph that passes from the current node directly to the respective candidate node and then to the goal node, with or without a number of intervening nodes successively between the respective candidate node and the goal node along a corresponding path; and

after finding the least cost path for each of the candidate nodes with respect to the trajectories of the set of trajectories,

for each of the candidate nodes, compute a respective value that represents an average value of a respective cost associated with each least cost path for the respective candidate node across all of the trajectories; and

select one of the candidate nodes based at least in part on the computed respective values.

15. A method of operation in a motion planning system that employs graphs with nodes that represent states and edges that represent transitions between states, the method comprising:

for each available next node with respect to a current node in a first graph, calculating, via at least one processor, a respective associated representative cost to reach a goal node from the current node via the respective next node, the respective associated representative cost which reflects a respective representative cost associated with each available path from the current node to the goal node via the respective next node in light of an assessment of a probability of collision with one or more agents in an environment based on a nondeterministic behavior of each of the one or more agents in the environment, the agents which can vary any one or more of a position, a velocity, a trajectory, a path of travel, or a shape over time;

selecting, via at least one processor, a next node based on the calculated respective associated representative costs for each available next node; and

commanding, via at least one processor, a movement of a primary agent based at least in part on the selected next node, wherein calculating a respective associated representative cost to reach a goal node from the current node via the respective next node, comprises:

for each prospective path between the current node and the goal node via the respective next node,

for each edge between the current node and the goal node along the respective prospective path,

determining a respective associated representative cost; and

assigning the determined respective associated representative cost for each edge to the respective edge for each edge between the current node and the goal node along the respective prospective path;

determining a least cost path for the respective next node from the respective prospective paths between the current node and the goal node via the respective next node based at least on part on the assigned determined respective associated representative costs; and

assigning a value representative of the determined least cost path to the respective next node.

16. The method of claim 15 wherein determining a least cost path for the respective next node from the respective prospective paths between the current node and the goal node via the respective next node based at least on part on the assigned determined respective associated representative costs comprises determining a least cost path that includes a cost of traversing from the current node to the respective next node.

17. The method of claim 16 wherein determining a respective associated representative cost for each edge between the current node and the goal node along the respective prospective path, comprises:

for each edge between the current goal and the goal node along the respective prospective path,

assessing a risk of a collision with one or more agents in the environment based on one or more probabilistic functions that respectively represent the nondeterministic behavior of each of the one or more agents in the environment.

18. The method of claim 17 wherein assessing a risk of a collision with one or more agents in the environment based on one or more probabilistic functions that respectively represent the nondeterministic behavior of each of the one or more agents in the environment comprises:

sampling the probabilistic functions that respectively represent the nondeterministic behavior of each of the one or more agents in the environment in light of a series of actions represented by respective ones of each edge between the respective next node and each successive node along the respective prospective path.

19. The method of claim 17 wherein assessing a risk of a collision with one or more agents in the environment based on one or more probabilistic functions that respectively represent the nondeterministic behavior of each of the one or more agents in the environment comprises:

sampling the probabilistic functions that respectively represent the nondeterministic behavior of each of the one or more agents in the environment in light of a series of actions represented by respective ones of each edge between the respective next node and each successive node along the respective prospective path to a present node, the present node being a further node along the respective prospective path reached during the assessing of the risk of collision.

20. The method of claim 17 wherein assessing a risk of a collision with one or more agents in the environment based on one or more probabilistic functions that respectively represent the nondeterministic behavior of each of the one or more agents in the environment comprises:

for each of the agents, repeatedly sampling the respective probabilistic function that respectively represents the nondeterministic behavior of the respective agent.

21. The method of claim 20 wherein the repeatedly sampling the respective probabilistic function that respectively represents the nondeterministic behavior of the respective agent includes repeatedly sampling the respective probabilistic function for a plurality of iterations, a total number of the iterations based at least in part on an available amount of time before the commanding must occur.

22. The method of claim 17 wherein assessing a risk of a collision with one or more agents in the environment based on one or more probabilistic functions that respectively represent the nondeterministic behavior of each of the one or more agents in the environment comprises:

for each of the agents, repeatedly sampling the probabilistic functions that respectively represent the nondeterministic behavior of each of the one or more agents in the environment in light of a series of actions represented by respective ones of each edge between the respective next node and each successive node along the respective prospective path.

23. The method of claim 17 wherein assessing a risk of a collision with one or more agents in the environment based on one or more probabilistic functions that respectively represent the nondeterministic behavior of each of the one or more agents in the environment comprises:

for each of the agents, repeatedly sampling the probabilistic functions that respectively represent the nondeterministic behavior of each of the one or more agents in the environment in light of a series of actions represented by respective ones of each edge between the respective next node and each successive node along the respective prospective path to a present node, the present node being a further node along the respective prospective path reached during the assessing of the risk of collision.

24. The method of claim 17 wherein the assessing of the risk of collision involves simulation of traversal of the respective prospective paths.

25. The method of claim 17 wherein assessing a risk of a collision with one or more agents in the environment based on one or more probabilistic functions that respectively represent the nondeterministic behavior of each of the one or more agents in the environment comprises:

assessing a risk of collision via dedicated risk assessment hardware based at least on a probabilistically determined respective trajectory of each of the one or more agents in the environment, where the respective associated representative costs are based at least in part on the assessed risk of collision.

26. The method of claim 17 wherein assessing a risk of a collision with one or more agents in the environment based on one or more probabilistic functions that respectively represent the nondeterministic behavior of each of the one or more agents in the environment comprises: assessing a risk of a collision with one or more agents in the environment based on one or more probabilistic functions that respectively represent the nondeterministic behavior of at least a secondary one of the agents in the environment, the primary one of the agents being an agent for which the motion planning is being performed.

27. The method of claim 15 , further comprising:

initializing the first graph before calculating a respective associated representative cost to reach a goal node from the current node via the respective next node.

28. The method of claim 27 wherein initializing the first graph, comprises:

performing a static collision assessment to identify any collisions with one or more static objects in the environment;

for each node in the first graph, computing a respective cost to reach a goal node from the respective node; and

for each node in the first graph, logically associating the respective computed cost to reach a goal node with the respective node.

29. A processor-based system to perform motion planning that employs graphs with nodes that represent states and edges that represent transitions between states, the system comprising:

at least one processor; and

at least one nontransitory processor-readable medium that stores at least one of processor-executable instructions or data which, when executed by the at least one processor, causes the at least one processor to:

for each available next node with respect to a current node of a primary agent for which the motion planning is being performed in a first graph, calculate a respective associated representative cost to reach a goal node from the current node via the respective next node, the respective associated representative cost which reflects a respective representative cost associated with each available path from the current node to the goal node via the respective next node in light of an assessment of a probability of collision of the primary agent with one or more other agents in an environment based on a nondeterministic behavior of each of the one or more other agents in the environment, the nondeterministic behavior comprising varying any one or more of a position, a velocity, a trajectory, a path of travel, or a shape over time;

select a next node based on the calculated respective associated representative costs for each available next node; and

command a movement of the primary agent based at least in part on the selected next node, wherein to calculate a respective associated representative cost to reach a goal node from the current node via the respective next node, the at least one processor:

for a set of the edges comprising at least the edges between the current node and the goal node along any prospective path,

determines a respective associated representative cost of each of the edges;

assigns the determined respective associated representative cost for each edge to the respective edge in the set of edges;

determines a least cost path for the respective next node from the respective prospective paths between the current node and the goal node via the respective next node based at least on part on the assigned determined respective associated representative costs; and

assigns a value representative of the determined least cost path to the respective next node.

Assignments (1)
CONFIRMATORY LICENSE Recorded May 1, 2025
From: REALTIME ROBOTICS, INC.
To: NATIONAL SCIENCE FOUNDATION
Reel/Frame 071145/0695 →
Continuity (2)
Provisional Application 62775257 · Dec 4, 2018
Related Publication 20220057803A1 · Feb 24, 2022
References Cited (374)
US 4163183A · Engelberger et al. · 1979 [cited by applicant]
US 4300198A · Davini · 1981 [cited by applicant]
US 4862373A · Meng · 1989 [cited by applicant]
US 4949277A · Trovato et al. · 1990 [cited by applicant]
US 5347459A · Greenspan et al. · 1994 [cited by applicant]
US 5544282A · Chen et al. · 1996 [cited by applicant]
US 5795297A · Daigle · 1998 [cited by applicant]
US 6004016A · Spector · 1999 [cited by applicant]
US 6049756A · Libby · 2000 [cited by applicant]
US 6089742A · Warmerdam et al. · 2000 [cited by applicant]
US 6259988B1 · Galkowski et al. · 2001 [cited by applicant]
US 6470301B1 · Barral · 2002 [cited by applicant]
US 6493607B1 · Bourne et al. · 2002 [cited by applicant]
US 6526372B1 · Orschel et al. · 2003 [cited by applicant]
US 6526373B1 · Barral · 2003 [cited by applicant]
US 6529852B2 · Knoll et al. · 2003 [cited by applicant]
US 6539294B1 · Kageyama · 2003 [cited by applicant]
US 6629037B1 · Nyland · 2003 [cited by applicant]
US 6671582B1 · Hanley · 2003 [cited by applicant]
US 7577498B2 · Jennings et al. · 2009 [cited by applicant]
US 7609020B2 · Kniss et al. · 2009 [cited by applicant]
US 7865277B1 · Larson et al. · 2011 [cited by applicant]
US 7940023B2 · Kniss et al. · 2011 [cited by applicant]
US 8082064B2 · Kay · 2011 [cited by applicant]
US 8315738B2 · Chang et al. · 2012 [cited by applicant]
US 8571706B2 · Zhang et al. · 2013 [cited by applicant]
US 8666548B2 · Lim · 2014 [cited by applicant]
US 8825207B2 · Kim et al. · 2014 [cited by applicant]
US 8825208B1 · Benson · 2014 [cited by applicant]
US 8855812B2 · Kapoor · 2014 [cited by applicant]
US 8880216B2 · Izumi et al. · 2014 [cited by applicant]
US 8972057B1 · Freeman et al. · 2015 [cited by applicant]
US 9092698B2 · Buehler et al. · 2015 [cited by applicant]
US 9102055B1 · Konolige et al. · 2015 [cited by applicant]
US 9227322B2 · Graca et al. · 2016 [cited by applicant]
US 9280899B2 · Biess et al. · 2016 [cited by applicant]
US 9327397B1 · Williams et al. · 2016 [cited by applicant]
US 9333044B2 · Olson · 2016 [cited by applicant]
US 9434072B2 · Buehler et al. · 2016 [cited by applicant]
US 9475192B2 · Liang et al. · 2016 [cited by applicant]
US 9539058B2 · Tsekos et al. · 2017 [cited by applicant]
US 9632502B1 · Levinson et al. · 2017 [cited by applicant]
US 9645577B1 · Frazzoli et al. · 2017 [cited by applicant]
US 9687982B1 · Jules et al. · 2017 [cited by applicant]
US 9687983B1 · Prats · 2017 [cited by applicant]
US 9701015B2 · Buehler et al. · 2017 [cited by applicant]
US 9707682B1 · Konolige et al. · 2017 [cited by applicant]
US 9731724B2 · Yoon · 2017 [cited by applicant]
US 9981382B1 · Strauss et al. · 2018 [cited by applicant]
US 9981383B1 · Nagarajan · 2018 [cited by applicant]
US 9993923B2 · Terada · 2018 [cited by applicant]
US 10035266B1 · Kroeger · 2018 [cited by applicant]
US 10099372B2 · Vu et al. · 2018 [cited by applicant]
US 10124488B2 · Lee et al. · 2018 [cited by applicant]
US 10131053B1 · Sampedro et al. · 2018 [cited by applicant]
US 10300605B2 · Sato · 2019 [cited by applicant]
US 10303180B1 · Prats · 2019 [cited by applicant]
US 10430641B2 · Gao · 2019 [cited by applicant]
US 10705528B2 · Wierzynski et al. · 2020 [cited by applicant]
US 10723024B2 · Konidaris et al. · 2020 [cited by applicant]
US 10782694B2 · Zhang et al. · 2020 [cited by applicant]
US 10792114B2 · Hashimoto et al. · 2020 [cited by applicant]
US 10959795B2 · Hashimoto et al. · 2021 [cited by applicant]
US 11213945B2 · Kuwahara et al. · 2022 [cited by applicant]
US 11358337B2 · Czinger et al. · 2022 [cited by applicant]
US 11623494B1 · Amicar et al. · 2023 [cited by applicant]
US 20020013675A1 · Knoll et al. · 2002 [cited by applicant]
US 20020074964A1 · Quaschner et al. · 2002 [cited by applicant]
US 20030155881A1 · Hamann et al. · 2003 [cited by applicant]
US 20040249509A1 · Rogers et al. · 2004 [cited by applicant]
US 20050071048A1 · Watanabe et al. · 2005 [cited by applicant]
US 20050216181A1 · Estkowski et al. · 2005 [cited by applicant]
US 20060235610A1 · Ariyur et al. · 2006 [cited by applicant]
US 20060247852A1 · Kortge et al. · 2006 [cited by applicant]
US 20070106422A1 · Jennings et al. · 2007 [cited by applicant]
US 20070112700A1 · Den Haan et al. · 2007 [cited by applicant]
US 20080012517A1 · Kniss et al. · 2008 [cited by applicant]
US 20080114492A1 · Miegel et al. · 2008 [cited by applicant]
US 20080125893A1 · Tilove et al. · 2008 [cited by applicant]
US 20080186312A1 · Ahn et al. · 2008 [cited by applicant]
US 20080234864A1 · Sugiura et al. · 2008 [cited by applicant]
US 20090055024A1 · Kay · 2009 [cited by applicant]
US 20090192710A1 · Eidehall et al. · 2009 [cited by applicant]
US 20090234499A1 · Nielsen et al. · 2009 [cited by applicant]
US 20090295323A1 · Papiernik et al. · 2009 [cited by applicant]
US 20090326711A1 · Chang et al. · 2009 [cited by applicant]
US 20090326876A1 · Miller · 2009 [cited by applicant]
US 20100145516A1 · Cedoz et al. · 2010 [cited by applicant]
US 20100235033A1 · Yamamoto et al. · 2010 [cited by applicant]
US 20110036188A1 · Fujioka et al. · 2011 [cited by applicant]
US 20110066282A1 · Bosscher et al. · 2011 [cited by applicant]
US 20110153080A1 · Shapiro et al. · 2011 [cited by applicant]
US 20110211938A1 · Eakins et al. · 2011 [cited by applicant]
US 20110264111A1 · Nowlin et al. · 2011 [cited by applicant]
US 20120010772A1 · Pack et al. · 2012 [cited by applicant]
US 20120083964A1 · Montemerlo et al. · 2012 [cited by applicant]
US 20120215351A1 · McGee et al. · 2012 [cited by applicant]
US 20120297733A1 · Pierson et al. · 2012 [cited by applicant]
US 20120323357A1 · Izumi et al. · 2012 [cited by applicant]
US 20130076866A1 · Drinkard et al. · 2013 [cited by applicant]
US 20130346348A1 · Buehler et al. · 2013 [cited by applicant]
US 20140012419A1 · Nakajima · 2014 [cited by applicant]
US 20140025201A1 · Ryu et al. · 2014 [cited by applicant]
US 20140025203A1 · Inazumi · 2014 [cited by applicant]
US 20140058406A1 · Tsekos · 2014 [cited by applicant]
US 20140067121A1 · Brooks et al. · 2014 [cited by applicant]
US 20140079524A1 · Shimono et al. · 2014 [cited by applicant]
US 20140121833A1 · Lee et al. · 2014 [cited by applicant]
US 20140121837A1 · Hashiguchi et al. · 2014 [cited by applicant]
US 20140147240A1 · Noda et al. · 2014 [cited by applicant]
US 20140156068A1 · Graca et al. · 2014 [cited by applicant]
US 20140249741A1 · Levien et al. · 2014 [cited by applicant]
US 20140251702A1 · Berger et al. · 2014 [cited by applicant]
US 20140277718A1 · Izhikevich et al. · 2014 [cited by applicant]
US 20140309916A1 · Bushnell · 2014 [cited by applicant]
US 20150005785A1 · Olson · 2015 [cited by applicant]
US 20150037131A1 · Girtman et al. · 2015 [cited by applicant]
US 20150051783A1 · Tamir et al. · 2015 [cited by applicant]
US 20150134111A1 · Nakajima · 2015 [cited by applicant]
US 20150239127A1 · Barajas et al. · 2015 [cited by applicant]
US 20150261899A1 · Atohira et al. · 2015 [cited by applicant]
US 20150266182A1 · Strandberg · 2015 [cited by applicant]
US 20150273685A1 · Linnell et al. · 2015 [cited by applicant]
US 20160001775A1 · Wilhelm et al. · 2016 [cited by applicant]
US 20160008078A1 · Azizian et al. · 2016 [cited by applicant]
US 20160016315A1 · Kuffner, Jr. et al. · 2016 [cited by applicant]
US 20160107313A1 · Hoffmann et al. · 2016 [cited by applicant]
US 20160112694A1 · Nishi et al. · 2016 [cited by applicant]
US 20160121486A1 · Lipinski et al. · 2016 [cited by applicant]
US 20160121487A1 · Mohan et al. · 2016 [cited by applicant]
US 20160154408A1 · Eade et al. · 2016 [cited by applicant]
US 20160161257A1 · Simpson et al. · 2016 [cited by applicant]
US 20160299507A1 · Shah et al. · 2016 [cited by applicant]
US 20160324587A1 · Olson · 2016 [cited by applicant]
US 20160357187A1 · Ansari · 2016 [cited by applicant]
US 20170004406A1 · Aghamohammadi · 2017 [cited by applicant]
US 20170028559A1 · Davidi et al. · 2017 [cited by applicant]
US 20170057087A1 · Lee · 2017 [cited by applicant]
US 20170120448A1 · Lee et al. · 2017 [cited by applicant]
US 20170123419A1 · Levinson et al. · 2017 [cited by applicant]
US 20170132334A1 · Levinson et al. · 2017 [cited by applicant]
US 20170146999A1 · Cherepinsky et al. · 2017 [cited by applicant]
US 20170157769A1 · Aghamohammadi et al. · 2017 [cited by applicant]
US 20170168485A1 · Berntorp et al. · 2017 [cited by applicant]
US 20170168488A1 · Wierzynski et al. · 2017 [cited by applicant]
US 20170193830A1 · Fragoso et al. · 2017 [cited by applicant]
US 20170210008A1 · Maeda · 2017 [cited by applicant]
US 20170219353A1 · Alesiani · 2017 [cited by applicant]
US 20170252922A1 · Levine et al. · 2017 [cited by applicant]
US 20170252924A1 · Vijayanarasimhan et al. · 2017 [cited by applicant]
US 20170305015A1 · Krasny et al. · 2017 [cited by applicant]
US 20170315530A1 · Godau et al. · 2017 [cited by applicant]
US 20180001472A1 · Konidaris et al. · 2018 [cited by applicant]
US 20180001476A1 · Tan et al. · 2018 [cited by applicant]
US 20180029231A1 · Davis · 2018 [cited by applicant]
US 20180029233A1 · Lager · 2018 [cited by applicant]
US 20180032039A1 · Huynh et al. · 2018 [cited by applicant]
US 20180074505A1 · Lv et al. · 2018 [cited by applicant]
US 20180113468A1 · Russell · 2018 [cited by applicant]
US 20180136662A1 · Kim · 2018 [cited by applicant]
US 20180150077A1 · Danielson et al. · 2018 [cited by applicant]
US 20180172450A1 · Lalonde et al. · 2018 [cited by applicant]
US 20180173242A1 · Lalonde et al. · 2018 [cited by applicant]
US 20180189683A1 · Newman · 2018 [cited by applicant]
US 20180222050A1 · Vu et al. · 2018 [cited by applicant]
US 20180222051A1 · Vu et al. · 2018 [cited by applicant]
US 20180229368A1 · Leitner et al. · 2018 [cited by applicant]
US 20180281786A1 · Oyaizu et al. · 2018 [cited by applicant]
US 20180326582A1 · Yokoyama et al. · 2018 [cited by applicant]
US 20180339456A1 · Czinger et al. · 2018 [cited by applicant]
US 20190015981A1 · Yabushita et al. · 2019 [cited by applicant]
US 20190039242A1 · Fujii et al. · 2019 [cited by applicant]
US 20190086925A1 · Fan et al. · 2019 [cited by applicant]
US 20190143518A1 · Maeda · 2019 [cited by applicant]
US 20190163191A1 · Sorin et al. · 2019 [cited by applicant]
US 20190164430A1 · Nix · 2019 [cited by applicant]
US 20190196480A1 · Taylor · 2019 [cited by applicant]
US 20190216555A1 · DiMaio et al. · 2019 [cited by applicant]
US 20190232496A1 · Graichen et al. · 2019 [cited by applicant]
US 20190234751A1 · Takhirov · 2019 [cited by applicant]
US 20190240835A1 · Sorin et al. · 2019 [cited by applicant]
US 20190262993A1 · Cole et al. · 2019 [cited by applicant]
US 20190293443A1 · Kelly et al. · 2019 [cited by applicant]
US 20190391597A1 · Dupuis · 2019 [cited by applicant]
US 20200069134A1 · Ebrahimi Afrouzi et al. · 2020 [cited by applicant]
US 20200097014A1 · Wang · 2020 [cited by applicant]
US 20200215686A1 · Vijayanarasimhan et al. · 2020 [cited by applicant]
US 20200331146A1 · Vu et al. · 2020 [cited by applicant]
US 20200338730A1 · Yamauchi et al. · 2020 [cited by applicant]
US 20200338733A1 · Dupuis et al. · 2020 [cited by applicant]
US 20200353917A1 · Leitermann et al. · 2020 [cited by applicant]
US 20200368910A1 · Chu et al. · 2020 [cited by applicant]
US 20210009351A1 · Beinhofer et al. · 2021 [cited by applicant]
US 20220339875A1 · Czinger et al. · 2022 [cited by applicant]
US 20230063205A1 · Nerkar et al. · 2023 [cited by applicant]
CN 101837591A · 2010 [cited by applicant]
CN 102186638A · 2011 [cited by applicant]
CN 102814813A · 2012 [cited by applicant]
CN 103722565A · 2014 [cited by applicant]
CN 104407616A · 2015 [cited by applicant]
CN 104858876A · 2015 [cited by applicant]
CN 106660208A · 2017 [cited by applicant]
CN 107073710A · 2017 [cited by applicant]
CN 107486858A · 2017 [cited by applicant]
CN 108297059A · 2018 [cited by applicant]
CN 108789416A · 2018 [cited by applicant]
CN 108858183A · 2018 [cited by applicant]
CN 108942920A · 2018 [cited by applicant]
CN 109521763A · 2019 [cited by applicant]
CN 109782763A · 2019 [cited by applicant]
CN 114073585A · 2022 [cited by applicant]
CN 108453702B · 2022 [cited by applicant]
EP 1901150A1 · 2008 [cited by applicant]
EP 2306153A2 · 2011 [cited by applicant]
EP 3250347A1 · 2017 [cited by applicant]
EP 3486612A1 · 2019 [cited by applicant]
EP 3725472A1 · 2020 [cited by applicant]
JP 11249711A · 1999 [cited by applicant]
JP 11296229A · 1999 [cited by applicant]
JP 2002073130A · 2002 [cited by applicant]
JP 2003127077A · 2003 [cited by applicant]
JP 2005032196A · 2005 [cited by applicant]
JP 2006224740A · 2006 [cited by applicant]
JP 2007257274A · 2007 [cited by applicant]
JP 2008502488A · 2008 [cited by applicant]
JP 200865755A · 2008 [cited by applicant]
JP 2008134165A · 2008 [cited by applicant]
JP 2009116860A · 2009 [cited by applicant]
JP 2010061293A · 2010 [cited by applicant]
JP 2010210592A · 2010 [cited by applicant]
JP 201175382A · 2011 [cited by applicant]
JP 2012056023A · 2012 [cited by applicant]
JP 2012190405A · 2012 [cited by applicant]
JP 2012243029A · 2012 [cited by applicant]
JP 2013193194A · 2013 [cited by applicant]
JP 2014184498A · 2014 [cited by applicant]
JP 2015044274A · 2015 [cited by applicant]
JP 2015517142A · 2015 [cited by applicant]
JP 2015208811A · 2015 [cited by applicant]
JP 2016099257A · 2016 [cited by applicant]
JP 2017136677A · 2017 [cited by applicant]
JP 2018505788A · 2018 [cited by applicant]
JP 2018144158A · 2018 [cited by applicant]
JP 2018144166A · 2018 [cited by applicant]
KR 19980024584A · 1998 [cited by applicant]
KR 1020110026776A · 2011 [cited by applicant]
KR 20130112507A · 2013 [cited by applicant]
KR 20150126482A · 2015 [cited by applicant]
KR 1020170018564A · 2017 [cited by applicant]
KR 1020170044987A · 2017 [cited by applicant]
KR 1020170050166A · 2017 [cited by applicant]
KR 20180125646A · 2018 [cited by applicant]
TW 201318793A · 2013 [cited by applicant]
WO 9924914A1 · 1999 [cited by applicant]
WO 2015113203A1 · 2015 [cited by applicant]
WO 2016122840A1 · 2016 [cited by applicant]
WO 2017168187A1 · 2017 [cited by applicant]
WO 2017214581A1 · 2017 [cited by applicant]
WO 2018043525A1 · 2018 [cited by applicant]
WO 2019183141A1 · 2019 [cited by applicant]
WO 2020040979A1 · 2020 [cited by applicant]
WO 2020117958A1 · 2020 [cited by applicant]
Extended European Search Report issued in European Application No. 19893874.8, mailed Jan. 5, 2022, 13 bages. [cited by applicant]
International Search Report and Written Opinion issued in International Application No. PCT/US2021/061427, mailed Apr. 29, 2022, 14 pages. [cited by applicant]
International Search Report and Written Opinion issued in International Application No. PCT/US2021/013610, mailed Apr. 22, 2021, 9 pages. [cited by applicant]
Non-Final Office Action issued in U.S. Appl. No. 16/909,096, mailed May 6, 2022, 49 pages. [cited by applicant]
International Search Report and Written Opinion issued in International Application No. PCT/US2021/056317, mailed Feb. 11, 2022, 13 pages. [cited by applicant]
Office Action issued in Japanese Application No. 2021-171704, mailed Jan. 28, 2022, 3 pages. [cited by applicant]
Office Action issued in Japanese Application No. 2021-171726, mailed Jan. 26, 2022, 4 pages. [cited by applicant]
Notice of Allowance issued in U.S. Appl. No. 16/308,693, mailed Sep. 23, 2021, 23 pages. [cited by applicant]
Office Action Issued in Japanese Application No. 2018-564836, Mailed Date: May 19, 2020, 3 Pages. [cited by applicant]
International Search Report and Written Opinion issued in International Application No. PCT/US2020/034551, Mailed Date: Aug. 31, 2020, 16 pages. [cited by applicant]
International Search Report issued in PCT/US2019/064511, Mailed Date: Mar. 27, 2020, 12 pages. [cited by applicant]
International Search Report issued in International Application No. PCT/US2020/039193, Mailed Date: Sep. 29, 2020, 7 pages. [cited by applicant]
Non-Final Office Action Issued in U.S. Appl. No. 16/308,693, Mailed Date: Dec. 11, 2020, 23 Pages. [cited by applicant]
Non-Final Office Action Issued in U.S. Appl. No. 16/240,086, Mailed Date: Feb. 11, 2021, 57 Pages. [cited by applicant]
Non-Final Office Action Issued in U.S. Appl. No. 16/268,290, Mailed Date: Jan. 27, 2021, 54 Pages. [cited by applicant]
Non-Final Office Action Issued in U.S. Appl. No. 16/308,693, Mailed Date: May 14, 2021, 26 Pages. [cited by applicant]
Office Action Issued in Taiwanese Application No. 106119452, Mailed Date: Jun. 16, 2021, 19 Pages. [cited by applicant]
Non-Final Office Action Issued in U.S. Appl. No. 16/268,290, Mailed Date: Jun. 17, 2021, 35 Pages. [cited by applicant]
Non-Final Office Action Issued in U.S. Appl. No. 16/308,693, mailed Jun. 1, 2020, 16 pages. [cited by applicant]
Reconsideration Report by Examiner before Appeal issued in Japanese Application No. 2018-564836, mailed Jun. 2, 2021, 2 pages. [cited by applicant]
Final Office Action issued in U.S. Appl. No. 16/240,086, mailed Aug. 2, 2021, 88 pages. [cited by applicant]
Extended European Search Report issued in European Application No. 19851097.6, dated Jul. 23, 2021, 15 pages. [cited by applicant]
J. A. Corrales et al. “Safe human-robot interaction based on dynamic sphere-swept line bounding volumes” Robotic and Computer-Integrated Manufacturing 27, 2011, 9 pages. [cited by applicant]
Angel P. Del Pobil et al. “A New Representation for Collision Avoidance and Detection” Proceedings of the 1992 IEEE International Conference on Robotics and Automation, May 1992, 7 pages. [cited by applicant]
Yuichi Sato et al. “Efficient Collision Detection Using Fast Distance-Calculation Algorithms for Convex and Non-Convex Objects” Proceedings of the 1996 IEEE International Conference on Robotics and Automation, Apr. 1996… [cited by applicant]
Alexander Martín Turrillas, “Improvement of a Multi-Body Collision Computation Framework and its Application to Robot (Self-) Collision Avoidance” German Aerospace Center (DLR) Institute of Robotics and Mechatronics, Ma… [cited by applicant]
Non-Final Office Action issued in U.S. Appl. No. 16/268,290, mailed Jun. 17, 2021, 35 pages. [cited by applicant]
International Search Report and Written Opinion issued in International Application No. PCT/US2020/047429, mailed Nov. 23, 2020, 9 pages. [cited by applicant]
Notice of Allowance issued in U.S. Appl. No. 16/268,290, mailed Sep. 24, 2021, 8 pages. [cited by applicant]
Extended European Search Report issued in European Application No. 20832308.9, mailed Jul. 18, 2022, 10 pages. [cited by applicant]
Extended European Search Report issued in European Application No. 20857383.2, mailed Jul. 25, 2022, 10 pages. [cited by applicant]
Second Office Action issued in U.S. Appl. No. 16/909,096, mailed Sep. 7, 2022, 54 pages. [cited by applicant]
First Office Action issued in U.S. Appl. No. 16/999,339, mailed Sep. 14, 2022, 18 pages. [cited by applicant]
First Office Action issued in U.S. Appl. No. 16/883,376, mailed Sep. 27, 2022, 26 pages. [cited by applicant]
Extended European Search Report issued in European Application No. 21744840.6, mailed Nov. 7, 2022, 14 pages. [cited by applicant]
Notice of Allowance issued in U.S. Appl. No. 17/153,662, mailed Dec. 6, 2022, 15 pages. [cited by applicant]
Search Report issued in Taiwanese Application No. 108104094, completed Feb. 4, 2023, 2 pages. [cited by applicant]
Office Action issued in Japanese Application No. 2021-571340, mailed Feb. 2, 2023, 10 pages. [cited by applicant]
Search Report issued in Chinese Application No. 201980024188.4, completed Feb. 17, 2023, 6 pages. [cited by applicant]
First Office Action issued in U.S. Appl. No. 16/981,467, mailed Mar. 16, 2023, 19 pages. [cited by applicant]
First Office Action issued in U.S. Appl. No. 17/506,364, mailed Apr. 28, 2023, 50 pages. [cited by applicant]
Extended European Search Report issued in European Patent Application No. 20818760.9, mailed May 10, 2023, 9 pages. [cited by applicant]
Search Report issued in Chinese Application No. 202080059714.3, mailed May 23, 2023, 3 pages. [cited by applicant]
Search Report issued in Chinese Application No. 202080040382.4, completed May 24, 2023, 6 pages. [cited by applicant]
Search Report issued in Chinese Application No. 202080055382.1, completed Jun. 26, 2023, 4 pages. [cited by applicant]
Search Report issued in Chinese Application No. 201980055188.0, completed Jun. 30, 2023, 2 pages. [cited by applicant]
International Search Report and Written Opinion issued in International Application No. PCT/US2023/064012, Mailed Jul. 10, 2023, 15 pages. [cited by applicant]
Office Action issued in Japanese Application No. 2021-571340, mailed Aug. 8, 2023, 8 pages. [cited by applicant]
First Office Action issued in U.S. Appl. No. 17/270,597, mailed Aug. 18, 2023, 25 pages. [cited by applicant]
Second Office Action issued in U.S. Appl. No. 17/506,364, mailed Aug. 25, 2023, 55 pages. [cited by applicant]
Extended European Search Report issued in European Application Case No. 21789270.2 mailed Sep. 1, 2023, 23 pages. [cited by applicant]
Search Report issued in Tawanese Application No. 108130161, completed Sep. 2, 2023, 3 pages. [cited by applicant]
Office Action issued in Japanese Application No. 2022-562247, mailed Sep. 25, 2023, 7 pages. [cited by applicant]
Office Action issued in Japanese Application No. 2022-556467, mailed Sep. 28, 2023, 10 pages. [cited by applicant]
MacFarlane, S. et al., “Jerk-bounded manipulator trajectory planning: design for real-time applications,” IEEE Transactions on Robotics and Automation, Feb. 19, 2003, pp. 42-52, vol. 19, issue 1. [cited by applicant]
Dong, Jingyan et al., “Feed-rate optimization with jerk constraints for generating minimum-time trajectories,” International Journal of Machine Tools and Manufacture, Oct. 2007, (Accessible: Mar. 24, 2007), pp. 1941-195… [cited by applicant]
Haschke, R. et al., “On-line planning of time-optimal, jerk-limited trajectories,” 2008 IEEE/RSJ International Conference on Intelligent Robots and Systems, Sep. 2008, pp. 3248-3253, IEEE, Nice, France. [cited by applicant]
Bharathi, Akilan et al., “Feedrate optimization for smooth minimum-time trajectory generation with higher order constraints,” The International Journal of Advanced Manufacturing Technology, Feb. 2016, (Accessible: Jun. … [cited by applicant]
Lin, Jianjie et al., “An Efficient and Time-Optimal Trajectory Generation Approach for Waypoints Under Kinematic Constraints and Error Bounds,” 2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (I… [cited by applicant]
Perumaal, S. Saravana et al., “Automated Trajectory Planner of Industrial Robot for Pick-and-Place Task,” International Journal of Advanced Robotic Systems, Feb. 2013, (Accessible: Jan. 1, 2013), p. 100, vol. 10, issue … [cited by applicant]
Gasparetto, A., and V. Zanotto, “A new method for smooth trajectory planning of robot manipulators,” Mechanism and Machine Theory, Apr. 2007, (Accessible: Jun. 5, 2006), pp. 455-471, vol. 42, issue 4. [cited by applicant]
Gasparetto, A., A. Lanzutti, et al., “Experimental validation and comparative analysis of optimal time-jerk algorithms for trajectory planning,” Robotics and Computer-Integrated Manufacturing, Apr. 2012, (Accessible: Se… [cited by applicant]
Mattmüller, Jan et al., “Calculating a near time-optimal jerk-constrained trajectory along a specified smooth path,” The International Journal of Advanced Manufacturing Technology, Dec. 2009, (Accessible: Apr. 19, 2009)… [cited by applicant]
Kavraki et al, “Probabilistic roadmaps for path planning in high-dimensional spaces”, on Robotics and Automation, vol. 12, No. 4, pp. 566-580, Aug. 1996. [cited by applicant]
Schwesinger, Ulrich, “Motion Planning in Dynamic Environments with Application to Self-Driving Vehicles,” (Doctoral dissertation), ETH, 2017, 65 pages, Zurich. [cited by applicant]
Li, Mingkang et al., “A Novel Cost Function for Decision-Making Strategies in Automotive Collision Avoidance Systems,” 2018 IEEE International Conference on Vehicular Electronics and Safety (ICVES), Sep. 2018, pp. 1-8, … [cited by applicant]
Potthast, Christian et al., “Seeing with your hands: A better way to obtain perception capabilities with a personal robot,” Advanced Robotics and Its Social Impacts, Oct. 2011, pp. 50-53, IEEE, Menlo Park, CA, USA. [cited by applicant]
López-Damian, Efraín et al., “Probabilistic view planner for 3D modelling indoor environments,” 2009 IEEE/RSJ International Conference on Intelligent Robots and Systems, Oct. 2009, pp. 4021-4026, IEEE, St. Louis, MO. [cited by applicant]
Kececi, F. et al., “Improving visually servoed disassembly operations by automatic camera placement,” Proceedings of the 1998 IEEE International Conference on Robotics and Automation, May 1998, pp. 2947-2952, vol. 4, IE… [cited by applicant]
Pires, E. J. Solteiro et al., “Robot Trajectory Planning Using Multi-objective Genetic Algorithm Optimization,” Genetic and Evolutionary Computation—GECCO 2004, Lecture Notes in Computer Science (LNCS), Jun. 2004, pp. 6… [cited by applicant]
Pashkevich, A. P. et al., “Multiobjective optimisation of robot location in a workcell using genetic algorithms,” UKACC International Conference on Control '98, Sep. 1998, pp. 757-762, vol. 1998, publication No. 455, IE… [cited by applicant]
Ratliff, Nathan et al., “CHOMP: Gradient optimization techniques for efficient motion planning,” 2009 IEEE International Conference on Robotics and Automation, May 2009, pp. 489-494, IEEE, Kobe. [cited by applicant]
Lim, Zhen Yang et al., “Multi-objective hybrid algorithms for layout optimization in multi-robot cellular manufacturing systems,” Knowledge-Based Systems, Mar. 2017, (Accessible: Jan. 3, 2017), pp. 87-98, vol. 120. [cited by applicant]
Barral, D. et al., “Simulated Annealing Combined with a Constructive Algorithm for Optimising Assembly Workcell Layout,” The International Journal of Advanced Manufacturing Technology, Apr. 20, 2001, pp. 593-602, vol. 1… [cited by applicant]
Tao, Long et al., “Optimization on multi-robot workcell layout in vertical plane,” 2011 IEEE International Conference on Information and Automation, Jun. 2011, pp. 744-749, IEEE, Shenzhen, China. [cited by applicant]
Klampfl, Erica et al., “Optimization of workcell layouts in a mixed-model assembly line environment,” International Journal of Flexible Manufacturing Systems, Oct. 10, 2006, pp. 277-299, vol. 17, Springer. [cited by applicant]
Kalawoun, Rawan, “Motion planning of multi-robot system for airplane stripping,” (Doctoral dissertation) Universite Clermont Auvergne [2017-2020], Sep. 11, 2019, 167 pages. [cited by applicant]
Kapanoglu, Muzaffer et al., “A pattern-based genetic algorithm for multi-robot coverage path planning minimizing completion time,” Journal of Intelligent Manufacturing, Aug. 2012, (Accessible: May 13, 2010), pp. 1035-10… [cited by applicant]
Hassan, Mahdi, et al. “Modeling and stochastic optimization of complete coverage under uncertainties in multi-robot base placements,” 2016 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Oct.… [cited by applicant]
Hassan, Mahdi et al. “An approach to base placement for effective collaboration of multiple autonomous industrial robots,” 2015 IEEE International Conference on Robotics and Automation (ICRA), May 2015, pp. 3286-3291, I… [cited by applicant]
Hassan, Mahdi et al., “Task oriented area partitioning and allocation for optimal operation of multiple industrial robots in unstructured environments,” 2014 13th International Conference on Control Automation Robotics … [cited by applicant]
Hassan, Mahdi et al. “Simultaneous area partitioning and allocation for complete coverage by multiple autonomous Industrial robots,” Autonomous Robots, Dec. 2017, (Accessible: Apr. 13, 2017), pp. 1609-1628, vol. 41, iss… [cited by applicant]
Notice of Allowance issued in U.S. Appl. No. 16/240,086, mailed Dec. 24, 2021, 28 pages. [cited by applicant]
“Motion Planning” 2009, 37 pages. [cited by applicant]
Jia Pan et al. “Efficient Configuration Space Construction and Optimization for Motion Planning” Engineering, Mar. 2015, vol. 1, Issue 1, 12 pages. [cited by applicant]
Chao Chen “Motion Planning for Nonholonomic Vehicles with Space Exploration Guided Heuristic Search” 2016, 140 pages. [cited by applicant]
Second Office Action issued in Japanese Application No. 2022054900, mailed Jul. 18, 2023, 6 pages. [cited by applicant]
Office Action issued in Japanese Application No. 2022-054900, mailed Feb. 7, 2023, 7 pages. [cited by applicant]
Office Action issued in U.S. Appl. No. 17/682,732, mailed Nov. 2, 2022, 45 pages. [cited by applicant]
Kavraki et al, “Probabilistic roadmaps for path planning in high-dimensional configuration spaces”, IEEE Transactions on Robotics and Automation, vol. 12, No. 4, pp. 566-580, Aug. 1996. [cited by applicant]
International Search Report and Written Opinion Issued in PCT Application No. PCT/US17/36880, Mailed Date: Oct. 10, 2017, 15 Pages. [cited by applicant]
Hauck, Scott et al. “Configuration Compression for the Xilinx XC6200 FPGA,” IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, vol. 18, No. 8, 1998, 9 Pages. [cited by applicant]
Atay et al., “A Motion Planning Processor on Reconfigurable Hardware,” All Computer Science and Engineering Research, Sep. 23, 2005, 13 Pages, Report No. WUCSE-2005-46, Department of Computer Science & Engineering—Washi… [cited by applicant]
Rodriguez, Carlos et al. “Planning manipulation movements of a dual-arm System considering obstacle removing,” Robotics and Autonomous Systems, Elsevier Science Publishers, Amsterdam, NL, vol. 62, No. 12, Aug. 1, 2014, … [cited by applicant]
International Search Report and Written Opinion Issued in PCT Application No. PCT/US2016/012204, Mailed Date: Mar. 21, 2016, 10 Pages. [cited by applicant]
First Office Action Issued in Japanese Patent Application No. 2017-557268, Mailed Date: Aug. 7, 2018, 15 Pages. [cited by applicant]
Extended European Search Report Issued in European Application No. 16743821.7, Mailed Date: Apr. 10, 2018, 9 Pages. [cited by applicant]
Second Office Action Issued in Japanese Patent Application No. 2017-557268, Mailed Date: Feb. 26, 2019, 5 Pages. [cited by applicant]
Invitation to Pay Additional Fees and, Where Applicable, Protest Fee Issued in PCT/US17/36880, Mailed Date: Aug. 14, 2017, 2 pages. [cited by applicant]
Extended European Search Report Issued in European Application No. 17811131.6, Mailed Date: Apr. 24, 2019, 16 Pages. [cited by applicant]
Sean Murray et al., “Robot Motion Planning on a Chip”, Robotics: Science and Systems 2016, Jun. 22, 2016, 9 pages. [cited by applicant]
International Search Report and Written Opinion Issued in PCT/US2019/012209, Mailed Date: Apr. 25, 2019, 26 pages. [cited by applicant]
Sean Murray et al., “The microarchitecture of a real-time robot motion planning accelerator”, 2016 49th Annual IEEE/ACM International Symposium on Microarchitecture (Micro), IEEE, Oct. 15, 2016, 12 pages. [cited by applicant]
Extended European Search Report Issued in European Application No. 18209405.2, Mailed Date: Aug. 2, 2019, 10 Pages. [cited by applicant]
International Search Report and Written Opinion Issued in International Application No. PCT/US2019/023031, Mailed Date: Aug. 14, 2019, 19 pages. [cited by applicant]
International Search Report and Written Opinion Issued in International Application No. PCT/US2019/016700, Mailed Date: May 20, 2019, 14 pages. [cited by applicant]
Merriam-Webster, “Definition of Or”, Retrieved Sep. 9, 2019, 12 pages, https://www.merriam-webster.com/dictionary/or. [cited by applicant]
Non-Final Office Action Issued in U.S. Appl. No. 15/546,441, Mailed Date: Sep. 17, 2019, 52 pages. [cited by applicant]
Office Action Issued in Japanese Application No. 2018-564836, Mailed Date: Dec. 3, 2019, 3 Pages. [cited by applicant]
International Search Report and Written Opinion Issued in International Application No. PCT/US2019/045270, Mailed Date: Nov. 25, 2019, 13 pages. [cited by applicant]
Mike Stilman et al., “Manipulation Planning Among Movable Objects”, Proceedings of the IEEE Int. Conf. on Robotics and Automation (ICRA '07), Apr. 2007, 6 pages. [cited by applicant]
David E. Johnson et al., “Bound Coherence for Minimum Distance Computations”, Proceedings of the 1999 IEEE International Conference on Robotics & Automation, May 1999, 6 pages. [cited by applicant]