Motion Planning with Dynamics, Physics-based Simulations, and Linear Temporal Objectives Erion Plaku Laboratory for Computational Sensing and Robotics Johns Hopkins University
Frontiers of Planning The goal is to be able to specify a task and have the planning system compute a sequence of actions to accomplish the task Surgery Exploration Videogames & Training Simulations Navigation Service Reconfigurable Robots Search & Rescue Entertainment Air-Traffic Control
(Simplified) Planning Schema The goal is to be able to specify a task and have the planning system compute a sequence of actions to accomplish the task physical physical world task system system model world model task model Planning solution system Controller commands
Classic AI Planning physical Applications physical world task system Robotics Decision making set of actions discrete world task model Resource handling Game playing AI Planning Model checking … sequence of actions Planners STRIPS [Stanford] hardware Graphplan [CMU] Controller commands Blackbox [AT&T Labs] … Advantages BLOCK WORLD A Effectively handles sequence of C B Large number of states and actions move actions B A C Rich task models, e.g., reachability initial goal and temporal objectives Limitations Planning in a Discrete world continuous setting? Finite set of discrete actions Difficult to design general controllers that can follow sequence of actions
Geometric Path Planning Applications physical robot physical world task Robotics Assembly robot geometry world geometry goal placement Manipulation Character animation Geometric Path Planning Computational biology … collision-free path hardware Controller commands Advantages Effectively handles Collision avoidances High-dimensional continuous spaces
Limitations of Geometric Path Planning 1. Geometric path planning ignores robot dynamics Geometric paths are robot interactions with the environment difficult to follow external forces, e.g., friction, gravity 2. Current methods in geometric path planning cannot handle Temporal objectives : reach desired states w.r.t. a linear ordering of time, i.e., “A or B” “A and B” “B after A” “B next to A” Example: “inspect all the contaminated areas, then visit one of the decontamination stations, and then return to the base” Planning with rich models of the robot and physical world? Significantly increases problem complexity Renders current planners computationally impractical Planning with temporal objectives? Significantly increases problem complexity Currently possible only in a discrete setting
Approach Motion Planning Discrete Planning Probabilistic Sampling Artificial Intelligence Computer Logic Control Theory planning problem: physical system, physical world, task discrete model Discrete Planning discrete plan Feasibility & progress estimation rich model Motion Planning
SyCLoP: Synergic Combination of Layers of Planning Motion Planning Discrete Planning synergic Probabilistic Sampling Artificial Intelligence combination Computer Logic Control Theory planning problem: physical system, physical world, task discrete model Discrete Planning discrete plan Feasibility & progress estimation Feasibility & progress estimation rich model Motion Planning rich-model solution Tasks Rich Models Plaku, Kavraki, Vardi: Reachability Nonlinear Dynamics TRO05, ICRA07, RSS07 Temporal objectives CAV07, ICRA08, Physical Realism FMSD08 , TACAS08 Hybrid Systems
Overview Motion Planning: Background & Related Work SyCLoP: Synergic Combination of Layers of Planning Applications of SyCLoP to Motion Planning with Dynamics Physics-based Simulations T emporal Objectives Discussion
Motion-Planning Problem MPP = ( S, INVALID, s 0 , GOAL, U, f ) S GOAL collection of variables State that describe the system S Space and world state s ∈ S {true,false INVALID s 0 } s ∈ S {true, GOAL false} Control U controls/actions Space Compute a trajectory ζ : [0, T] → S Control Simulation such that s 1. ζ (0) = s 0 u f s new 2. INVALID( ζ (t)) = false, ∀ t ∈ [0, T] t 3. GOAL( ζ (T)) = true Motion obeys physical constraints Accounts for system dynamics Accounts for interactions of the system with the world
Tree-Search Framework in Motion Planning Search the state space S by growing a tree T rooted at the initial state s 0 REPEAT UNTIL GOAL IS REACHED s 0 S 1. Select a state s from T 2. Select a control u s 3. Select a time duration t 4. Extend tree from s by applying the control u for t time units Control Simulation GOAL s u f s new t
Related Work Probabilistic Roadmap Method PRM [Kavraki, Svestka, Latombe, Overmars ‘96] Obstacle based PRM [Amato, Bayazit, Dale ’98] Expansive Space Tree (EST) [Hsu et al., ‘97, ’00] Rapidly-exploring Random T ree (RRT) [Kuffner, LaValle ‘99, ‘01] Gaussian PRM [Boor, Overmars, van der Stappen ‘01] Single Query Bidirectional Lazy T ree (SBL) [Sanchez, Latombe ’01] Extended Execution RRT (ERRT) [Bruce, Veloso ’02] Guided Expansive Space T ree [Phillips et al. ’03] Random Bridge Building Planner [Hsu, Jiang, Reif, Sun ’03] Adaptive Dynamic Domain RRT (ADRRT) [Yershova et al., ‘04, ‘05] PDST [Ladd, Kavraki ‘04, ’05] Utility-guided RRT [Burns, Brock ’07] Particle RRT [Nik, Reid ’07] GRIP [Bekris, Kavraki ’07] Multipartite RRT [Zucker et al., ‘07] …
Issues in Current Motion-Planning Approaches On challenging motion-planning problems Exploration frequently gets stuck Progress slows down Possible causes (i) Exploration guided by limited information, such as distance metrics and nearest neighbors (ii) Lack of global sense of direction toward goal (iii) Difficult to discover new promising directions toward goal
Overview Motion Planning: Background & Related Work SyCLoP: Synergic Combination of Layers of Planning Applications of SyCLoP to Motion Planning with Dynamics Physics-based Simulations T emporal Objectives Discussion
SyCLoP: Synergic Combination of Layers of Planning planning problem: physical system, physical world, task discrete model Discrete Planning discrete plan Feasibility & progress estimation rich model Motion Planning rich-model solution
SyCLoP: Synergic Combination of Layers of Planning Discrete Model provides simplified high-level planning layer Decomposition of state initial space into regions R 3 R 4 R 2 R 1 Graph encodes adjacency of regions R 6 R 8 R 1 R 2 R 3 R 4 R 5 initial R 7 R 5 R 6 R 7 R 8 R 12 R 9 R 10 R 11 R 12 R 11 goal goal R 9 R 10 discrete plans : sequences of regions connecting initial to goal
SyCLoP: Synergic Combination of Layers of Planning Discrete Plan sequence of regions connecting initial to goal initial R 3 R 4 R 2 R 1 R 6 R 8 R 1 R 2 R 3 R 4 R 5 initial R 7 R 5 R 6 R 7 R 8 R 12 R 9 R 10 R 11 R 12 R 9 R 11 goal goal R 10
SyCLoP: Synergic Combination of Layers of Planning Core Loop Discrete discrete Planning plan initial Motion Planning goal Extend tree branches along regions specified by current discrete plan
SyCLoP: Synergic Combination of Layers of Planning Core Loop Discrete discrete Planning plan Feasibility & progress estimation initial Motion Planning goal Update feasibility & progress estimation based on information gathered by motion planning
SyCLoP: Synergic Combination of Layers of Planning Core Loop Discrete discrete Planning plan Feasibility & progress estimation initial Motion Planning goal Compute new discrete plan based on updated feasibility/progress estimation
SyCLoP: Synergic Combination of Layers of Planning Core Loop Discrete discrete Planning plan Feasibility & progress estimation initial Motion Planning goal Extend branches along discrete plan & updated feasibility/progress estimation
SyCLoP: Synergic Combination of Layers of Planning Core Loop Discrete discrete Planning plan Feasibility & progress estimation initial Motion Planning rich-model solution goal Repeat core loop until the search tree reaches a goal state
SyCLoP: Synergic Combination of Layers of Planning Discrete Planning Which discrete plan to select at each iteration? Combinatorially many possibilities R 1 R 2 R 3 R 4 initial Estimate feasibility of including R 5 R 6 R 7 R 8 region R in plan R 9 R 10 R 11 R 12 goal Search problem on the weighted discrete-model graph Methodical Search Compute discrete plan Greedy as shortest path with Search high probability p Compute plan as random path with probability (1 – p)
SyCLoP: Synergic Combination of Layers of Planning Motion Planning Discrete plan: σ = R 1 , R 2 , …, R n Extend tree along discrete plan REPEAT FOR A SHORT TIME Select region R i from σ initial Select state s from R i Extend branch from s goal
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