MIN Faculty Department of Informatics Challenges of Humanoid Motion Planning for Navigation Jasper Güldenstein University of Hamburg Faculty of Mathematics, Informatics and Natural Sciences Department of Informatics Technical Aspects of Multimodal Systems 05. November 2018 J. Güldenstein – Challenges of Humanoid Motion Planning for Navigation 1 / 32
Outline Introduction and Motivation Dynamic Window Approach Dynamic Footstep Planning Footstep Planning for 3D Environments Conclusion 1. Introduction and Motivation 2. Dynamic Window Approach 3. Dynamic Footstep Planning 4. Footstep Planning for 3D Environments 5. Conclusion J. Güldenstein – Challenges of Humanoid Motion Planning for Navigation 2 / 32
Introduction and Motivation Introduction and Motivation Dynamic Window Approach Dynamic Footstep Planning Footstep Planning for 3D Environments Conclusion ◮ humanoid robots are mobile robots ◮ approaches for traditional mobile robots (with wheels) only work for flat terrain ◮ humanoid robots can step on or over obstacles ◮ navigation space is limited by balancing criteria ◮ environment is dynamic → dynamic replanning is required J. Güldenstein – Challenges of Humanoid Motion Planning for Navigation 3 / 32
Dynamic Window Approach [FBT] Introduction and Motivation Dynamic Window Approach Dynamic Footstep Planning Footstep Planning for 3D Environments Conclusion ◮ global path has been computed by a standard pathfinding algorithm (A* etc.) ◮ motion capabilities of the robot are known ◮ velocity limits ( v , ω ) ◮ acceleration limits ( ˙ v , ˙ ω ) ◮ current position x ( t ) , y ( t ) , θ ( t ) and velocity v ( t ) , ω ( t ) is known J. Güldenstein – Challenges of Humanoid Motion Planning for Navigation 4 / 32
Dynamic Window Approach [FBT] Introduction and Motivation Dynamic Window Approach Dynamic Footstep Planning Footstep Planning for 3D Environments Conclusion future position can be calculated � t n x ( t n ) = x ( t 0 ) + v ( t ) · cos ( θ ( t )) dt (1) t 0 � t n y ( t n ) = y ( t 0 ) + v ( t ) · sin ( θ ( t )) dt (2) t 0 J. Güldenstein – Challenges of Humanoid Motion Planning for Navigation 5 / 32
Dynamic Window Approach [FBT] Introduction and Motivation Dynamic Window Approach Dynamic Footstep Planning Footstep Planning for 3D Environments Conclusion velocities depend on current velocities v ( t ) , ω ( t ) and accelerations v (ˆ ω (ˆ ˙ t ) , ˙ t ) � t n � t � � v (ˆ t ) d ˆ x ( t n ) = y ( t 0 ) + v ( t 0 ) + ˙ t t 0 t 0 (3) � ˆ � � t � � � t ω (˜ t ) d ˜ d ˆ · cos θ ( t ) + ω ( t 0 ) + ˙ t t dt t 0 t 0 J. Güldenstein – Challenges of Humanoid Motion Planning for Navigation 6 / 32
Dynamic Window Approach [FBT] Introduction and Motivation Dynamic Window Approach Dynamic Footstep Planning Footstep Planning for 3D Environments Conclusion velocities depend on current velocities v ( t ) , ω ( t ) and accelerations v (ˆ ω (ˆ ˙ t ) , ˙ t ) � t n � t � � v (ˆ t ) d ˆ x ( t n ) = y ( t 0 ) + v ( t 0 ) + ˙ t t 0 t 0 (3) � ˆ � � t � � � t ω (˜ t ) d ˜ d ˆ · cos θ ( t ) + ω ( t 0 ) + ˙ t t dt t 0 t 0 � t n � t � � v (ˆ t ) d ˆ y ( t n ) = y ( t 0 ) + v ( t 0 ) + ˙ t t 0 t 0 (4) � ˆ � � t � � � t ω (˜ t ) d ˜ d ˆ · sin θ ( t ) + ω ( t 0 ) + ˙ t t dt t 0 t 0 J. Güldenstein – Challenges of Humanoid Motion Planning for Navigation 6 / 32
Dynamic Window Approach [FBT] Introduction and Motivation Dynamic Window Approach Dynamic Footstep Planning Footstep Planning for 3D Environments Conclusion ◮ discrete simulation of possible trajectories ◮ evaluation of trajectories based on ◮ target heading ◮ clearance ◮ velocity ◮ distance to path ◮ finer granularity leads to ◮ closer to optimal solution ◮ computationally more expensive ◮ longer simulation time leads to ◮ minimum should be the (maximum) deceleration time ◮ computationally more expensive ◮ longer reaction time to changes in the environment J. Güldenstein – Challenges of Humanoid Motion Planning for Navigation 7 / 32
Dynamic Window Approach [FBT] Introduction and Motivation Dynamic Window Approach Dynamic Footstep Planning Footstep Planning for 3D Environments Conclusion Video Break [Tar] J. Güldenstein – Challenges of Humanoid Motion Planning for Navigation 8 / 32
Figure 1: Visualization of local and global plan for a humanoid robot J. Güldenstein – Challenges of Humanoid Motion Planning for Navigation 9 / 32
Dynamic Window Approach [FBT] Introduction and Motivation Dynamic Window Approach Dynamic Footstep Planning Footstep Planning for 3D Environments Conclusion Video Break 2 J. Güldenstein – Challenges of Humanoid Motion Planning for Navigation 10 / 32
Dynamic Window Approach [FBT] Introduction and Motivation Dynamic Window Approach Dynamic Footstep Planning Footstep Planning for 3D Environments Conclusion Conclusion ◮ quick reactions to changes in the environment (faster than global replanning) ◮ computationally inexpensive ◮ collision free trajectory ◮ used in many real world robots ◮ planning restricted to x , y , θ J. Güldenstein – Challenges of Humanoid Motion Planning for Navigation 11 / 32
Dynamic Footstep Planner [GHB] Introduction and Motivation Dynamic Window Approach Dynamic Footstep Planning Footstep Planning for 3D Environments Conclusion Figure 2: Visualization of planned footsteps between and above obstacles [GH] J. Güldenstein – Challenges of Humanoid Motion Planning for Navigation 12 / 32
Dynamic Footstep Planner [GHB] Introduction and Motivation Dynamic Window Approach Dynamic Footstep Planning Footstep Planning for 3D Environments Conclusion ◮ control feet position instead of velocities and accelerations ◮ walking engine needs to support this J. Güldenstein – Challenges of Humanoid Motion Planning for Navigation 13 / 32
Dynamic Footstep Planner [GHB] Introduction and Motivation Dynamic Window Approach Dynamic Footstep Planning Footstep Planning for 3D Environments Conclusion Figure 3: possible parameters of the foot placement vector [GHB] J. Güldenstein – Challenges of Humanoid Motion Planning for Navigation 14 / 32
Dynamic Footstep Planner [GHB] Introduction and Motivation Dynamic Window Approach Dynamic Footstep Planning Footstep Planning for 3D Environments Conclusion State is modeled as position of supporting foot: s = ( x , y , θ ) (5) State transition is modeled as taking one step: a = (∆ x , ∆ y , ∆ θ ) (6) Cost of state transition is modeled as: c ( s , s ′ ) = � ( x , y ) , ( x ′ , y ′ ) � + k + d ( s ′ ) (7) Where � ( x , y ) , ( x ′ , y ′ ) � is the distance travelled, k is a constant cost to minimize steps taken and d ( s ′ ) is distance to closest obstacle J. Güldenstein – Challenges of Humanoid Motion Planning for Navigation 15 / 32
Dynamic Footstep Planner [GHB] Introduction and Motivation Dynamic Window Approach Dynamic Footstep Planning Footstep Planning for 3D Environments Conclusion Efficient collision checking between foot and environment is necessary J. Güldenstein – Challenges of Humanoid Motion Planning for Navigation 16 / 32
Dynamic Footstep Planner [GHB] Introduction and Motivation Dynamic Window Approach Dynamic Footstep Planning Footstep Planning for 3D Environments Conclusion Heuristic for path evaluation was chosen statistically h 1 = ω 1 � ( x , y ) , ( x start , y start ) � + kS 1 ( s , s start ) (8) h 2 = ω 1 � ( x , y ) , ( x start , y start ) � + kS 1 ( s , s start ) + ω 2 | θ − θ start | (9) h 3 = ω 1 D ( s , s start ) + kS 2 ( s , s start ) (10) With ω 1 , ω 2 as scaling factors, S 1 as expected number of footsteps based on distance, k as constant cost per step, D as length of 2D Path and S 2 as expected number of footsteps along D J. Güldenstein – Challenges of Humanoid Motion Planning for Navigation 17 / 32
Dynamic Footstep Planner [GHB] Introduction and Motivation Dynamic Window Approach Dynamic Footstep Planning Footstep Planning for 3D Environments Conclusion Heuristic for path evaluation was chosen statistically h 1 = ω 1 � ( x , y ) , ( x start , y start ) � + kS 1 ( s , s start ) (8) h 2 = ω 1 � ( x , y ) , ( x start , y start ) � + kS 1 ( s , s start ) + ω 2 | θ − θ start | (9) h 3 = ω 1 D ( s , s start ) + kS 2 ( s , s start ) (10) With ω 1 , ω 2 as scaling factors, S 1 as expected number of footsteps based on distance, k as constant cost per step, D as length of 2D Path and S 2 as expected number of footsteps along D h 3 was chosen through statistical evaluation J. Güldenstein – Challenges of Humanoid Motion Planning for Navigation 17 / 32
Dynamic Footstep Planner [GHB] Introduction and Motivation Dynamic Window Approach Dynamic Footstep Planning Footstep Planning for 3D Environments Conclusion Figure 4: sets of possible foot placements [GHB] J. Güldenstein – Challenges of Humanoid Motion Planning for Navigation 18 / 32
Dynamic Footstep Planner [GHB] Introduction and Motivation Dynamic Window Approach Dynamic Footstep Planning Footstep Planning for 3D Environments Conclusion Figure 4: sets of possible foot placements [GHB] F 12 was chosen through statistical analysis J. Güldenstein – Challenges of Humanoid Motion Planning for Navigation 18 / 32
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