From 8911b835dd46e675eb83b630a4072740523ae636 Mon Sep 17 00:00:00 2001 From: gao634 Date: Thu, 18 Jun 2026 16:29:54 -0500 Subject: [PATCH 1/2] init --- papers/pakr/index.html | 731 +++++++++++++++++++++++++++++++++++++++++ 1 file changed, 731 insertions(+) create mode 100644 papers/pakr/index.html diff --git a/papers/pakr/index.html b/papers/pakr/index.html new file mode 100644 index 00000000..2674d32d --- /dev/null +++ b/papers/pakr/index.html @@ -0,0 +1,731 @@ + + + + + + + + + McVAMP: Vectorizing Projection in Manifold-Constrained Motion Planning for Real-Time Whole Body Control + + + + + + + + + + + + + + + + + + + + + + +
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McVAMP: Vectorizing Projection in Manifold-Constrained Motion + Planning for Real-Time Whole Body Control

+
+ + Shrutheesh R. Iyer, + + I-Chia Chang, + + Andrew Z Liu, + + Yan Gu, + and + + Zachary Kingston + +
+ +
+ Purdue University +
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+ + + + + + + Paper + + + + + + + + arXiv + + + + + + + + + Video + + + + + + + + + Code + + +
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+ McVAMP solves manifold-constrained motion planning problems in + milliseconds, providing the ability to generate feasible motions while reacting to dynamic + environments. Here, we show McVAMP solving a plane-constrained planning problem in a dynamic maze + environment, + by globally replanning in response to changes in the environment. +

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+ +
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+ +
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+

Abstract

+
+

+ Many robot planning tasks require satisfaction of one or more constraints throughout the entire + trajectory. + For geometric constraints, manifold-constrained motion planning algorithms are capable of planning + a collision-free path between start and goal configurations on the constraint submanifolds specified by + the task. + Current state-of-the-art methods can take tens of seconds to solve these tasks for complex systems such as + humanoid robots, making real-world use impractical, especially in dynamic settings. +

+

+ Inspired by recent advances in hardware accelerated motion planning, we present a CPU SIMD-accelerated + manifold-constrained motion planner that revisits projection-based constraint satisfaction through the + lens of parallelization. + By transforming relevant components into parallelizable structures, we use SIMD parallelism to plan + constraint-satisfying solutions. +

+

+ Our approach achieves up to 100 to 2000x speed-ups over the state-of-the-art, making real-time + constrained motion planning feasible for the first time. + We demonstrate our planner on a real humanoid robot and show real-time whole-body quasi-static plan + generation. +

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+ + + +
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+

Video

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+ +
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+ +
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+ +
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+

Methodology

+
+

+ We implement a vectorized manifold-projection operator that performs the motion-extension and validation + for a constrained RRT-connect planner. By using SIMD parallelism, we are able to perform the projection + step for multiple samples in parallel along a connection vector, + which significantly speeds up the projection step and helps invalidate infeasible solutions faster, + allowing us to solve complex constrained planning problems in milliseconds. +

+
+ +
+
+ Constrained extend step towards random sampled configuration +
(a) Constrained Extend step towards random sampled config
+
+
+ Multiple candidate projections around sampled point +
(b) Multiple candidate projections around sampled configuration
+
+
+ Recursive interpolation and projection up to desired resolution +
(d) Recursive interpolation and projection up to desired resolution +
+
+
+ Vectorized projection of interpolated configurations +
(c) Vectorized projection of interpolated configurations
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+ + + + +
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+

Results

+

7-DoF Franka Emika Panda Arm End Effector Constraint

+
+

+ A 7-DoF Franka Emika Panda arm with an end effector pose constraint. Here we demonstrate the planner's + ability to conform to position and orientation constraints + while solving complex motion planning problems in the presence of obstacles. +

+
+ + + +
+ 1 / 2 +
+ + + + + + + + + + + + + + +

30-DoF Humanoid Digit Robot Multiple Constraints

+
+

+ A 30-DoF humanoid robot transporting a box with multiple constraints: (i) Feet fixed to the ground, (ii) + Relative pose constraint between the hands, (iii) Closed link constraint at the knees, and (iv) Center + of mass within the support polygon. The robot is able to react to dynamic obstacles in the environment + while maintaining all constraints. +

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+ View 3D viz +
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Performance

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+ Quantitative comparisons across planning tasks are shown below for the 7-DoF Panda arm and a 14-DoF bimanual + IIWA arm. +

+
+ +
+
+ 7-DoF Panda line and plane constraints comparison plot +
+
(i) 7-DoF Panda for line and plane constraints comparison +
+
+ + +
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+ Maze benchmark comparison plot +
(ii) Solving a maze benchmark
+
+
+ Bimanual transport problem comparison plot +
(iii) Bimanual transport problem comparisons
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+ + +
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+

BibTeX (preprint)

+ 
@misc{iyer2026vectorizingprojectionmanifoldconstrainedmotion,
+      title={Vectorizing Projection in Manifold-Constrained Motion Planning for Real-Time Whole-Body Control}, 
+      author={Shrutheesh R Iyer and I-Chia Chang and Andrew Z. Liu and Yan Gu and Zachary Kingston},
+      year={2026},
+      eprint={2604.13323},
+      archivePrefix={arXiv},
+      primaryClass={cs.RO},
+      url={https://arxiv.org/abs/2604.13323}, 
+}
+
+
+
+
+ + + + + + + \ No newline at end of file From f0bdfad9ef694ceef9f918cdec35253ff867c423 Mon Sep 17 00:00:00 2001 From: gao634 Date: Tue, 7 Jul 2026 22:15:57 -0500 Subject: [PATCH 2/2] pakr and fix links of other pages --- papers/mcvamp/index.html | 3 +- papers/pRRTC/index.html | 8 +- papers/pakr/index.html | 855 +++++++----------- papers/pakr/static/css/bulma-carousel.min.css | 1 + papers/pakr/static/css/bulma-slider.min.css | 1 + papers/pakr/static/css/bulma.css.map.txt | 1 + papers/pakr/static/css/bulma.min.css | 1 + .../pakr/static/css/fontawesome.all.min.css | 5 + papers/pakr/static/css/index.css | 427 +++++++++ papers/pakr/static/images/favicon.png | Bin 0 -> 24935 bytes .../static/results/aorrt_iterations_col.png | Bin 0 -> 336822 bytes papers/pakr/static/results/aorrt_time_col.png | Bin 0 -> 317262 bytes papers/pakr/static/results/aosol1.png | Bin 0 -> 623250 bytes papers/pakr/static/results/aosol2.png | Bin 0 -> 343673 bytes papers/pakr/static/results/aosol3.png | Bin 0 -> 452086 bytes papers/pakr/static/results/sol1.png | Bin 0 -> 656095 bytes papers/pakr/static/results/sol2.png | Bin 0 -> 340567 bytes papers/pakr/static/results/sol3.png | Bin 0 -> 472906 bytes papers/pakr/static/results/table1.png | Bin 0 -> 86682 bytes papers/pakr/static/results/table2.png | Bin 0 -> 97051 bytes papers/pakr/static/results/table3.png | Bin 0 -> 45398 bytes papers/pakr/static/results/table4.png | Bin 0 -> 84353 bytes papers/pakr/static/results/uni_solutions.png | Bin 0 -> 273383 bytes papers/pakr/static/videos/pakr_clip.webm | Bin 0 -> 624120 bytes papers/pakr/static/videos/pakr_clip1.7.webm | Bin 0 -> 447126 bytes papers/pakr/static/videos/pakr_clip3.webm | Bin 0 -> 119712 bytes papers/pakr/static/videos/pakr_clip4.webm | Bin 0 -> 47003 bytes papers/pakr/static/videos/pakr_clip5.webm | Bin 0 -> 90923 bytes papers/spasm/index.html | 4 +- 29 files changed, 799 insertions(+), 507 deletions(-) create mode 100644 papers/pakr/static/css/bulma-carousel.min.css create mode 100644 papers/pakr/static/css/bulma-slider.min.css create mode 100644 papers/pakr/static/css/bulma.css.map.txt create mode 100644 papers/pakr/static/css/bulma.min.css create mode 100644 papers/pakr/static/css/fontawesome.all.min.css create mode 100644 papers/pakr/static/css/index.css create mode 100644 papers/pakr/static/images/favicon.png create mode 100644 papers/pakr/static/results/aorrt_iterations_col.png create mode 100644 papers/pakr/static/results/aorrt_time_col.png create mode 100644 papers/pakr/static/results/aosol1.png create mode 100644 papers/pakr/static/results/aosol2.png create mode 100644 papers/pakr/static/results/aosol3.png create mode 100644 papers/pakr/static/results/sol1.png create mode 100644 papers/pakr/static/results/sol2.png create mode 100644 papers/pakr/static/results/sol3.png create mode 100644 papers/pakr/static/results/table1.png create mode 100644 papers/pakr/static/results/table2.png create mode 100644 papers/pakr/static/results/table3.png create mode 100644 papers/pakr/static/results/table4.png create mode 100644 papers/pakr/static/results/uni_solutions.png create mode 100644 papers/pakr/static/videos/pakr_clip.webm create mode 100644 papers/pakr/static/videos/pakr_clip1.7.webm create mode 100644 papers/pakr/static/videos/pakr_clip3.webm create mode 100644 papers/pakr/static/videos/pakr_clip4.webm create mode 100644 papers/pakr/static/videos/pakr_clip5.webm diff --git a/papers/mcvamp/index.html b/papers/mcvamp/index.html index 542b99b7..f1151a68 100644 --- a/papers/mcvamp/index.html +++ b/papers/mcvamp/index.html @@ -58,9 +58,10 @@ Grasp Diffusion - + GPU RRT-Connect + GPU-Accelerated Kinodynamic Planning diff --git a/papers/pRRTC/index.html b/papers/pRRTC/index.html index e06923b2..f6c7403f 100644 --- a/papers/pRRTC/index.html +++ b/papers/pRRTC/index.html @@ -464,14 +464,18 @@
Grasp Diffusion
arXiv 2508.17482
- +
Manifold-Constrained Motion Planning
arXiv 2604.13323
 - +
Fast Sequential Manipulation
arXiv 2510.07674
 + +
GPU-Accelerated Kinodynamic Planning
+
arXiv 2607.03987
+ diff --git a/papers/pakr/index.html b/papers/pakr/index.html index 2674d32d..0c3c4555 100644 --- a/papers/pakr/index.html +++ b/papers/pakr/index.html @@ -3,27 +3,18 @@ - - + + - McVAMP: Vectorizing Projection in Manifold-Constrained Motion Planning for Real-Time Whole Body Control + PAKR: Fast Asymptotically Optimal Kinodynamic Planning via Vectorization - - - - - - - - @@ -43,24 +34,14 @@ -
- - More Research - + More Research
- - Particle Optimization for Sequential Manipulation - - - Search as Inference - - - Grasp Diffusion - - - GPU RRT-Connect - + Particle Optimization for Sequential Manipulation + Search as Inference + Grasp Diffusion + GPU RRT-Connect + Constrained Vectorized Motion Planning
@@ -74,68 +55,43 @@
-

McVAMP: Vectorizing Projection in Manifold-Constrained Motion - Planning for Real-Time Whole Body Control

+

PAKR: Fast Asymptotically Optimal Kinodynamic Planning via Vectorization

- - Shrutheesh R. Iyer, - - I-Chia Chang, - - Andrew Z Liu, - - Yan Gu, + Yitian Gao, + Andrew Lu, and - - Zachary Kingston - + Zachary Kingston
-
Purdue University
-
- - - - - + + Paper - - - - + + arXiv - - - - - + + Video - - - - - + + Code
-
@@ -147,14 +103,11 @@

McVAMP: Vectorizing Projection in Manif

- McVAMP solves manifold-constrained motion planning problems in - milliseconds, providing the ability to generate feasible motions while reacting to dynamic - environments. Here, we show McVAMP solving a plane-constrained planning problem in a dynamic maze - environment, - by globally replanning in response to changes in the environment. + Here we show 6d double integrator trajectories on a tree environment. As the cost threshold decreases, + the planner finds more optimal solutions, narrowing the spread of the trajectories.

@@ -164,51 +117,47 @@

-

Abstract

- Many robot planning tasks require satisfaction of one or more constraints throughout the entire - trajectory. - For geometric constraints, manifold-constrained motion planning algorithms are capable of planning - a collision-free path between start and goal configurations on the constraint submanifolds specified by - the task. - Current state-of-the-art methods can take tens of seconds to solve these tasks for complex systems such as - humanoid robots, making real-world use impractical, especially in dynamic settings. + Sampling-based motion planners have been shown to be effective for systems with complex + kinodynamic constraints and high dimensionality. + However, these algorithms struggle to achieve real-time performance, leading to recent + efforts to parallelize planning. + While GPU-accelerated planners have achieved significant speedups, existing approaches + require specialized CUDA programming that limits accessibility and portability.

- Inspired by recent advances in hardware accelerated motion planning, we present a CPU SIMD-accelerated - manifold-constrained motion planner that revisits projection-based constraint satisfaction through the - lens of parallelization. - By transforming relevant components into parallelizable structures, we use SIMD parallelism to plan - constraint-satisfying solutions. + We present Parallel Asymptotically Optimal Kinodynamic RRT (PAKR), a massively parallel + kinodynamic planner leveraging JAX and the XLA compiler to achieve GPU acceleration + through standard Python tooling. + By combining our parallel planner with the AO-x meta-algorithm, we achieve asymptotic + optimality through fast iterative replanning.

- Our approach achieves up to 100 to 2000x speed-ups over the state-of-the-art, making real-time - constrained motion planning feasible for the first time. - We demonstrate our planner on a real humanoid robot and show real-time whole-body quasi-static plan - generation. + We provide a theoretical analysis of probabilistic completeness, analyze the effects of + batch size and branching factor on convergence, and demonstrate scalability to complex + dynamics using the MuJoCo-XLA simulator. + Experiments show competitive runtimes with state-of-the-art GPU planners and superior solution quality.

- -

Video

-
-
@@ -219,353 +168,120 @@

Video

Methodology

- We implement a vectorized manifold-projection operator that performs the motion-extension and validation - for a constrained RRT-connect planner. By using SIMD parallelism, we are able to perform the projection - step for multiple samples in parallel along a connection vector, - which significantly speeds up the projection step and helps invalidate infeasible solutions faster, - allowing us to solve complex constrained planning problems in milliseconds. + Utilizing the Python-JAX jit compiler, we compile the RRT planner into a single GPU kernel, minimizing device transfer overhead. + The planner performs node selection, action sampling, forward simulation, and tree building in large batches, enabling efficient parallelism. + With a fast single-solve time, we can iteratively replan with decreasing cost thresholds to achieve asymptotic optimality at high frequencies.

- -
-
- Constrained extend step towards random sampled configuration -
(a) Constrained Extend step towards random sampled config
-
-
- Multiple candidate projections around sampled point -
(b) Multiple candidate projections around sampled configuration
-
-
- Recursive interpolation and projection up to desired resolution -
(d) Recursive interpolation and projection up to desired resolution -
-
-
- Vectorized projection of interpolated configurations -
(c) Vectorized projection of interpolated configurations
-
-
- -
- - -

Results

-

7-DoF Franka Emika Panda Arm End Effector Constraint

+ +

KinoPAX Experiments

- A 7-DoF Franka Emika Panda arm with an end effector pose constraint. Here we demonstrate the planner's - ability to conform to position and orientation constraints - while solving complex motion planning problems in the presence of obstacles. + These environments were taking from KinoPAX, a CUDA implementation of accelerated kinodynamic planning. + Three dynamics models are used: 6d double integrator, 6d dubins airplane, and 12d quadrotor.

- -
-
@@ -573,135 +289,270 @@

30-DoF Humanoid Digit Robot Multiple Co

Performance

- Quantitative comparisons across planning tasks are shown below for the 7-DoF Panda arm and a 14-DoF bimanual - IIWA arm. + We evaluate the performance of PAKR against KinoPAX, a gpu-accelerated planner, and two optimal planners: iDb-A* and SST*. + We also analyze the convergence behavior of PAKR with respect to iterations and time, demonstrating its + ability to find high-quality solutions efficiently.

-
-
- 7-DoF Panda line and plane constraints comparison plot + +
+
+ PAKR convergence analysis — iterations +
+
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+ PAKR convergence analysis — time
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(i) 7-DoF Panda for line and plane constraints comparison +
+ PAKR convergence analysis showing median cost and interquartile range (IQR) across 100 runs + for the double integrator in environment A with a cost threshold of 1.49.
- -
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- Maze benchmark comparison plot -
(ii) Solving a maze benchmark
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- Bimanual transport problem comparison plot -
(iii) Bimanual transport problem comparisons
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Env AEnv BEnv C
DynamicsPlannerTimeNodesTimeNodesTimeNodes
6D DIKinoPAX5.0ms164k3.5ms144k6.3ms193k
PAKR2.5ms9k1.8ms21k5.5ms19k
6D DAKinoPAX4.4ms63k3.7ms72k7.6ms107k
PAKR5.4ms19k5.9ms32k14.9ms57k
12D QCKinoPAX17.8ms285k17.8ms285k24.6ms333k
PAKR14.9ms71k17.1ms147k51.4ms173k
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Comparison of PAKR vs. KinoPAX across dynamics models and environments. Bold denotes best per cell.
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Environment AEnvironment BEnvironment C
DynamicsTime1Cost1TimefCostfTime1Cost1TimefCostfTime1Cost1TimefCostf
6D DI2.3ms1.7628.0ms1.511.8ms2.0320.0ms1.544.9ms3.1145.0ms2.33
6D DA4.8ms1.7122.0ms1.565.9ms1.696.0ms1.6614.8ms3.4232.0ms2.98
12D QC13.1ms2.1620.1ms1.9817.1ms2.4231.0ms2.1155.6ms3.98165.4ms3.62
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Convergence results for PAKR on KinoPAX environments and models. Median times and costs of the initial and final solutions.
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ProblemAlg.SR%Time1Cost1Costf
Unicycle 1iDb-A*100254ms5.80s5.10s
SST*100600ms8.34s4.41s
PAKR1001.3ms4.62s4.46s
Unicycle 2iDb-A*124637ms8.70s8.70s
SST*100398ms14.15s6.95s
PAKR1001.4ms5.40s4.75s
AcrobotiDb-A*1001450ms5.24s4.96s
SST*743298ms4.36s3.39s
PAKR10013ms3.87s3.22s
QuadcopteriDb-A*1001387ms2.56s2.21s
SST*4185457ms9.64s9.42s
PAKR100175ms7.54s6.23s
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DynoBench comparison against iDb-A* and SST*. Unicycle 1 uses velocity control; Unicycle 2 uses force control.
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Branching Factor (A)
BatchMetric21664128
4kSuccess (%)100.0100.099.094.0
Time (ms)19.516.126.741.9
Iters22.036.069.0104.0
Nodes37.6k57.7k107.5k168.1k
8kSuccess (%)100.0100.097.093.0
Time (ms)24.513.119.026.7
Iters15.021.039.057.0
Nodes54.3k70.9k124.9k181.9k
16kSuccess (%)100.0100.097.087.0
Time (ms)47.214.317.114.3
Iters12.014.025.025.0
Nodes89.9k103.8k162.7k163.3k
32kSuccess (%)100.0100.099.086.0
Time (ms)115.326.920.119.9
Iters10.012.017.020.0
Nodes154.6k175.5k232.3k277.0k
+
Batch size and branching factor sensitivity on 12D Quadcopter (Env A). Bold values are global minimums for time, iteration count, and tree size.
+
- - +

BibTeX (preprint)

- 
@misc{iyer2026vectorizingprojectionmanifoldconstrainedmotion,
-      title={Vectorizing Projection in Manifold-Constrained Motion Planning for Real-Time Whole-Body Control}, 
-      author={Shrutheesh R Iyer and I-Chia Chang and Andrew Z. Liu and Yan Gu and Zachary Kingston},
+      
@misc{gao2026fastasymptoticallyoptimalkinodynamic,
+      title={Fast Asymptotically Optimal Kinodynamic Planning via Vectorization}, 
+      author={Yitian Gao and Andrew Lu and Zachary Kingston},
       year={2026},
-      eprint={2604.13323},
+      eprint={2607.03987},
       archivePrefix={arXiv},
       primaryClass={cs.RO},
-      url={https://arxiv.org/abs/2604.13323}, 
-}
-
-

+      url={https://arxiv.org/abs/2607.03987}, 
+    }
-