- The paper presents a continuous B-spline action representation that replaces discrete action chunking with smooth and flexible trajectories.
- It details an adaptive fitting method and segment alignment mechanism that accelerate task execution and maintain precision.
- Empirical results demonstrate up to 4x speedups in manipulation tasks while retaining robustness, highlighting practical deployment potential.
B-spline Policy: Continuous Action Representations for Accelerated Robotic Manipulation
Motivation and Paradigm Shift
The imperative to accelerate robotic task execution has motivated the adoption of B-spline action representations as an alternative to discrete-time action chunking in visuomotor policy learning. While action chunking stabilizes long-horizon policy training, it enforces a uniform temporal resolution and introduces discontinuities at chunk boundaries—both limiting the feasibility of high-speed, precise manipulation. Classical motion planning and computer graphics have leveraged spline-based representations to circumvent similar issues, with B-splines noted for smoothness, compact parameterizations, and locality.
This paper proposes a continuous B-spline action representation that replaces the standard chunk-based scheme, thereby facilitating temporal flexibility, intrinsic smoothness, temporal rescaling, and local error isolation. The B-spline policy directly predicts curve parameters (knots, control points) from high-dimensional sensory observations and can be integrated as a drop-in replacement into standard imitation-learning pipelines.
Methodology
Action Representation and Fitting
B-spline actions are parameterized by knot vectors and control points, defining smooth curves in continuous time. Trajectories are fitted adaptively to demonstration data—densely allocating knots in high-curvature regions and sparsely in smooth segments—using an iterative FITPACK-inspired algorithm for error-bounded approximation. This conversion yields a compact representation adaptable to arbitrary control frequencies.
Policy outputs are fixed-size segments comprising adjacent knots and control points, irrespective of temporal chunk length. These parameters are predicted at each policy inference step, supporting seamless integration into architectures such as Diffusion Policy and ACT.
High-frequency Execution and Temporal Rescaling
Decoupling policy inference rate from the low-level control rate allows for sampling B-spline segments at frequencies substantially higher than the policy rate. Temporal rescaling is performed by adjusting the mapping between real-time and curve parameterization, enabling accelerated execution without retraining. The geometric trajectory is preserved while traversal speed is increased, supporting consistent acceleration across tasks.
Pipelined Execution and Segment Alignment
Long-horizon manipulation tasks necessitate continuous prediction and execution of successive B-spline segments. Boundary discontinuities emerge from naive segment concatenation, exacerbated by prediction noise and controller latency. The paper addresses this by introducing an inference-time segment alignment mechanism, which matches the initial state of the new segment to the current execution state, minimizing mean squared error over a search window. This alignment stabilizes transitions, critical for robustness during aggressive speedups.
Experimental Evaluation
Real-world Manipulation Tasks
Three challenging manipulation tasks—Cube Picking (precision), Table Cleaning (long-horizon), and Speed Stacking (bimanual)—were evaluated using 6-DoF ARX5 arms and multiple camera modalities as input.
Numerical Results:
- Task completion time: B-spline policy consistently reduced average completion time across all configurations, with pronounced improvements in long-horizon scenarios (e.g., Table Cleaning reduced from 23.57s to 11.80s at 4× speedup, while maintaining or improving success rates).
- Success rate: BSP maintained or improved robustness over baselines in most settings. Aggressive speedup could induce controller tracking failures, particularly evident in Speed Stacking at 4× where success dropped to zero due to hardware constraints.
- Trajectory smoothness: Qualitative analyses demonstrated substantially smoother motion, with reduced jerk and improved execution fidelity compared to action chunking—especially under high-speed rollout conditions.
Simulation Benchmarks
B-spline policy matched or exceeded baseline performance on RoboMimic and RoboCasa, and demonstrated superior robustness and acceleration on Push-T. At 4× speedup, Diffusion Policy + BSP delivered higher coverage scores (0.73 vs. 0.59) and over 50% reduction in completion time (7.19s to 2.87s). The approach generalizes well across simulated domains, confirming that continuous representations do not compromise imitation learning performance.
Theoretical and Practical Implications
Representation Flexibility and Stability
The local support property of B-splines ensures that prediction errors remain confined, enhancing trajectory stability. Temporal adaptivity aligns representational granularity with task demands, optimizing both learning and downstream control.
Integration and Deployment
B-spline policy architecture requires minimal modifications to existing imitation learning backbones, validating practicality for deployment. The segment alignment mechanism is essential for maintaining high trajectory continuity, especially as policy execution speed increases.
Limitations
Hardware constraints currently cap acceleration; low-cost arm controllers fail to track rapid actions reliably at extreme speedup factors, leading to task failures. Improved controller stiffness and accuracy are suggested for future investigation.
Future Directions
Continuous action representations open prospects for:
- Adaptive execution scheduling, leveraging segment alignment with real-time feedback.
- Interfacing with model-based control for further robustness gains.
- Scaling to generalist manipulation policies capable of rapid transfer across diverse task domains.
- Exploring higher-order spline representations and learning-based adaptive knot selection.
Conclusion
B-spline Policy provides a robust, smooth, and temporally flexible action parameterization that accelerates manipulation policies without sacrificing success rate. The integration of inference-time segment alignment further extends stability to high-speed execution regimes. Empirical evidence substantiates substantial improvements in completion time, trajectory quality, and robustness relative to action-chunking baselines. The approach represents a highly practical and theoretically justified advancement in continuous action representations for robotic policy learning (2607.09648).