cuRobo: GPU-Accelerated Trajectory Optimization

• cuRobo Parallelized Trajectory Optimization is a framework that leverages GPU-based parallelism to generate high-fidelity, real-time motion trajectories using a hybrid of gradient and particle-based methods.
• The system integrates batched collision checking, geometric planning, and gradient-based optimization to achieve planning times as low as 30 ms on desktop GPUs and significant speedups on embedded devices.
• Empirical results show superior performance with high success rates, smoother trajectories, and up to 12× lower maximum jerk, making it suitable for industrial robotics applications.

cuRobo Parallelized Trajectory Optimization refers to a set of frameworks, algorithms, and software libraries for rapid, large-scale trajectory generation in robotics, where massive computational parallelism—particularly on GPU hardware—is exploited to accelerate optimization for motion planning under complex constraints. The paradigmatic implementation is provided by the cuRobo library, which combines batched gradient-based and sampling-based optimizers, GPU-accelerated geometric planning, and parallel collision checking to enable real-time, high-fidelity motion generation for manipulators and mobile robots. The following sections outline the technical structure of cuRobo Parallelized Trajectory Optimization, situate it in the context of related research, and detail its core principles and performance characteristics.

1. GPU-Based Parallel Optimization in cuRobo

The central design of cuRobo’s motion generation pipeline is based on launching a large batch of independent optimization seeds, each representing a candidate collision-free robot trajectory. These seeds are optimized simultaneously using a hybrid approach:

• Gradient information is computed in parallel for each candidate, leveraging all available GPU threads for fast processing.
• An L-BFGS optimizer maintains a history buffer per seed to estimate second-order step directions. The update process incorporates a parallel “noisy line search” step: multiple potential step lengths are applied to each candidate’s direction, and the results are evaluated in parallel to efficiently select those satisfying Wolfe or Armijo conditions. If no step satisfies these criteria, a “noisy” fallback with a small magnitude is chosen to mitigate stalls or numerical instability.
• An optional particle-based phase is run prior to L-BFGS, in which many seeds undergo stochastic updates (typically Gaussian perturbations). Particles are reweighted and resampled according to an exponential utility function:

$$\Theta_{\mu} \leftarrow (1 - k_{\mu})\,\Theta_{\mu-1} + k_{\mu}\,w \cdot \theta_{n,[1,T]}$$

This rescales and moves the batch mean towards promising regions of parameter space.

This architecture capitalizes on the independence of trajectory evaluations, which is particularly well-suited to GPU hardware where thousands of threads can simultaneously evaluate costs, gradients, constraint violations, and collision distances for large populations of trajectories. This “sample-and-optimize” paradigm underpins the library’s dramatic speedups.

2. Mathematical Structure and Constraints

The robot trajectory optimization problem is formulated as a constrained nonlinear minimization over a temporal sequence of robot states $\Theta = (\theta_1, \ldots, \theta_T)$. The objective function comprises multiple cost terms:

• Pose or task cost, e.g. $$C_{\text{goal}}(X_g, \Theta_T) = \| X_g - \operatorname{FK}(\Theta_T) \|^2$$.
• Smoothness, consisting of joint velocity, acceleration, and jerk penalties:

$C_{\text{smooth}}(\Theta_t) = w_v \| \dot{\theta}_t \|^2 + w_a \| \ddot{\theta}_t \|^2 + w_j \| \dddot{\theta}_t \|^2$

• Collision avoidance terms, implemented as penalties for overlapping spheres in a robot link decomposition; e.g., the self-collision penalty:

$$C_r(K_s(\theta_t)) = \beta_1 \max_{i,j \in S} \left( \max(0,\, s_{i,r} + s_{j,r} - \|s_{i,x} - s_{j,x}\| ) \right)$$

Similar terms penalize collisions with workspace obstacles or enforce safety margins.

Finite-difference derivatives are computed with a high-order stencil to allow for smooth trajectory generation with explicit jerk minimization.

3. Parallel Geometric and IK Planning

cuRobo supplies a geometric seed generator that samples collision-free configurations in parallel:

• Nodes are sampled within an informed ellipse about the start and goal.
• Parallel nearest-neighbor search and connection is performed to grow a sparse roadmap.
• A parallel “steering” primitive attempts to connect pairs of nodes; each edge discretization and collision check is performed as an independent task on the GPU.

Inverse kinematics queries are handled by custom CUDA kernels, enabling parallel forward and backward kinematics and allowing for collision-free IK solving at rates exceeding 7000 queries/s, as benchmarked in multi-DOF systems.

4. Empirical Performance and Scaling

Benchmarking on desktop GPUs (e.g. NVIDIA RTX 4090) and embedded devices (e.g. Jetson AGX Orin) demonstrates median planning times of $\sim$30 ms (desktop) and 28× speedup (Jetson) relative to CPU-bound approaches. The pipelined architecture and batched execution yield nearly linear scalability with the number of seeds. On large-scale industrial tasks, the library maintains a 99.8% success rate, consistently generates shorter C-space paths, and achieves up to 12× lower maximum jerk than previous optimization pipelines.

Key metrics observed:

• Full planning times $\sim$30 ms (desktop, 60× faster than traditional methods).
• Batch IK queries exceed 7000/s (80× faster than common libraries).
• Superior joint trajectory smoothness and lower jerk.

5. Integration and Deployment

cuRobo has been adopted in industrial automation settings, notably for multi-axis robots (e.g. arms with 7th-axis gantries), through direct URDF integration or by modeling additional axes as static obstacles to suit system requirements. In online industrial deployments, the GPU-resident cuRobo engine is synchronized with digital twin simulators. It supports high-frequency replanning (e.g. 500 Hz for up to 512 seeds, 64 timesteps each) enabled by circular-buffered communication and parallel collision checking.

Planning for extended DOF systems has been demonstrated with 12-DOF assemblies and complex workcell layouts, yielding average trajectory planning times (including collision avoidance) well below 100 ms even in dynamic, cluttered environments.

6. Relation to Other Parallel Optimization Frameworks

The parallelized, batched approach underlying cuRobo is compatible with advances such as trajectory splitting and consensus-ADMM (Wang et al., 2021, Yu et al., 14 Jul 2025), where long trajectories are broken into parallel subproblems, each optimized with imposed consensus constraints. cuRobo’s structure also makes it applicable to scenarios demanding hybrid discrete-graph global search and local trajectory optimization, as in PINSAT (Natarajan et al., 17 Jan 2024), and to dynamics-aware real-time planning for mobile platforms.

Distinct from convex relaxation methods relying on SDPs (Kang et al., 9 Jun 2024), cuRobo’s pipeline achieves high practical speed via direct parallelization (rather than global certificates), making it particularly effective for motion generation in high-DOF manipulators with black-box or data-driven constraints.

7. Library Ecosystem and Availability

The cuRobo library is open-source, implemented in PyTorch and CUDA, exposing C++ and Python APIs. Core kernels include batched kinematics, parallel signed distance and continuous collision checking, and parallel gradient-based and particle-based optimizers. Integration points with reinforcement learning environments, digital twins (e.g. NVIDIA Isaac Sim), and mapping systems (e.g. nvblox) are supported. Real-world applications include rapid pick-and-place, coordinated multi-robot planning, and dynamic industrial assembly. The library and supplementary documentation are maintained at https://curobo.org.

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cuRobo Parallelized Trajectory Optimization constitutes a high-performance, robust, and scalable approach to motion generation in robotics, exploiting modern GPU hardware to solve complex, constraint-rich trajectory optimization problems in real time. Its architecture and algorithmic principles are validated by benchmark results and industrial deployments, situating it as a leading paradigm for massively parallel motion planning.