Vision-Guided Grasping Algorithm

Updated 13 December 2025

Vision-guided grasping algorithms are systems that integrate visual perception with motion planning to localize objects and plan collision-free trajectories in dynamic, unstructured settings.
They employ advanced sampling-based planners and hybrid dynamical system models, such as the HySST algorithm, to manage both continuous motions and discrete contact transitions.
Empirical evaluations show marked improvements in planning time, optimality, and memory efficiency, underscoring the practical potential of these algorithms in robotics.

A vision-guided grasping algorithm integrates perception and motion planning to enable robotic systems to localize, plan, and execute grasping actions on objects in unstructured or dynamic environments. The core challenge lies in coupling the uncertainty and high dimensionality of visual sensing with the discrete and continuous dynamics of end-effector motion, often necessitating hybrid dynamical system models and advanced sampling-based motion planners.

1. Problem Definition and Motivation

Vision-guided grasping tasks require the robot to extract object pose and scene structure from visual data, synthesize feasible grasp candidates, and plan an optimal (or near-optimal) collision-free trajectory from its current state to execute the selected grasp. This integration exposes several core technical issues:

Uncertainty in object pose due to sensor noise and occlusion.
High-dimensional planning, especially under kinematic and dynamic constraints.
Hybrid dynamics when contacts induce discrete transitions or non-smooth changes in system evolution.
The need for real-time or computationally efficient planning.

Sampling-based motion planning algorithms, particularly optimal variants such as RRT* and its descendants, are the de facto standard for high-dimensional and kinodynamic grasping scenarios.

2. Hybrid Dynamical System Formulation

In complex grasping, the robot's configuration evolves under a hybrid dynamical system: continuous flows (arm motions, end-effector approach) are punctuated by discrete jumps (contact, grasp closure, or collision events). Formally, the system is modeled on a hybrid time domain with two evolution regimes:

Flow regime: governed by ODEs describing actuator/sensor dynamics.
Jump regime: instantaneous state transitions, e.g., contact-induced switching or discrete control modes.

The HySST algorithm ("HySST: A Stable Sparse Rapidly-Exploring Random Trees Optimal Motion Planning Algorithm for Hybrid Dynamical Systems" (Wang et al., 2023)) establishes a generic framework for optimal motion planning in such systems, introducing techniques directly applicable to vision-guided grasping.

3. Algorithmic Frameworks

3.1 HySST Algorithm for Hybrid Motion Planning

HySST maintains a directed search tree $𝒯=(V,E)$ over the robot's state space. Each vertex $v\in V$ has a state $x_v\in ℝ^n$ and an accumulated cost-to-come $c(v)$ . Edges $e=(v_1,v_2)$ encode hybrid solution pairs $(\varphi_e,u_e)$ representing feasible flow/jump trajectories between states.

Key algorithmic steps:

At each iteration, select a random regime (flow or jump), sample a target, and select the lowest-cost nearby node for extension.
Extend the current node by simulating the appropriate dynamical regime to yield a new candidate state.
Use a fixed set of “witness” points. For each witness $w$ , maintain only one representative vertex $\operatorname{rep}(w)$ with the minimal cost in its ρ-ball neighborhood. All other nearby vertices are pruned.
Solutions are composed via concatenation on hybrid time domains to ensure consistent path and cost accumulation.

Algorithm pseudocode is developed to handle randomized regime switching, witness-based sparsification and cost-filtering, and efficient hybrid trajectory propagation.

3.2 Other Relevant Planning Strategies

Connections exist to guided and bidirectional sampling-based planners:

Potential-guided variants (e.g., PB-RRT*, PIB-RRT*) bias samples along attractive fields to accelerate convergence in cluttered grasping scenarios (Tahir et al., 2018).
Bidirectional and multi-tree structures offer improved search efficiency in high-complexity environments (IB-RRT* (Qureshi et al., 2017), Bi-AM-RRT* (Zhang et al., 2023)).
Real-world tasks (dynamic grasping in unstructured scenes) require planners with demonstrated near-optimality and memory efficiency.

4. Theoretical Guarantees and Properties

HySST's theoretical underpinnings guarantee asymptotic near-optimality under hybrid dynamics. Notably:

As the number of iterations $N\to\infty$ , the probability that the best plan's cost exceeds $(1+\alpha\delta)c^*$ goes to zero, with $c^*$ the optimal cost and $\alpha,\delta$ dependent on clearance and system regularity.
Witness-based pruning ensures that the lowest-cost representative per region is always retained, preserving optimality even under aggressive sparsification.
The approach relaxes classical positive clearance requirements by inflating the underlying continuous/discrete domains, which is critical for scenarios where optimal grasping motions “graze” constraints or obstacles.

Proof structure relies on probabilistic tube coverage, probabilistic selection, and the preservation of near-optimal chains under the witness scheme (Wang et al., 2023).

5. Parameterization, Complexity, and Scalability

Critical algorithmic parameters include:

$\delta$ (best-near radius): determines locality for parent selection; must be selected relative to the system's clearance.
$\rho$ (witness radius): adapts the granularity of sparsification, balancing memory footprint with the fidelity of local optimality.
Input libraries for flow (piecewise constant controls) and jump regimes (discrete control options) define the reachability and dynamical richness of the planner.

Complexity per iteration is dictated by nearest search and witness membership queries. With appropriate spatial indexing, complexity scales as $O(N\log N)$ for $N$ samples. This scaling holds up to high-dimensional systems relevant for dexterous grasping.

6. Empirical Performance in Grasping Contexts

Benchmark scenarios demonstrate HySST's efficacy:

For a 2D actuated bouncing ball, HySST reduced planning time by over $5\times$ and node count by $4\times$ compared to non-sparse hybrid RRT variants, while achieving 100% success and costs within 1% of optimal.
In a 6D collision-resilient tensegrity multicopter example (analogous to collision-aware grasping with environmental contacts), HySST exploited jumps (collisions) to produce shorter, dynamically feasible trajectories, outperforming continuous-only planners unable to utilize discrete transitions.

The architecture yields sparse trees, rapid convergence, and substantially lower memory utilization—properties crucial for practical vision-guided grasping in cluttered and hybrid domains (Wang et al., 2023).

7. Relevance and Future Directions

Advanced vision-guided grasping algorithms rooted in hybrid dynamical planning (as exemplified by HySST) provide a formal bridge between perception-driven uncertainty, non-smooth hybrid actions (like contact, release, dynamic pushes), and optimality in object acquisition. The witness-mediated sparsification and hybrid regime randomization generalize and unify features present in classical and potential-driven RRT* variants.

A plausible implication is that future algorithms will further integrate perception feedback, adaptive regime switching, and real-time hybrid trajectory replanning, especially as robotics moves toward more dexterous, robust, and autonomous grasping capabilities in uncertain environments.

Key Reference: