Manipulation Centricity Metric in Robotics

• Manipulation centricity is a metric that quantifies the suitability and efficiency of actions for robotic or human manipulation by factoring in task constraints and environmental context.
• It encompasses diverse methodologies including grasp manipulability, sequential task planning, configuration space metrics, and unified 3D performance measures.
• Applications span robotic grasp planning, teleoperation, reinforcement learning, and network control, driving optimized, task-adaptive strategies despite computational challenges.

A manipulation centricity metric is a task-coupled quantitative measure that evaluates the suitability, efficiency, or feasibility of actions, configurations, or information for robotic or human manipulation, by specifically reflecting task requirements, constraints, and comfort in context. In robotics and control, manipulation centricity formalizes the idea that not all grasps, trajectories, or strategies are equally conducive to successful manipulation—some are geometrically or kinodynamically preferable, lead to higher dexterity, more robust force closure, or facilitate subsequent task steps. Multiple lines of research have operationalized manipulation centricity in various forms, encompassing grasp manipulability measures, configuration space metrics, haptic metrics, task-dependent selection criteria, performance indices for human teleoperation, curriculum learning distance measures, and multimodal representations for language-guided manipulation.

1. Grasp Manipulability and Situated Manipulation Metrics

Manipulation centricity was first formalized in the context of grasp planning as a “situated grasp manipulability” metric, which quantifies the dexterity or comfort of the arm when realizing a candidate grasp during a manipulation task such as pick-and-place (Quispe et al., 2016). For a robot arm with joint configuration $q$ and Jacobian $J(q)$, the Yoshikawa manipulability is defined as: $m(q) = \sqrt{\det(J(q)J(q)^{\top})}$ Since a grasp candidate can admit multiple collision-free inverse kinematics (IK) solutions due to arm redundancy and environmental obstacles, the situated grasp manipulability for a candidate is computed as the average manipulability over all valid solutions: $$m_{g} = \frac{1}{N} \sum_{i=1}^{N} m(q_i) = \frac{1}{N} \sum_{i=1}^{N} \sqrt{\det(J(q_i)J(q_i)^{\top})}$$ Only collision-free configurations contribute, making $m_g$ highly contextual—environment, task goals, and object pose affect which grasps are comfortable or feasible. In planning, candidates are prioritized by their $m_g$ values evaluated at the start (pick) or goal (place) pose, often preferring those maximizing dexterity at the goal due to the “end-comfort” effect.

2. Sequential and Task-Adaptive Grasp Selection Metrics

For tasks requiring multiple sequential steps (e.g. pick-and-place, pouring), manipulation centricity expands to accommodate constraints across stages (Quispe, 2017). The arm-and-hand metric $m_{ag}$ blends:

• Arm metric $m_a(g)$: Number of collision-free IK solutions for grasp $g$, reflecting comfort and redundancy.
• Grasp metric $m_g(g)$: Proximity of the grasp approach to the object’s center of mass.

Due to different units, $m_{ag}$ is computed by tiered ordering: first binning grasps by quality of $m_a$ (mean $\mu_a$ and std $\sigma_a$ define "very good" – "bad" tiers), then ranking each group via $m_g$ (lowest distance preferred). For tasks with tight goal constraints (e.g. placing inside a box), averaging $m_{ag}$ between start and goal is beneficial; when goal constraints are weak (pouring), evaluation at start suffices. Quantitative experiments show $m_{ag}$-driven selection yields shorter paths, faster planning, and higher success rates.

3. Configuration Space and Behavioral Manipulation Metrics

In motion planning, manipulation centricity is formalized via the metric in configuration space (Jeon et al., 2018). Standard planners minimize Euclidean distance $||q_s-q||^2$ for configuration selection, but efficiency and naturalness depend on the metric $M$: $||q_s - q||^2_M = (q_s - q)^{\top} M (q_s - q)$ Diagonal terms of $M$ weight joint costs (penalizing awkward motions like excessive elbow flexion), while off-diagonal terms encode joint correlations (encouraging coupled, human-preferred movements). Non-Euclidean metrics produce behaviors closer to human preference, especially for “contraction” tasks, supporting manipulation centricity as the degree to which the chosen solution aligns with natural, task-centric strategies.

4. Manipulation Centricity in Curriculum and RL Exploration

Advanced manipulation learning methods (especially with obstacles or sparse rewards) operationalize centricity via graph-based curriculum metrics (Bing et al., 2020). Here, the true “distance” between goals is computed on an obstacle-avoiding graph $G$ rather than in workspace Euclidean norm: $d_G(g_1, g_2) = \hat{d}_G(\nu(g_1), \nu(g_2))$ This graph-induced metric prioritizes intermediate goals not merely by proximity but by achievable, manipulation-centric paths in the actual environment. Using such centric metrics in hindsight goal selection substantially improves sample efficiency and success rates in RL-based manipulation.

5. Manipulation Centricity for Human Performance: Unified 3D Metrics

In virtual reality and teleoperation, manipulation centricity underpins standardized performance metrics incorporating both translation and rotation in 3D object manipulation (Triantafyllidis et al., 2021). Extending Fitts’ law, the unified difficulty index is: $ID_t = \log_2 \left( \frac{2A}{F + W} + 1 \right)$

$$ID_r = \log_2 \left( \frac{2\alpha}{\omega^2} + 1 \right)$$

Combined in the overall performance model: $$MT = a + b \left[ c \cdot ID_t + d \cdot ID_r \right]$$ Manipulation centricity here denotes the model’s ability to accurately capture and predict movement times for complex 3D tasks—translational, rotational, and weighted by task parameters.

6. Manipulation Centricity as a Controllability and Network Metric

In network control, “manipulation centricity” emerges in the context of edge centrality measures quantifying first-order impact of structural modifications on global performance metrics defined via the controllability Gramian (Chanekar et al., 2021). The Edge Centrality Matrix (ECM) encodes the sensitivity of metrics (trace, logdet, inverse trace) to edge perturbations and is additive over input actuators, serving as a manipulation-centric ranking for targeted modifications to optimize controllability, robustness, or resilience.

7. Applications, Implications, and Future Directions

Manipulation centricity metrics are pivotal across domains—robotic grasp planning, sequential task adaptation, human-machine interface assessment, RL curriculum design, and network controllability. Their contextual, task-coupled nature enables selection and prioritization of actions that are maximally successful, efficient, and comfortable. Limitations remain, including the computational overhead of evaluating metrics over large spaces (e.g. all collision-free IK solutions), potential sensitivity to environmental modeling errors, and challenges scaling to highly dynamic or multi-agent scenarios. Future research encompasses integration with multimodal perceptual representations (e.g., vision, haptic, language), extension to deformable and multi-object manipulation, development of automated task-adaptive scaling for centricity scoring, and theoretical analysis of centricity properties in high-dimensional control spaces.

Manipulation centricity acts as a unifying principle for reasoning about action quality, adaptability, and feasibility—whether for a robotic arm, a teleoperated user in VR, a reinforcement learning agent, or a networked control system. Its rigorously defined, task-sensitive metrics anchor the design, evaluation, and optimization of advanced manipulation systems across physical and virtual domains.