Hybrid Position-Force Control

Updated 3 November 2025

Hybrid position-force control is a paradigm that coordinates positional and force commands along orthogonal subspaces for robust contact interactions.
Algorithmic advances, including closed-form and optimization-based methods, systematically partition control actions to maximize system robustness and safety.
Applications in robotic assembly, manipulation, and locomotion demonstrate high success rates even under uncertain and dynamic environmental conditions.

Hybrid position-force control refers to control strategies in robotics and automation wherein the regulation of both position (or velocity) and force (or contact compliance) is coordinated, typically by assigning them to orthogonal subspaces or task directions. This paradigm addresses contact-rich interactions, where robots must not only follow positional trajectories but also sustain or modulate forces arising from interaction with the environment, tools, or objects. Hybrid position-force control is foundational both in classical manipulation and in contemporary settings such as uncertain assembly tasks, advanced manufacturing, legged locomotion, contact-rich whole-body control, and human-robot collaboration.

1. Fundamental Principles of Hybrid Position-Force Control

Hybrid position-force control exploits the orthogonality of controllable subspaces: robot motion is regulated by position or velocity tracking in some directions and by force (or impedance) control in others. This is operationalized by partitioning the task space into mutually orthogonal position- and force-controlled axes, typically using a selection matrix or diagonal weighting matrices. Formally, for an end-effector with state $\mathbf{x}$ and force $\mathbf{F}$ , and selection matrix $S$ (diagonal), the robot executes:

$\begin{split} & \text{Position control on axes %%%%3%%%% where } S_{ii}=1 \ & \text{Force control on axes %%%%4%%%% where } S_{jj}=0 \end{split}$

Hybrid controllers synthesize their output by transforming these commands back to the joint space (via the robot Jacobian), delivering desired motion or force while respecting dynamic and kinematic system constraints.

Classic schemes (Raibert & Craig 1981) set these subspaces a priori according to the geometry of nominal contact, while modern methods often compute them as a function of environmental constraints, task requirements, or, as in recent research, dynamically optimize or even learn them from data.

2. Algorithmic Advances: Synthesis of Optimal Hybrid Subspaces

The selection of how many and which directions should be force- or position-controlled is non-trivial in general multi-body contact scenarios. Early heuristic approaches have been superseded by algorithmic and optimization-based methods that systematically determine the dimension, direction, and magnitude of velocity- and force-controlled actions. Notable algorithmic contributions include:

Closed-form methods for optimal hybrid force-velocity control maximize kinematic conditioning, ensuring robustness to model errors and physical singularities. For a general system with holonomic constraints $Jv=0$ and a control goal $Gv=b_G$ , the axes for each subspace are chosen to minimize the system's condition number:

$\boxed{ \min_{C} \kappa\left(\begin{bmatrix} \hat J \ \hat C \end{bmatrix}\right) }$

where $C$ defines the velocity-controlled directions; the remaining orthogonal subspace is force-controlled. The axes, dimensions, and control magnitudes are found by closed-form calculation, guaranteeing completeness (solution always found if one exists) and significant computational efficiency over iterative search-based schemes (speedup of 7–40 $\times$ on benchmarked instances), with superior robustness to kinematic singularity (Hou et al., 2020).

Optimization-based hybrid control frameworks use cost functions that combine mutual orthogonality of velocity-controlled axes, proximity to the null-space of holonomic constraints (hence, robustness against constraint violation), and fulfillment of task goals. This yields a robust decomposition and has been shown to generalize to multi-object, contact-rich manipulation, with efficient QP or LP solvers used to compute force actions subject to friction and guard conditions (Hou et al., 2019).

These methods automate what was heuristically or manually configured in classical architectures, enabling real-time robust hybrid position-force (or force-velocity) execution for complex, contact-rich motion plans.

3. Integration with Environmental Constraints and Contact Mechanics

A key contemporary development is the maximization of environmental constraint utilization. Classical approaches treated environmental features as passive termination or constraint conditions. Emerging strategies treat environment contact as an active guide.

In pushing-based hybrid assembly skills, the robot not only tolerates but intentionally exploits contact with environmental jigs and fixtures. The skill comprises a sequence of hybrid actions parameterized by alternating position shifts and controlled contact force (e.g., Z-direction). The controller's partitioning is defined by diagonal matrices $(K, K')$ ; X, Y (and orientation) are position-controlled, Z is force-controlled:

$K= \begin{bmatrix} 1 & 0 & 0 & 0 & 0 & 0 \ 0 & 1 & 0 & 0 & 0 & 0 \ 0 & 0 & 0 & 0 & 0 & 0 \ 0 & 0 & 0 & 1 & 0 & 0 \ 0 & 0 & 0 & 0 & 1 & 0 \ 0 & 0 & 0 & 0 & 0 & 1 \end{bmatrix}, \quad K'=I-K$

This enables controlled pushing/sliding of workpieces along constraints, employing friction and normal/contact force analysis to guarantee conditions for successful mechanical guidance. Notably, friction coefficients are set such that the object slides along fixture surfaces rather than sticking to the gripper:

$F_{o-h} = -\mu_2 F_{N1} \cos\theta, \qquad F_{v-o} = \mu_1 F_{N1} \cos\theta, \quad (\mu_1 > \mu_2)$

Such strategies have achieved perfect (100%) success rates in real mobile manipulator experiments with substantial pose errors (2–4 mm), vastly outperforming both classical spiral search and state-of-the-art learning-based policies (Shi et al., 2022).

4. Application Domains and Empirical Performance

Hybrid position-force control is fundamental to a spectrum of domains, including:

Robotic assembly: Active engagement with jigs, fixtures, and uncertainty, for robust insertion and alignment. Advanced hybrid skills have demonstrated 100% success in assembly under large uncertainty, outperforming both classical search and deep-RL baselines (Shi et al., 2022).
Contact-rich manipulation: Block tilting, tile levering, surface polishing, and collaborative grasping—where force regulation and position tracking must be balanced. Algorithmically synthesized hybrid controllers deliver high success rates (e.g., 100/100 block tilt with closed-form control (Hou et al., 2020); 47/50 with prior search (Hou et al., 2019)).
Locomotion and whole-body balancing: Required for legged robots and humanoids that leverage multi-contact (feet, hands) for stability, with hybrid controllers (including admittance and QP-based approaches) enabling manipulation of underactuated robots (Rouxel et al., 2023).
Safety-critical human-robot interaction: Power-aware and passivity-guaranteed hybrid force-impedance controllers ensure role-flexibility and safety, dynamically detaching/reattaching control in non-passive, contact-rich settings (Shao et al., 20 Oct 2025).

Empirical evaluations consistently report improved robustness, repeatability, and error metrics over both position-only and force-only (or simple hybrid) baselines across these settings.

5. Control Law Structures, Execution, and Tuning

The hybrid controller is typically realized via the following:

Command partitioning: At each control cycle, velocity (position) and force commands are synthesized along the respective subspaces, often structured as:

$\begin{aligned} & \text{Action sequence:} \begin{cases} {[+P^d_{x}, 0, +F_z]}, \ {[-2P^d_{x}, 0, +F_z]}, \ldots \end{cases} \ & \text{Force-control:}~F_z = \text{const}\ & \text{Position-control:}~P^d_{x,y} = \pm \Delta \end{aligned}$

Projection operators and nullspace decomposition: Velocity-controlled axes are set via nullspace projection (e.g., $U = \text{Null}(J)$ ), and optimization selects $C$ so as to maximize robustness while ensuring feasibility.
Constraint feasibility and force computation: Force-control magnitudes are solved as QPs subject to Newton–Euler dynamics, contact, friction, and guard constraints.
Parameterization: Step sizes (position increments) are chosen to at least twice the expected error bound; force setpoints result from quantitative analysis of friction and expected constraint forces.

Parameter selection in advanced approaches arises from formal constraints and optimization objectives (e.g., condition number minimization), rather than empirical tuning.

6. Limitations, Trade-offs, and Future Directions

While hybrid position-force control achieves significant advances in robustness, reproducibility, and task success, trade-offs and open challenges remain:

Complexity vs. interpretability: Automated and optimization-based approaches yield robust control but may produce non-intuitive control axes, with physical interpretability giving way to mathematical optimality.
Resource requirements: Certain methods require full system state and may involve large matrix operations; closed-form solutions ameliorate many such bottlenecks but scaling to very high-DOF systems may require additional structure.
Dynamic and non-holonomic constraints: Most methods focus on quasi-static or holonomic constraints, with dynamic or non-holonomic contact modes (e.g., sliding, rolling) less explored or requiring extension.
Learning-based extensions: Hybrid controllers based on learning seek to merge data-driven performance with model-based guarantees (e.g., adjusting or learning selection matrices or subspace projections adaptively in real time), but remain an area of active research for stability, safety, and transferability.

Continued integration of hybrid position-force control with real-time perception, higher-level planning, and formal guarantee mechanisms (e.g., passivity, constraint satisfaction) will remain a central focus in robotic manipulation and assembly automation.

Summary Table: Key Methods and Their Properties

Aspect	Approach / Result	Reference
Hybrid subspace computation	Closed-form, optimal conditioning (OCHS)	(Hou et al., 2020)
Environmental constraint use	Controlled pushing, friction analysis, surface guidance	(Shi et al., 2022)
Controller parameterization	Diagonal partition, step size $>2 \times$ error, force setpoint	(Shi et al., 2022)
Robustness metric	System "crashing index" (condition number of constraints)	(Hou et al., 2020)
Empirical performance	Assembly success: 100%; Block tilt: 100/100	(Shi et al., 2022 Hou et al., 2020)

This encapsulates the theoretical and empirical foundations for hybrid position-force control, its state-of-the-art algorithmic infrastructure, explicit contact exploitation, tuning, performance, and contemporary challenges in robotic contact-rich task execution.