Hybrid Position-Force Controller

• Hybrid position-force control is a strategy that simultaneously regulates motion and interaction force, balancing trajectory accuracy with compliant contact handling.
• It partitions the task space into directions dedicated to position control and force control, using switching mechanisms and decoupling techniques to manage transitions.
• This approach underpins applications in assembly, manufacturing, and medical robotics, where real-time feedback and adaptive compliance ensure robust performance.

A hybrid position-force controller is a control strategy for robotic and mechatronic systems that enables simultaneous or switched regulation of position (motion) and interaction force. Such controllers are essential in manipulation, assembly, and environments where contacts may be intermittent or force regulation is as crucial as position tracking. Typical hybrid schemes achieve this by partitioning the task space into directions where either motion or force is actively controlled, facilitating tasks that require both accurate trajectory following and compliant contact management.

1. Fundamental Concepts and Control Architectures

Hybrid position-force control is predicated on the observation that, during tasks involving environmental interaction, controlling all directions in position or in force is generally mutually exclusive due to physical constraints. The canonical approach decomposes the control authority along orthogonal directions: some axes are assigned to position control (ensuring trajectory or pose tracking), while others are reserved for force control (regulating the applied contact force).

Early formulations involve strict partitioning and selection matrices that define, for each degree of freedom (DOF), whether position or force is controlled. For single-DOF systems or when only one DOF is actively involved in contact, a switching mode controller is often sufficient, switching between motion control in free space and force control during contact (1503.00603). In more general, multi-DOF contexts, control action is synthesized by projecting the control effort into orthogonal subspaces associated with the desired force and motion directions (Nasiri et al., 5 Apr 2024).

The hybrid controller structure is reflected in control laws such as:

• Motion control (free space): closed-loop position (or acceleration) control
• Contact/force control: regulation toward a force reference using sensory feedback and environment models

Augmentations include feedforward terms, integral correction for steady-state rejection, dead-zone pre-compensation (as in hydraulic actuators (Pasolli et al., 2020)), and modular switching logic.

2. Switching and Decoupling Mechanisms

A central methodological theme is the switching or decoupling of motion and force regulation based on task-phase or contact state. In single-DOF tasks, switching occurs based on a geometric or force-based criterion:

• Position control is active when the manipulator is not in contact ($x \leq 0$)
• Force control activates upon contact ($x > 0$), utilizing a Kelvin–Voigt model for environmental interaction (1503.00603)

In more complex robots, a smooth and invertible mapping from joint to task space is leveraged to decouple the control tasks. For example, the hybrid controller in (Xie et al., 2020) separates the DOFs for motion tracking and force regulation using task-space mapping and Jacobian-based transformations, enabling separate controllers for each objective as long as their goals are not mutually exclusive.

For hydraulic actuators, autonomous switching is realized by a hysteresis relay, mitigating chattering and ensuring smooth transitions through gain and mapping reconfiguration, not by switching out entire feedback loops (Pasolli et al., 2020).

3. Stability Analysis and Compliance Design

The stability of hybrid controllers—particularly those with discontinuous switching—is nontrivial. Detailed analyses employ switched-system theory, Lyapunov methods, and multiple Lyapunov function frameworks to establish conditions for closed-loop stability. For instance, the presence of arbitrary switching between stable subsystems can induce instability unless sufficient damping is present (1503.00603). Sufficient conditions, such as negative product of return map scalars ($\Lambda_1 \Lambda_2 < 1$), guarantee global uniform exponential stability (GUES) for the unperturbed system.

A critical insight is that practical stability often requires considerably more damping in the force control law than is realistic or desirable. To address this, mechanical compliance is introduced—such as compliant wrists or series elastic components—in the manipulator to lower the effective environment stiffness and natural frequency of impact, thereby avoiding the necessity for unrealistically high controller gains (1503.00603). Reduction models demonstrate that a well-designed compliant element (with tuned stiffness $k_t$ and damping $b_t$) ensures stable impact dynamics without loss of performance.

4. Extensions: Learning-Based and Dynamic Hybrid Controllers

Recent advances extend classic hybrid control through learning-based and adaptive strategies. For rapidly changing constraint directions, as in dynamic contact tasks, learning a time-varying constraint frame aligned to the desired force direction enables more general and robust hybrid control (Conkey et al., 2018). Demonstrated trajectories are used to fit dynamic movement primitives (DMPs) that synchronize spatial and force objectives, capturing both intentional and compensatory contact forces (such as friction), and supporting adaptation to novel tasks.

In environments with uncertain or partial models, learning-based hybrid schemes relax the dependence on precise object pose and model feedback. Neural precondition predictors allow skill planners to select effective hybrid force-velocity (HFVC) strategies for non-prehensile manipulation under model uncertainty (Liang et al., 2022). Reinforcement learning has been employed to co-train robot policies that integrate position and force control without direct force sensing, using historical state embedding for force estimation and compensation (Zhi et al., 27 May 2025). In legged and humanoid robots, these approaches enable compliant interaction, payload adaptation, and robustness to external disturbance by learning hybrid position-force policies with explicit or learned disturbance compensation modules (Zhang et al., 31 May 2025).

5. Practical Implementation Strategies and Applications

Hybrid position-force control has been validated across a diverse range of robotic platforms and tasks:

• Manufacturing: Precision force-controlled applications such as thermoplastic tape laying, grinding, or insertion tasks exploit real-time surface normal estimation and friction correction for robust hybrid control on 7-DoF manipulators with F/T sensors (Nasiri et al., 5 Apr 2024).
• Assembly: Inserting objects into fixtures using a series of hybrid position and pushing actions, robots maximally utilize environmental constraints for alignment, achieving high success even with significant pose uncertainties (Shi et al., 2022).
• Medical Robotics: A 6-DoF hybrid controller for robotic endodontic treatment employs both force and position feedback to adapt to patient movement while compensating for file bending, yielding millimeter-level accuracy in preclinical dental scenarios (Cheng et al., 2023).
• Grasping: Hybrid controllers integrating tactile feedback with position and force control phases minimize object displacement during grasp, explicitly compensating external forces and gravity (Lach et al., 2023).
• Whole-Body Multi-Contact: On humanoid robots controlled in position, whole-body force control is achieved by exploiting the joint elasticity as an implicit compliance, with force targets enforced through retargeting and real-time quadratic programs (Rouxel et al., 2023).
• Aerial Manipulation: Hybrid NMPC (Nonlinear Model Predictive Control) enables integrated MAV-manipulator systems to execute precise aerial writing via simultaneous position and force regulation (Tzoumanikas et al., 2020).

These implementations typically rely on high-frequency feedback (e.g., >500 Hz control cycles), real-time optimization, and, when necessary, soft or compliant interfaces to mediate contact transitions.

6. Key Mathematical Models and Performance Characterization

Several mathematical constructs are central to hybrid position-force control:

• Switched-state models for error dynamics:

$$\dot{z} = A_i z + N w_i(t), \quad z \in \Omega_i(t),\quad i \in \{1,2\}$$

with controller structure and stability parameters individualized for mode $i$ (1503.00603).

• Mapping between desired force and position in contact:

$\hat{k}_e x_d(t) + \hat{b}_e \dot{x}_d(t) = F_d(t)$

• Decoupled control via projection matrices for force ($\Omega_f$) and motion ($\Omega_m$) subspaces:

$\Omega_f = N (N^\top N)^{-1} N^\top$

$\Omega_m = T (T^\top T)^{-1} T^\top$

with $N$ and $T$ as bases for force and motion directions, respectively (Nasiri et al., 5 Apr 2024).

Performance is typically evaluated in terms of:

• Impact force reduction during contact transitions
• Steady-state and transient tracking errors (in both position and force)
• Success rates in manipulation/assembly experiments
• Robustness under external disturbances and model uncertainties

For instance, in assembly under uncertainty, hybrid position-force skills exploiting environmental constraints achieved 100% success rates compared to much lower rates for search-based or learning-based baselines (Shi et al., 2022).

7. Contemporary Developments and Trends

Contemporary research broadens hybrid position-force control along several axes:

• Learning-based synthesis and adaptation, including reinforcement learning for joint position-force command policies in complex, contact-rich tasks (Zhi et al., 27 May 2025); use of neural observers for real-time disturbance estimation (Zhang et al., 31 May 2025).
• Model-free or sensorless hybrid control, including approaches that infer contact transitions via loop shaping and output-only feedback, without dedicated force sensors (Ruderman, 29 Nov 2024).
• Closed-form optimization for real-time hybrid force-velocity control with guaranteed kinematic conditioning to mitigate singularity and unexpected internal forces (Hou et al., 2020).
• Whole-body force control for position-controlled humanoids, leveraging explicit flexibility models and real-time quadratic programming (Rouxel et al., 2023).

Across these strands, the core challenge remains ensuring safe, robust, and high-performance behavior in uncertain, contact-rich environments, with practical systems increasingly leveraging compliance (mechanical and control) and data-driven adaptation to balance conflicting objectives of precision and compliance.