An Optimization-Augmented Control Framework for Single and Coordinated Multi-Arm Robotic Manipulation (2506.16555v1)

Abstract: Robotic manipulation demands precise control over both contact forces and motion trajectories. While force control is essential for achieving compliant interaction and high-frequency adaptation, it is limited to operations in close proximity to the manipulated object and often fails to maintain stable orientation during extended motion sequences. Conversely, optimization-based motion planning excels in generating collision-free trajectories over the robot's configuration space but struggles with dynamic interactions where contact forces play a crucial role. To address these limitations, we propose a multi-modal control framework that combines force control and optimization-augmented motion planning to tackle complex robotic manipulation tasks in a sequential manner, enabling seamless switching between control modes based on task requirements. Our approach decomposes complex tasks into subtasks, each dynamically assigned to one of three control modes: Pure optimization for global motion planning, pure force control for precise interaction, or hybrid control for tasks requiring simultaneous trajectory tracking and force regulation. This framework is particularly advantageous for bimanual and multi-arm manipulation, where synchronous motion and coordination among arms are essential while considering both the manipulated object and environmental constraints. We demonstrate the versatility of our method through a range of long-horizon manipulation tasks, including single-arm, bimanual, and multi-arm applications, highlighting its ability to handle both free-space motion and contact-rich manipulation with robustness and precision.

• The paper introduces a three-mode control paradigm that integrates optimization-based planning and force control for robust single and multi-arm manipulation.
• It decomposes tasks into subtasks and dynamically switches between pure optimization, force control, and hybrid modes to handle contact-rich challenges.
• Experimental results demonstrate low trajectory and force RMSE across tasks, validating the framework’s practical efficacy and stability.

Optimization-Augmented Control for Multi-Arm Robotic Manipulation

The paper presents a modular, optimization-augmented control framework that synthesizes the strengths of optimization-based motion planning and force control to enable robust single and multi-arm robotic manipulation. This approach addresses a longstanding challenge: neither force nor trajectory optimization alone suffices for complex, contact-rich, long-horizon manipulation tasks, particularly with multiple cooperating arms.

Context and Motivation

Traditional robotics control methods distinctly favor either force regulation or optimized motion planning:

• Optimization-based planning can generate collision-free, long-horizon trajectories incorporating kinematic constraints but lacks adaptability for high-frequency, contact-rich interactions.
• Force control (e.g., hybrid impedance/admittance schemes) delivers precise interaction and compliance for tasks involving direct contact, but is unsuitable for extended or synchronized motion with strict orientation requirements, especially in multi-arm scenarios.

The presented framework recognizes that effective manipulation in realistic settings invariably requires both precise force adaptation and robust trajectory execution. It introduces seamless task- and context-based switching between pure optimization, pure force control, and a hybrid mode.

Methodological Contributions

At the core is a three-mode control paradigm, with task decomposition as the operative principle:

1. Task Decomposition: Tasks are manually segmented into subtasks, each assigned a control mode according to force and trajectory demands. For instance, approaching an object uses pure optimization, while force-intensive interaction (e.g., object rotation) uses force control; hybrid control is reserved for situations needing both (e.g., bimanual transport).
2. Control Modes:
   • Pure Optimization: Employs KOMO (K-Order Markov Optimization) to synthesize collision-free trajectories, which are subsequently tracked with PID control.
   • Pure Force Control: Uses PI controllers for contact force regulation, optionally combined with Cartesian impedance control for position compliance. This controller dominates during phases where dynamic contact dominates, and precise orientation is less critical.
   • Hybrid Optimization and Force Control: Simultaneously tracks planned trajectories and regulates contact forces. The methodology assumes, and empirically validates, that decoupling force and motion control (by orthogonality of motion and force vectors) stabilizes the joint control without significant interference.

Algorithmically, each control loop computes torques from both optimization and force control channels, summing them to produce the final joint actuation commands. Practical considerations such as selection of antipodal contact points and pre-contact pose initialization further reinforce stability.

The key operational design is summarized in the following pseudocode, as presented in the paper:

while not at target: tau_optimization = PID(q_target - q) tau_contact = PI(F_target - F_actual) tau_position = Impedance(x_target - x) tau_cmd = tau_optimization + tau_contact + tau_position tau = InverseDynamics(q, q_dot, tau_cmd) Send tau to robot Update robot state

Experimental Validation

The framework’s efficacy is systematically evaluated across four categories:

• Single-Arm Manipulation (Box Relocation): The arm approaches, rotates, and repositions a box, demonstrating seamless switching between controller modes.
• Bimanual Box Transportation: Two arms coordinate to transport a cube a meter across space, showing stable synchrony and pose maintenance.
• Bimanual Peg-in-Hole: Complex handover and insertion tasks requiring simultaneous force and pose control.
• Four-Arm Reorientation: Multi-stage, four-arm manipulation involving real-time restructuring of grasps and cooperative object orientation.

Strong quantitative results include:

• End-effector RMSE in trajectory as low as 1.6–2.1 cm, with joint angle RMSE per joint ≈1° during coordinated manipulation.
• Contact force RMSEs of 2.8 N per arm, despite significant force spikes at trajectory phase changes.

The framework completed all tested tasks robustly where monolithic controllers (pure force or pure optimization) failed.

Theoretical and Practical Implications

Theoretical Implications

The integration of optimization and force control in a selectively modular fashion demonstrates:

• The feasibility of practical stability for hybrid force/trajectory control through controller summation and low-level orthogonality assumptions (force and motion).
• That decomposition of long-horizon manipulation into context-appropriate control phases can circumvent the theoretical limitations of monolithic approaches, facilitating convergence and task success where single paradigms fail.
• The importance of grasp/contact point selection as an integral part of the closed-loop control strategy.

Practical Implementation Considerations

• Manual task decomposition introduces a bottleneck; automating this—potentially via learning or heuristic rules—would improve scalability.
• The framework relies on accurate dynamics modeling and contact force sensing. In real-world deployments, sensor noise and unmodeled dynamics may demand robustification extensions.
• Computational cost is primarily dominated by KOMO trajectory optimization; for real-time deployment, replanning strategies may need further acceleration or parallelization.
• The architecture is platform-agnostic, tested in NVIDIA PhysX-based simulation with Franka Panda arms, demonstrating portability to general multi-DOF manipulation platforms.

Limitations and Directions for Future Research

• Automated Task Decomposition: Future research should focus on data-driven or rule-based decomposition of manipulation tasks, allowing fully autonomous mode switching at runtime.
• Real-World Hardware Validation: While simulation-based, the approach should be ported and validated on physical multi-arm systems, particularly exploring robustness to sensor and actuation uncertainties.
• Real-Time Adaptive Replanning: Integrating environmental feedback (e.g., vision, tactile) for online adaptation and failure recovery is a natural next step.
• Hybridization with Learning-Based Methods: While the proposed approach is model-driven, hybridizing with imitation or reinforcement learning could support adaptation in less-structured, high-variability environments.

Conclusion

This paper delivers a significant practical advancement in manipulation control for single and multi-arm robots, explicitly demonstrating that robust performance across a broad class of realistic tasks requires the principled integration of force regulation and long-horizon optimized planning. The demonstrated empirical results underscore the value of modular, context-aware control. Extensions toward autonomy in decomposition, adaptation, and expanded sensory integration are well-positioned to further enhance general-purpose robotic manipulation.