Periodic Steady-State Control of a Handkerchief-Spinning Task Using a Parallel Anti-Parallelogram Tendon-driven Wrist

Non-prehensile object manipulation skills are important for real-world robot interactions, enabling highly dynamic tasks such as balancing a glass on a tray or the controlled sliding of items on a table. Among such tasks, those characterised by high-speed manipulation requirements and general sensitivity of the resulting hybrid dynamics are particularly hard to accomplish. Within these, juggling can be seen as a highly challenging maneuver to be solved. The key to robotic juggling is achieving dynamic stabilisation of an underactuated object. Since the object does not possess the ability of self-correction, its stability is entirely dependent on the forces applied to it. This creates a system that is sensitive to control inputs, where timing is critical to continuously counteract deviations and maintain the desired behavior. We develop a systematic method to control a 7-degree-of-freedom manipulator performing non-prehensile ball juggling with a tool. Our primary contribution is a model-based framework for generating juggling trajectories and stabilizing a periodic juggling motion for this hybrid system. The framework incorporates a two-stage optimal control approach to compute the underlying feasible motion patterns required for stable juggling. Offline-computed trajectories are then organised to enable real-time error correction without solving optimal control problems online. We demonstrate the effectiveness of the resulting controller by first evaluating its performance in a simulation environment and performing an experiment using a Franka Emika Panda robot.

Dexterous manipulation is fundamentally a problem of interaction dynamics: the hand must track precise finger trajectories, regulate the contact force exchanged with grasped objects, respect actuation and safety limits, and remain predictable when contact persists -- objectives in tension for any fixed-gain controller. A sustained contact torque $τ_{\text{ext}}$ through a joint stiffness $K_d$ produces the structural bias $e_\infty=τ_{\text{ext}}/K_d$, so stiffening for accuracy sacrifices contact safety while softening yields by design. We make these interaction dynamics explicit and actuator-agnostic through a constant-$A_d$ double-integrator backbone, instantiating the offset-free architecture established for physical human-robot interaction (pHRI) and preserving its modeling assumptions on the reduced residual dynamics. An algebraic feedforward reduces the tendon transmission -- hydraulic, cable, pneumatic, twisted-string, or series-elastic -- to a constant-coefficient double integrator, so the QP cost inverse is precomputed offline and a 10-step receding-horizon QP runs at 500,Hz under contact-force (ISO/TS 15066), actuation, and jerk constraints. An encoder-only augmented-Kalman disturbance state drives steady-state error to zero under constant contact loads in the nominal detectable case. In simulation, a hydraulically actuated finger -- the worked example, adding pressure and cavitation constraints -- attains 0.6,mrad RMS, 0.1,mrad steady-state, and 7.3,mrad peak deflection under 1.5,Nm contact: 153$\times$, 1500$\times$, and 21$\times$ better than classical impedance. The realized first-move stiffness (18$\to$323,Nm/rad with update rate) is independently verified, and the architecture scales to a 16-DOF LEAP Hand MuJoCo model, recovering from 2.5,N grasp disturbances within 0.7,s.

Parallel-jaw grippers are the default manipulator choice in robotics because they are simple, robust, and inexpensive. Their limited in-hand mobility, however, often forces large arm motions and restricts dexterous manipulation in confined workspaces. We present a parallel-gripper upgrade: a double-soft-belt-based finger module that preserves standard opening/closing while adding three in-hand degrees of freedom (DoF): translation, pitch, and roll. The mechanism is deliberately kept simple and engineered for inexpensive manufacturing and straightforward integration, preserving the reliability and precise control of traditional parallel grippers while greatly broadening the range of manipulation capabilities. To demonstrate the utility of the added DoFs, we integrate the gripper in two control pipelines. First, we adapt a model predictive controller for in-hand manipulation of known objects. Second, we introduce a lightweight teleoperation interface that enables simultaneous control of the robot arm and gripper (10 DoFs total) with minimal hardware. Across a suite of challenging manipulation tasks executed via teleoperation, MPC, and trained policies, the proposed gripper consistently improves dexterity and task feasibility compared to a conventional parallel gripper