Belt-Finger: An Affordable Soft Belt-Driven Gripper for Dexterous In-Hand Manipulation

Robotic manipulation has increasingly pursued human-like dexterous hands with many articulated degrees of freedom, offering rich manipulation capabilities at the cost of mechanical and control complexity. At the other extreme, parallel grippers are simple and robust, but provide little ability to manipulate an object after grasping it. Operating articulated objects such as threaded containers, manufacturing tools, and laboratory instruments often requires a second gripper, an external fixture, or coordinated arm motion. We introduce the Cartesian Hand, a 7-DoF end-effector that rethinks dexterous manipulation by combining independent grasping and relative manipulation within a single end-effector using only linear motion. Two independently actuated parallel grippers hold different parts of an object, while four translating fingertips generate relative motion between the grasped parts. Its configuration-independent fingertip kinematics allow manipulation to be composed from simple linear motion primitives. The Cartesian Hand is particularly suited to objects structured around common mechanisms such as threads, pivots, linear guides, plungers, and triggers. We demonstrate cap opening and closing, pipetting, pumping, two-handle manipulation, screwdriving, trigger actuation, and in-grasp reorientation across 35 objects spanning laboratory, manufacturing, and household settings. The same manipulation procedures transfer from a fixed-base robot arm to a humanoid, where we demonstrate bimanual laboratory manipulation using two Cartesian Hands. These results show that versatile in-hand manipulation capability can emerge from a mechanically simple architecture when independent grasping and relative motion are designed directly into the end-effector. We will open-source all software and hardware design. Our website is https://generalroboticslab.com/cartesian_handv1.

We present a primitive-informed sampling-based model predictive control (MPC) framework for multi-fingered dexterous manipulation. Sampling-based MPC evaluates candidate control trajectories through forward simulation without requiring gradients through complex contact dynamics. However, directly sampling these trajectories in the high-dimensional joint space of a dexterous hand is inefficient and makes performance strongly dependent on the sampling distribution. Our framework biases sampling using low-dimensional manipulation primitives that encode coordinated finger motions, while simultaneously optimizing joint-level residuals to adapt these motions to the current hand-object configuration. Task-related rollout constraints reject infeasible trajectories during forward simulation, improving the effective use of the sampling budget. We evaluate the approach on a 16 DoF Allegro hand using a synchronized MuJoCo digital twin. Ablations show that both the primitive and residual are necessary for reliable continuous in-hand rotation, that increasing the sampling budget alone does not recover this coordination, and that rollout constraints substantially improve success rate. A primitive extracted for one object size transfers to other sizes and remains effective under model mismatch. The framework further supports grasping, object reorientation, and coordinated arm-hand manipulation, using primitives extracted from both a simulation-trained policy and human hand-motion data.

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.