Scenario Convex Programs for Dexterous Manipulation under Modeling Uncertainties

TL;DR

This paper addresses robust dexterous manipulation under contact-uncertainty by casting object-level hand control as a robust pole-placement problem. It formulates a robust convex program (RCP) and then solves a scenario convex program (SCP) by sampling uncertain grasp maps and operating points, with probabilistic guarantees on feasibility and optimality. The approach leverages a regional $\mathscr{D}$-region LPIs for pole placement and demonstrates that incorporating operating-point variations via SCP improves robustness over discretized uncertainty methods. Numerical results on a planar two-finger setup show that the scenario-based optimal controller maintains poles inside the desired region and preserves contact stability across varied conditions, highlighting practical gains for wide-range dexterous manipulation. The work lays a foundation for probabilistically guaranteed, scenario-aware control in multi-fingered robotic manipulation, with future steps including experimental validation.

Abstract

This paper proposes a new framework to design a controller for the dexterous manipulation of an object by a multi-fingered hand. To achieve a robust manipulation and wide range of operations, the uncertainties on the location of the contact point and multiple operating points are taken into account in the control design by sampling the state space. The proposed control strategy is based on a robust pole placement using LMIs. Moreover, to handle uncertainties and different operating points, we recast our problem as a robust convex program (RCP). We then consider the original RCP as a scenario convex program (SCP) and solve the SCP by sampling the uncertain grasp map parameter and operating points in the state space. For a required probabilistic level of confidence, we quantify the feasibility of the SCP solution based on the number of sampling points. The control strategy is tested in simulation in a case study with contact location error and different initial grasps.

Figures (6)

• Figure 1: Geometry of the manipulated planar object. Contact point C2's position is uncertain (blue region). Object's pose is locally parametrized by $x_o = [P_x\ P_y\ P_{\theta}]^T$.
• Figure 2: IC1 Motion tracking performance of $C^{\Xi}_{feas}$ controller (blue dashed line), $C^{\Xi}_{opt}$ controller (green solid line), compared to the $C^{\Delta}$ controller (red dashed line) for the initial conditions $q^1_0$ and $x^1_{o_0}$ and the reference signals (black solid line).
• Figure 3: IC2 Motion tracking performance of $C^{\Xi}_{feas}$ controller (blue dashed line), $C^{\Xi}_{opt}$ controller (green solid line), compared to the $C^{\Delta}$ controller (red dashed line) for the initial conditions $q^2_0$ and $x^2_{o_0}$ and the reference signals (black solid line).
• Figure 4: IC2 Stroboscopic view of the system response with the $C^{\Xi}_{opt}$ controller for the initial conditions $q^2_0$ and $x^2_{o_0}$ (corresponding to the green curves in Fig. \ref{['fig:positions_trace_ic2_new']}. A rectangular object (black lines) is manipulated by two planar three-degree-of-freedom fingers (red lines). Contact forces (green lines) remain inside the friction cones (grey lines).
• Figure 5: Closed-loop poles evaluated on the IC1 test trajectory. With the $C^\Xi_{opt}$ controller design (green), the closed-loop poles remain within the desired D-stability region (grey area).

Theorems & Definitions (6)

• Theorem 1
• proof
• Lemma 1
• Theorem 2
• proof
• proof