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Virtual model control for compliant reaching under uncertainties
Yi Zhang, Daniel Larby, Fumiya Iida, Fulvio Forni
TL;DR
Safe reaching in cluttered, uncertain environments remains difficult for conventional planning and control methods. The paper applies virtual model control through six designs for reaching and obstacle avoidance. Its discussion reports predictable, compliant behavior and reduced interaction forces relative to classical inverse kinematics, while noting a trade-off with motion accuracy.
Problem
Safe reaching in uncertain clutter remains difficult because conventional methods depend on complex sensing and planning and often use stiff tracking with low sensitivity to external perturbations.
Source: §I · p. 1Method
The paper proposes six virtual-model designs for reaching and obstacle avoidance, using robot-connected mechanical components to shape motion and environmental interaction.
Source: §I · p. 1, A. Virtual model, virtual forces, and… · p. 2Results
The discussion reports predictable motion, minor consequences from an unknown obstacle, restored reaching after a person grabs the end effector, and significantly reduced interaction forces versus classical inverse kinematics.
Source: §V · pp. 6–7Takeaways & Limitations
Virtual model control offers an intuitive, flexible design approach for robots interacting with uncertain environments, using mechanical structures to shape compliant behavior.
Source: §V · p. 7The approach trades motion accuracy for controlled sensitivity to environmental interaction.
Source: §I · p. 1
Abstract
from arXiv · showhide
Virtual Model Control (VMC) is an approach to design a controller for force-controlled robots in complex uncertain environments. While this method was primarily investigated for legged robot locomotion in the past, it can be more generally applicable to other types of robotic systems. This paper investigates the VMC framework for reaching tasks in a force-controlled robotic arm. We propose six different approaches to designing virtual models in order to achieve reaching tasks in environments with obstacles and uncertainties. A force-controlled 8 degree-of-freedom humanoid robot was used to validate the proposed approach in the real world. We conducted three experiments to test the performance of VMC controllers in terms of predictability, sensitivity to external force, and adaptability against known and unknown obstacles. Experimental analyses show that, even though the proposed approach needs to sacrifice accuracy and trajectory optimality, it enables us to design complex reaching motions under uncertainties, in an intuitive and extendable manner.
I. INTRODUCTION
Reaching safely in uncertain clutter is difficult for conventional planning and control, which often rely on costly sensing and stiff tracking. The paper proposes virtual-model designs that combine planning and control while retaining compliant interaction with the environment.
I. INTRODUCTION
- Conventional methods struggle in clutter with inaccurate information, relying on complex sensing and planning and often stiff joint-space tracking with low sensitivity to external perturbations.The introduction contrasts these methods with restricted, well-known factory environments.Source: §I · p. 1
- Virtual model control connects robot mechanics to designed spring-damper mechanisms, whose interaction shapes behavior and integrates trajectory planning with motion control.The robot steers according to the total energy shaped by the virtual mechanisms and environment.Source: §I · p. 1
- The paper proposes six virtual-model designs for reaching in uncertain clutter, from simple reaching to obstacle and multi-obstacle avoidance.Geometric, moving-reference, and force-driven approaches add accuracy or design flexibility to simple reaching.Source: §I · p. 1
- Its explicit mechanical action supports predictable, intuitive controller design, while virtual spring stiffness trades motion accuracy for controlled sensitivity to environmental interaction.Designers tune virtual components to task requirements and can inspect the mechanisms to anticipate intended motion.Source: §I · p. 1
A. Virtual model, virtual forces, and motor torques
A virtual model controller connects a robot to a spring-damper mechanism that generates virtual forces. For fully actuated robots, the component forces are mapped through robot Jacobians into joint torques.
A. Virtual model, virtual forces, and motor torques
- A virtual model controller connects the robot to a mechanical arrangement of springs and dampers that generates driving virtual forces.The forces are translated into actuator commands using the robot geometry.Source: A. Virtual model, virtual forces, and… · p. 2
- For fully actuated robots, each virtual-component force is mapped to joint torques through the Jacobian of its point on the robot.The total torque command sums the Jacobian-transposed force contributions.Source: A. Virtual model, virtual forces, and… · p. 2
- The paper characterizes virtual model control as a passive interconnection of robot and virtual mechanics, with spring and damper choices shaping impedance.It presents passivity theory as the basis for stability.Source: A. Virtual model, virtual forces, and… · p. 2
B. Simple, geometrical, and force-driven reaching
The paper describes reaching mechanisms that use spring-damper forces for direct, geometrically constrained, moving-reference, and force-driven motions. These designs offer ways to shape the path and contact behavior while retaining compliance.
B. Simple, geometrical, and force-driven reaching
- A spring and damper between the end effector and desired position generate a virtual force when position or velocity deviates from the target.This simple form corresponds to proportional-derivative control in end-effector space.Source: B. Simple, geometrical, and… · p. 2
- For constrained motion, a rotating, spring-damper-connected L-shaped virtual structure shapes the end-effector force toward a circular path.The structure’s geometry and position, together with its mechanical parameters, determine the driving force.Source: B. Simple, geometrical, and… · pp. 2–3
- A moving reference advances along a straight path under a finite-time progress parameter, which the robot follows compliantly.The approach is described as mitigating force exertion over large distances.Source: B. Simple, geometrical, and… · p. 3
- A virtual cart pulled by a predefined constant force provides a way to control the force exerted by the end effector at contact.The end-effector force depends on the cart’s dynamics, including its mass and viscous friction.Source: B. Simple, geometrical, and… · p. 3
- When an obstruction stops the end effector, the virtual cart also stops and bounds the robot’s total force by the cart force; removing the obstacle smoothly restores motion.This mechanism supports interaction with a partially known environment.Source: B. Simple, geometrical, and… · p. 3
C. Obstacle avoidance and compliant interaction
The paper uses repulsive virtual spring-damper mechanisms for obstacle avoidance, with nonlinear stiffness increasing as the robot nears an obstacle. For unknown obstacles, compliant interaction makes the resulting motion and force depend on the virtual springs and obstacle mechanics.
C. Obstacle avoidance and compliant interaction
- Obstacle avoidance uses repulsive virtual springs and dampers, with nonlinear springs that stiffen as their length decreases.Combined with other mechanisms, this can prioritize avoidance near obstacles.Source: C. Obstacle avoidance and compliant… · p. 3
- For multiple obstacles, the avoidance force is the sum of the forces from individual repulsive spring-damper connections to the end effector.Each connection is defined using the end-effector displacement relative to an obstacle.Source: C. Obstacle avoidance and compliant… · p. 3
- With an unknown obstacle, contact force combines with virtual-mechanism forces; during obstruction, the end effector settles where spring force balances the obstacle reaction.The resulting force depends on virtual spring stiffness and obstacle mechanics, so soft and rigid obstacles have different effects.Source: C. Obstacle avoidance and compliant… · p. 3
III. ROBOT PLATFORM AND CONTROL ARCHITECTURE
The Sciurus17 platform supplies current-controlled actuators and joint-state feedback for virtual-model control. Its architecture maps virtual forces to joint torques and demanded currents without inverse kinematics; obstacle positions were encoded rather than detected by vision.
III. ROBOT PLATFORM AND CONTROL ARCHITECTURE
- Sciurus17 has 17 degrees of freedom across its upper body, including seven per arm, two for the head, and one for the torso.Its head also carries a RealSense D415 camera that can be used for obstacle detection.Source: §III · p. 3
- Virtual forces are translated into joint torques and then demanded currents using an approximate linear torque-to-current relationship.Virtual mechanism states are computed from joint position and velocity readings.Source: §III · p. 3
- Control uses forward kinematics and Jacobians rather than inverse kinematics, while experimental obstacle positions and radii are explicitly encoded.The paper describes vision-based obstacle detection as possible, but does not use it in these experiments.Source: §III · p. 4
A. Reaching in obstacle-free environment
In obstacle-free reaching, increasing spring stiffness improved speed and reduced error, while moving-reference reaching limited high forces and fast motions. The reported target errors were associated with insufficient spring force to overcome friction.
A. Reaching in obstacle-free environment
- k = 45 N/m attained smaller error and faster motion than k = 15 N/m at constant damping of 1.5 Ns/m.The k = 15 N/m spring force was insufficient to overcome friction near the end of the trajectory.Source: A. Reaching in obstacle-free environment · p. 4
- With k = 15 N/m, the end effector deviated along the y-axis during transients through interactions among spring force, arm inertia, and torque-current conversion inaccuracy.The conversion inaccuracy affected high-speed movements.Source: A. Reaching in obstacle-free environment · p. 4
- Moving-reference reaching limited high forces and fast motions and reduced y-axis deviation, but retained a 5 cm target error because spring force did not overcome friction.The moving reference used a trapezoidal speed profile with k = 45 N/m and damping of 1.5 Ns/m.Source: A. Reaching in obstacle-free environment · p. 4
B. Reaching while avoiding known obstacles
For known obstacles, the controller combines attraction toward a moving target with repulsive virtual springs around obstacles. The tested overlapping nonconvex obstacle arrangement produced fluctuations near local minima and motivated improved controller design.
B. Reaching while avoiding known obstacles
- Against a cylindrical obstacle, a repulsive nonlinear spring pushed the end effector away while the attractive reference spring drove it toward the goal.After clearing the obstacle, the end effector accelerated toward the goal.Source: B. Reaching while avoiding known… · p. 5
- Two cylindrical obstacles were avoided by assigning a repulsive virtual spring to each, without a significant computation increase from pre-planning or re-planning.The obstacles had 6 cm diameters.Source: B. Reaching while avoiding known… · p. 5
- Partially overlapping nonconvex obstacles caused trajectories to fluctuate near local minima of the elastic potential field, indicating a need for improved controller design.The trajectories ultimately avoided the obstacles.Source: B. Reaching while avoiding known… · p. 5
C. Reaching while interacting with unknown obstacles
This section tests reaching under undetected or inaccurately positioned obstacles, including a human obstruction and an unknown acrylic plate. The human interaction does not change the final error, and the robot eventually reaches its goal after sliding past the plate.
C. Reaching while interacting with unknown obstacles
- 4.53 N versus 35.77 N: VMC exerted less end-effector force than inverse-kinematics control during human obstruction.The comparison concerns peak force exerted during the obstruction.Source: C. Reaching while interacting with… · p. 5, Figure 8 · p. 6
- After a human blocked the end effector at x = 40 cm, motion resumed on release without affecting the final error.The reach used simple reaching VMC; Fig. 7 also contrasts its trajectories with inverse kinematics.Source: C. Reaching while interacting with… · p. 5, Figure 7 · p. 6
- With the acrylic plate's presence and position unknown, the end effector paused, slid along it, cleared it, and reached the goal.Contact held the end effector for around 0.5 seconds before the moving-reference spring exerted enough force to overcome friction.Source: C. Reaching while interacting with… · pp. 5–6
V. DISCUSSION AND CONCLUSIONS
The discussion presents VMC as an intuitive, predictable approach to integrating motion planning and control through task-tailored virtual mechanisms. Its design flexibility comes with unresolved questions about mechanism choice, tuning, and the precision–compliance trade-off.
V. DISCUSSION AND CONCLUSIONS
- Prior manipulation work used virtual components, but the authors say virtual mechanisms for robot planning had not been explored in previous publications.They cite,,, and as related uses of virtual components, and, for virtual-instrument controllers.Source: §V · p. 6
- VMC lets designers activate task-specific collections of virtual mechanisms at run time, with robot motion following their interaction with the environment.The discussion describes obstacle interaction as having minor consequences for reaching and human contact as temporarily halting motion before it resumes.Source: §V · pp. 6–7
- Unlike standard linear impedance combinations, VMC can design task-tailored nonlinear impedances, while finding the right impedance remains elusive.The discussion also relates virtual mechanisms to shaping the robot's closed-loop impedance.Source: §V · p. 7
- The authors frame VMC as an intuitive way to integrate planning and control, using nonlinear mechanical structures to tailor behavior.They describe its design as drawing on impedance compositionality, passivity, and additional compliant virtual dynamics.Source: §V · p. 7
- Mechanism and parameter choices were trial-and-error; optimal design, task prioritization, precision–compliance trade-offs, and adaptive mechanisms remain research directions.The authors describe the paper as only scratching the surface of VMC design.Source: §V · p. 7