Compliant Explicit Reference Governor for Contact Friendly Robotic Manipulators

Technical Summary: Compliant Explicit Reference Governor for Contact Friendly Robotic Manipulators

Problem Statement
Traditional robotic motion planning prioritizes collision avoidance to ensure safety, often treating environmental contact as a hindrance. However, modern robotics increasingly requires "contact-rich" capabilities where physical interaction is a resource. The core challenge lies in managing the transition between free motion and contact while satisfying two distinct types of constraints:

1. Hard Constraints: Non-negotiable limits such as joint ranges, torque bounds, and forbidden surfaces.
2. Soft Constraints: Conditions where contact is permissible but must be handled safely. These create highly non-convex "OR" conditions: the robot must either avoid contact entirely or operate under specific contact-safe restrictions.

Existing optimization-based strategies (e.g., Model Predictive Control) often require full redesigns of control laws and complex time-varying approximations of contact dynamics, which are unappealing for practitioners with legacy controllers. Conversely, hierarchical approaches like Control Barrier Functions or energy-based compliance often lack strict constraint guarantees or asymptotic stability. The Explicit Reference Governor (ERG) offers a hierarchical safety filter that modifies references without altering the underlying controller, but prior implementations treated contact as undesirable, halting motion upon contact. This paper addresses the need for a framework that allows safe, continuous operation during contact without modifying the low-level controller.

Methodology: The Compliant Explicit Reference Governor (CERG)
The authors propose the Compliant Explicit Reference Governor (CERG), a modular reference management system placed between a high-level planner and a low-level controller. The CERG enforces operational constraints and enables smooth transitions between free-motion and contact operations by manipulating the reference signal $v(t)$ sent to a pre-stabilized controller.

The methodology relies on three key components:

1. Pre-stabilization Layer: A standard PD controller with gravity compensation steers the robot toward a reference configuration $v$. The system's total energy (kinetic + virtual potential) is defined by a Lyapunov function $V(x, v)$, which is monotonically decreasing when $v$ is constant.
2. Compliant Dynamic Safety Margin (DSM): The core innovation is a DSM, $\Delta(x, v)$, designed to handle the disjunctive (OR) nature of contact constraints. The safety condition is formulated as:
   $$s(q(t)) < 0 \quad \lor \quad V(x(t), v(t)) \le E_{\max}$$
   where $s(q) < 0$ represents free motion and $V \le E_{\max}$ represents safe contact with bounded energy. The CERG constructs a composite DSM:
   $$\Delta(x, v) = \min(\Delta_h, \max(\Delta_s, \Delta_E))$$
   • $\Delta_h$: Enforces hard constraints (joint limits, etc.).
   • $\Delta_s$: A trajectory-based margin for the soft constraint surface $s(q)$.
   • $\Delta_E$: An energy-based margin defined as $\kappa_E(E_{\max} - V(x, v))$.
     This structure ensures that if the robot is in free motion, the energy constraint is relaxed; if contact occurs, the total system energy is strictly bounded by $E_{\max}$.
3. Soft Navigation Field (NF): Unlike hard constraints which repel the reference, the CERG employs a "soft" repulsion field $\rho_s(v)$ that allows the reference $v$ to penetrate the constraint boundary up to a limit $\delta_s$. This penetration is necessary to generate the force required for compliant contact. The total navigation field combines attraction to the target, repulsion from hard constraints, and this soft repulsion.

Key Contributions
The paper claims three primary contributions:

• Modular Reference Filtering: A framework that seamlessly transitions between contact-free and contact-rich motion while respecting joint angle, velocity, and torque constraints, without requiring controller redesign.
• Disjunctive Constraint Handling: A safety mechanism specifically designed for "OR-type" constraints, ensuring provable satisfaction of either avoiding contact or maintaining bounded energy during contact.
• Energy-Based Safety Guideline: A safety metric based on the total mechanical energy (potential + kinetic) of the closed-loop system. This metric is frame-invariant, ties directly to stability guarantees, and is easily interpretable.

Results and Validation
The CERG was validated numerically and experimentally on increasingly complex systems:

• Two-Link Planar Arm (Simulation): The CERG was tested with both joint-space and end-effector controllers. Results showed that CERG successfully reduced interaction forces compared to operating without it and respected energy bounds. The study noted that while end-effector space formulation minimizes Cartesian error, the joint-space formulation is preferable for hierarchical architectures.
• Franka Emika Panda Simulation (Drake): Using a compliant contact model with friction and dissipation, the CERG was tested on a task requiring the arm to slide along a wall. The simulation confirmed that CERG adhered to the $E_{\max}$ limit during contact, whereas a standard ERG (which stops upon contact) and an unmodified system failed to manage the energy transition effectively.
• Real-World Experiments (Franka Emika Panda): Two tasks were performed:
  1. Whiteboard Wiping: A task not highly sensitive to energy. CERG, ERG, and Impedance control all completed the task, but only CERG enforced hard constraints (preventing joint velocity violations) and energy limits during contact.
  2. Jenga Tower Pushing: A highly energy-sensitive task. The Impedance controller failed due to either joint limit violations or toppling the tower. The standard ERG failed to prevent toppling due to excessive contact energy. Only the CERG successfully pushed the tower without toppling it by strictly enforcing $E_{\max}$ during contact while allowing higher energy in free motion.

Significance and Claims
The paper asserts that the CERG provides a practical solution for contact-rich manipulation by acting as a "plug-and-play" safety filter. Its significance lies in enabling robots to treat contact as a resource rather than a hazard, without the computational burden of full MPC redesigns or the instability risks of unmodified controllers. The framework guarantees safety through provable constraints on total system energy, allowing for seamless phase transitions between free motion and contact. The authors conclude that the approach is feasible and effective, with future work planned to interface the CERG with task-oriented planners.