Passive Obstacle Aware Control to Follow Desired Velocities

TL;DR

This work proposes a novel approach for designing the passive damping controller that complies with obstacle-free zones while transitioning to increased damping near obstacles to ensure collision avoidance, and demonstrates superior collision rejection capabilities compared to the baseline.

Abstract

Evaluating and updating the obstacle avoidance velocity for an autonomous robot in real-time ensures robustness against noise and disturbances. A passive damping controller can obtain the desired motion with a torque-controlled robot, which remains compliant and ensures a safe response to external perturbations. Here, we propose a novel approach for designing the passive control policy. Our algorithm complies with obstacle-free zones while transitioning to increased damping near obstacles to ensure collision avoidance. This approach ensures stability across diverse scenarios, effectively mitigating disturbances. Validation on a 7DoF robot arm demonstrates superior collision rejection capabilities compared to the baseline, underlining its practicality for real-world applications. Our obstacle-aware damping controller represents a substantial advancement in secure robot control within complex and uncertain environments.

Figures (13)

• Figure 1: The proposed passive obstacle-aware controller lets the robot absorb external disturbances while ensuring collision avoidance. While tipping over the closed pasta box on this dinner table setup might be acceptable. Yet, the delicate wine glasses demand careful handling to prevent breakage.
• Figure 2: The desired velocity $\boldsymbol{f}^b(\boldsymbol{\xi})$ can result from a learned velocity field or pointing towards a desired attractor $\boldsymbol{\xi}^a$. The desired velocity is used to evaluate the obstacle avoidance velocity $\boldsymbol{f}(\boldsymbol{\xi})$, fed into the force controller to obtain the control force $\boldsymbol{\tau}_c$. In order to achieve collision avoidance, the distance function $\Gamma_o(\boldsymbol{\xi})$, the normal direction $\boldsymbol{n}_o(\boldsymbol{\xi})$, and the reference direction $\boldsymbol{r}_o(\boldsymbol{\xi})$ are evaluated for each obstacle $o = 1, ..., N^\mathrm{{obs}}$.
• Figure 3: The $\Gamma$-field is defined individually for each of the obstacles. At each position $\boldsymbol{\xi}$, we can evaluate the surface normal $\boldsymbol{n}(\boldsymbol{\xi})$. The velocity $\boldsymbol{f}(\boldsymbol{\xi})$ (gray) avoids collision with the obstacles and converges towards the attractor (star).
• Figure 4: The damping matrix enforcing desired velocity following $\mathcal{D}^{f}$ has the first basis vector $\boldsymbol{q}_1^{f}$ which points along the avoidance velocity $\boldsymbol{f}(\boldsymbol{\xi})$. The damping matrix to enforce collision avoidance $\mathcal{D}^{\mathrm{obs}}$ uses the normal $\boldsymbol{n}(\boldsymbol{\xi})$ to construct the first direction of the decomposition basis $\boldsymbol{q}^{\mathrm{obs}}_1$.
• Figure 5: Analyzing the system in velocity-space yields that the system is passive if it has a velocity $\dot{\boldsymbol{\xi}}$ larger than the desired velocity $\boldsymbol{f}(\boldsymbol{\xi})$, i.e., outside the dashed circle. However, the system can be non-passive for small velocities when $\left\langle {\dot{\boldsymbol{\xi}}}, \, {\Delta \boldsymbol{f}} \right\rangle < 0$ (yellow circle).

Theorems & Definitions (9)

• Definition II.1: Passivity willems1972dissipativesepulchre2012constructive
• Lemma III.1
• proof
• Theorem III.1
• proof
• Lemma IV.1
• proof
• Lemma 1.1
• proof