Confidence-Aware Decision-Making and Control for Tool Selection

TL;DR

The results indicate that control confidence is an early indicator of performance and thus, it can be used as a heuristic for making decisions when computation power is restricted or decision-making is intractable.

Abstract

Self-reflecting about our performance (e.g., how confident we are) before doing a task is essential for decision making, such as selecting the most suitable tool or choosing the best route to drive. While this form of awareness -- thinking about our performance or metacognitive performance -- is well-known in humans, robots still lack this cognitive ability. This reflective monitoring can enhance their embodied decision power, robustness and safety. Here, we take a step in this direction by introducing a mathematical framework that allows robots to use their control self-confidence to make better-informed decisions. We derive a mathematical closed-form expression for control confidence for dynamic systems (i.e., the posterior inverse covariance of the control action). This control confidence seamlessly integrates within an objective function for decision making, that balances the: i) performance for task completion, ii) control effort, and iii) self-confidence. To evaluate our theoretical account, we framed the decision-making within the tool selection problem, where the agent has to select the best robot arm for a particular control task. The statistical analysis of the numerical simulations with randomized 2DOF arms shows that using control confidence during tool selection improves both real task performance, and the reliability of the tool for performance under unmodelled perturbations (e.g., external forces). Furthermore, our results indicate that control confidence is an early indicator of performance and thus, it can be used as a heuristic for making decisions when computation power is restricted or decision-making is intractable. Overall, we show the advantages of using confidence-aware decision-making and control scheme for dynamic systems.

Figures (8)

• Figure 1: The schematic of our proposed confidence aware decision making and control scheme. The robot makes a decision and reports its confidence. The decision making criteria simulates the controller to evaluate the free energy objective that balances task performance, control effort and control confidence. The self evaluation (performance) and self reflection on its decision (confidence) makes the robot metacognitive. The first two gradients of $F$ fully describes our controller design (contoller and control confidence), while the integral of $F$ fully describes our decision maker. See Section \ref{['sec:theory']} for the mathematical details.
• Figure 2: Task error vs control confidence for 300 randomly selected tools (with exponential curve fit) for three tasks a) position task. b) velocity task and c) acceleration task. On average, the tools with higher control confidence performs better at the task than the tools with lower control confidence, for task 1 and 2. However, for task 3, the controller has the same confidence on all tools, which is in line with similar task errors for all tools.
• Figure 3: High confident tool (yellow and purple) settles near the goal $\theta_2^g$ (in dotted black) faster than the low confident tool (red and blue). The low-confident tool shows more variability in performance than the high-confident tool under a constant control perturbation of $\Delta T = -0.8Nm$ on the joints.
• Figure 4: Higher the control confidence on the tool, lower the absolute change in task error, under a control perturbation. This implies that the tool performance is less influenced by control perturbations for tools with higher $\Pi^u$. Therefore, the control confidence represents the reliability of the tool for task performance, under control perturbations.
• Figure 5: Tools with low control confidence show high variability in task performance when subjected to different levels of constant control perturbations during the velocity task. Tools with high control confidence show relatively low variability.