Panda Arm Control with RL Algorithms

Deep Reinforcement Learning Tasks on Panda Arm.

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In this project, we explore cutting‐edge reinforcement learning (RL) algorithms to control the Panda Arm, a highly dexterous robotic manipulator. Our aim is to leverage RL techniques to enable adaptive and precise control in complex manipulation tasks. We have implemented two state‐of‐the‐art algorithms: Deep Deterministic Policy Gradient (DDPG) and Proximal Policy Optimization (PPO).

Reinforcement Learning Overview for Panda Arm

The control of a robotic arm like the Panda involves high-dimensional state and action spaces. RL algorithms can learn policies directly from interaction data, which is especially useful when the dynamics are complex or partially unknown. In our experiments, we trained the Panda Arm in simulation and later transferred insights to the real system.

The Panda Arm simulated in a virtual environment, setting the stage for advanced RL training.

DDPG: Deep Deterministic Policy Gradient

DDPG is an actor-critic, model-free algorithm tailored for continuous action spaces. It utilizes a deterministic policy, making it suitable for robotics applications. Here’s a brief overview of its mathematical formulation:

  • Actor-Critic Architecture:
    The actor network approximates a deterministic policy ( \mu(s|\theta^\mu) ) that maps states to actions. The critic network estimates the action-value function ( Q(s, a|\theta^Q) ).

  • Critic Update:
    The loss function for the critic is defined as:

    \[L(\theta^Q) = \frac{1}{N} \sum_{i=1}^N \left( Q(s_i, a_i|\theta^Q) - y_i \right)^2,\]

    where the target ( y_i ) is computed by:

    \[y_i = r_i + \gamma \, Q'\left(s_{i+1}, \mu'\left(s_{i+1}|\theta^{\mu'}\right)\Big|\theta^{Q'}\right).\]

  • Actor Update:
    The policy parameters are updated using the gradient:

    \[\nabla_{\theta^\mu} J \approx \frac{1}{N} \sum_{i=1}^N \nabla_a Q(s, a|\theta^Q)\Big|_{a=\mu(s_i)} \nabla_{\theta^\mu}\mu(s_i|\theta^\mu).\]

This framework allows the Panda Arm to learn smooth, continuous control strategies by directly mapping sensory inputs to motor commands.

PPO: Proximal Policy Optimization

PPO is known for its reliability and ease of implementation. It improves upon previous policy gradient methods by using a clipped surrogate objective, which ensures that policy updates do not deviate excessively from the previous policy. The key idea is to maintain stability during training. The PPO objective is formulated as:

\[L^{CLIP}(\theta) = \hat{\mathbb{E}}_t \left[ \min\Big( r_t(\theta)\hat{A}_t, \; \text{clip}\Big(r_t(\theta), 1-\epsilon, 1+\epsilon\Big)\hat{A}_t \Big) \right]\]

where: \(( r_t(\theta) = \frac{\pi_\theta(a_t \mid s_t)}{\pi_{\theta_{\text{old}}}(a_t \mid s_t)} \) is the probability ratio between the new and old policies. \( \hat{A}_t \) is the estimated advantage at time \( t \). \( \epsilon \) is a hyperparameter that controls the clip range.\)

By constraining the update, PPO ensures a stable and monotonic improvement in the policy, making it an attractive option for real-world robotic control scenarios such as the Panda Arm.

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