Optimal Control of Walkers with Parallel Actuation

TL;DR

A comprehensive motion generation method that explicitly incorporates closed-loop kinematics and their associated constraints in an optimal control problem (OCP), integrating kinematic closure conditions and their analytical derivatives and enabling more accurate and efficient motion strategies.

Abstract

Legged robots with closed-loop kinematic chains are increasingly prevalent due to their increased mobility and efficiency. Yet, most motion generation methods rely on serial-chain approximations, sidestepping their specific constraints and dynamics. This leads to suboptimal motions and limits the adaptability of these methods to diverse kinematic structures. We propose a comprehensive motion generation method that explicitly incorporates closed-loop kinematics and their associated constraints in an optimal control problem, integrating kinematic closure conditions and their analytical derivatives. This allows the solver to leverage the non-linear transmission effects inherent to closed-chain mechanisms, reducing peak actuator efforts and expanding their effective operating range. Unlike previous methods, our framework does not require serial approximations, enabling more accurate and efficient motion strategies. We also are able to generate the motion of more complex robots for which an approximate serial chain does not exist. We validate our approach through simulations and experiments, demonstrating superior performance in complex tasks such as rapid locomotion and stair negotiation. This method enhances the capabilities of current closed-loop robots and broadens the design space for future kinematic architectures.

Figures (9)

• Figure 1: Examples of legged robots with closed-loop kinematics, ranging (top-left to bottom-right) from robots with a main serial chain (Fourier GR1 FourierGR1, Unitree H1 HumanoidRobotG1_Humanoid, Tesla Optimus TeslaOptimus, Adam AdamPnd), robot with an approximate serial chain (Digit AgilityProducts) and robots without an approximate serial chain(Kangaroo roigHardwareDesignControl2022a, Disney bipedal robot keving.gimDesignFabricationBipedal2018, Atrias hubicki2016atrias). Each red lock represents a visible closure of the kinematic chain.
• Figure 2: Robot model used for our benchmark. Each red lock represents a closure of the kinematic chain. In our model, we represent the chain as a tree-like structure with added contact constraints by splitting the bar in two at the lock position and adding 6D contact constraints
• Figure 3: Variation of the reduction ratio of the knee actuation with respect to the knee angle. The 0 angle corresponds to a nominal configuration of the robot while positive angles correspond to a stretched leg.
• Figure 4: Model of the Cleobot batto:hal-04717159, a fully parallel robot. It uses three parallel chains of equivalent inertia for the knee and ankle actuation and three other parallel chains for hip actuation
• Figure 5: Evolution of the Maximum and Mean knees controls as functions of the target CoM elevation in the squat motion. The target elevation is noted relative to the initial CoM height. For deeper squats, the required joint torques for the Approximate Serial trajectory yield excessive motor torques