Add preliminary PhysX 4.0 backend for PyBullet

Add inverse dynamics / mass matrix code from DeepMimic, thanks to Xue Bin (Jason) Peng
Add example how to use stable PD control for humanoid with spherical joints (see humanoidMotionCapture.py)
Fix related to TinyRenderer object transforms not updating when using collision filtering

examples/SharedMemory/plugins/stablePDPlugin/RBDModel.h

@@ -0,0 +1,71 @@
+#pragma once
+
+#include "SpAlg.h"
+#include "MathUtil.h"
+
+// this class is mostly to help with efficiency by precomputing some useful
+// quantities for RBD calculations
+class cRBDModel
+{
+public:
+	EIGEN_MAKE_ALIGNED_OPERATOR_NEW
+	cRBDModel();
+	~cRBDModel();
+
+	virtual void Init(const Eigen::MatrixXd& joint_mat, const Eigen::MatrixXd& body_defs, const tVector& gravity);
+	virtual void Update(const Eigen::VectorXd& pose, const Eigen::VectorXd& vel);
+
+	virtual int GetNumDof() const;
+	virtual int GetNumJoints() const;
+
+	virtual const tVector& GetGravity() const;
+	virtual void SetGravity(const tVector& gravity);
+
+	virtual const Eigen::MatrixXd& GetJointMat() const;
+	virtual const Eigen::MatrixXd& GetBodyDefs() const;
+	virtual const Eigen::VectorXd& GetPose() const;
+	virtual const Eigen::VectorXd& GetVel() const;
+	virtual int GetParent(int j) const;
+
+	virtual const Eigen::MatrixXd& GetMassMat() const;
+	virtual const Eigen::VectorXd& GetBiasForce() const;
+	virtual Eigen::MatrixXd& GetInertiaBuffer();
+
+	virtual tMatrix GetChildParentMat(int j) const;
+	virtual tMatrix GetParentChildMat(int j) const;
+	virtual cSpAlg::tSpTrans GetSpChildParentTrans(int j) const;
+	virtual cSpAlg::tSpTrans GetSpParentChildTrans(int j) const;
+
+	virtual tMatrix GetWorldJointMat(int j) const;
+	virtual tMatrix GetJointWorldMat(int j) const;
+	virtual cSpAlg::tSpTrans GetSpWorldJointTrans(int j) const;
+	virtual cSpAlg::tSpTrans GetSpJointWorldTrans(int j) const;
+
+	virtual const Eigen::Block<const Eigen::MatrixXd> GetJointSubspace(int j) const;
+	virtual tVector CalcJointWorldPos(int j) const;
+
+protected:
+	tVector mGravity;
+	Eigen::MatrixXd mJointMat;
+	Eigen::MatrixXd mBodyDefs;
+	Eigen::VectorXd mPose;
+	Eigen::VectorXd mVel;
+
+	Eigen::MatrixXd mJointSubspaceArr;
+	Eigen::MatrixXd mChildParentMatArr;
+	Eigen::MatrixXd mSpWorldJointTransArr;
+	Eigen::MatrixXd mMassMat;
+	Eigen::VectorXd mBiasForce;
+	Eigen::MatrixXd mInertiaBuffer;
+
+	virtual void SetPose(const Eigen::VectorXd& pose);
+	virtual void SetVel(const Eigen::VectorXd& vel);
+
+	virtual void InitJointSubspaceArr();
+
+	virtual void UpdateJointSubspaceArr();
+	virtual void UpdateChildParentMatArr();
+	virtual void UpdateSpWorldTrans();
+	virtual void UpdateMassMat();
+	virtual void UpdateBiasForce();
+};